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IBM SPSS Statistics 26 Step by Step

A Simple Guide and Reference

16th Edition

Answers to Selected Exercises

Darren George, Ph.D.

Canadian University College

Paul Mallery, Ph.D. La Sierra University

Contents

General Notes .............................................................................................................................................. 1 Chapter 3: Creating and Editing a Data File ............................................................................................ 2

3-2 .............................................................................................................................................................. 3 3-3 .............................................................................................................................................................. 3 3-5 .............................................................................................................................................................. 3 3-6 .............................................................................................................................................................. 3 3-7 .............................................................................................................................................................. 3 3-8 .............................................................................................................................................................. 4

Chapter 4: Managing Data ......................................................................................................................... 5 4-2 .............................................................................................................................................................. 7 4-3 .............................................................................................................................................................. 8 4-5 .............................................................................................................................................................. 9 4-6 .............................................................................................................................................................. 9 4-8 ............................................................................................................................................................ 10 4-9 ............................................................................................................................................................ 10 4-11 .......................................................................................................................................................... 10 4-12 .......................................................................................................................................................... 10 4-14 .......................................................................................................................................................... 10 4-15 .......................................................................................................................................................... 11

Chapter 5: Graphs ..................................................................................................................................... 13 5-1 ............................................................................................................................................................ 14 5-2 ............................................................................................................................................................ 14 5-4 ............................................................................................................................................................ 14 5-5 ............................................................................................................................................................ 15

Chapter 6: Frequencies ............................................................................................................................. 16 6-1 ............................................................................................................................................................ 17 6-3 ............................................................................................................................................................ 17 6-4 ............................................................................................................................................................ 18 6-6 ............................................................................................................................................................ 18 6-7 ............................................................................................................................................................ 19

Chapter 7: Descriptive Statistics .............................................................................................................. 20 7-1 ............................................................................................................................................................ 21 7-2 ............................................................................................................................................................ 21 7-4 ............................................................................................................................................................ 21

ii IBM SPSS Statistics 26 Step by Step Answers to Selected Exercises

Chapter 8: Crosstabulation and χ2 Analyses ......................................................................................... 23

8-1 ............................................................................................................................................................ 25 8-2 ............................................................................................................................................................ 26 8-3 ............................................................................................................................................................ 26 8-8 ............................................................................................................................................................ 26

Chapter 9: The Means Procedure ............................................................................................................ 28 9-1 ............................................................................................................................................................ 29 9-3 ............................................................................................................................................................ 30 9-5 ............................................................................................................................................................ 30

Chapter 10: Bivariate Correlation............................................................................................................ 32 10-1 .......................................................................................................................................................... 34 10-3 .......................................................................................................................................................... 35 10-4 .......................................................................................................................................................... 35 10-5 .......................................................................................................................................................... 35

Chapter 11: The T Test Procedure ............................................................................................................ 36 11-1 .......................................................................................................................................................... 38 11-2 .......................................................................................................................................................... 40 11-3 .......................................................................................................................................................... 41 11-4 .......................................................................................................................................................... 41 11-8 .......................................................................................................................................................... 42 11-9 .......................................................................................................................................................... 42

Chapter 12: The One-Way ANOVA Procedure ..................................................................................... 43 12-1 .......................................................................................................................................................... 45 12-2 .......................................................................................................................................................... 46 12-3 .......................................................................................................................................................... 48

12-4 .......................................................................................................................................................... 48 Chapter 14: Three-Way ANOVA ............................................................................................................. 50

14-1 .......................................................................................................................................................... 56 14-2 .......................................................................................................................................................... 59 14-3 .......................................................................................................................................................... 59 14-6 .......................................................................................................................................................... 60 14-7 .......................................................................................................................................................... 61 14-10 ........................................................................................................................................................ 62

Chapter 15: Simple Linear Regression.................................................................................................... 65 15-1 .......................................................................................................................................................... 69 15-2 .......................................................................................................................................................... 70 15-3 .......................................................................................................................................................... 70 15-5 .......................................................................................................................................................... 70

IBM SPSS Statistics 26 Step by Step Answers to Selected Exercises iii

15-8 .......................................................................................................................................................... 70 15-9 .......................................................................................................................................................... 70 15-11 ........................................................................................................................................................ 71

Chapter 16: Multiple Regression Analysis ............................................................................................. 72 16-1 .......................................................................................................................................................... 74 16-4 .......................................................................................................................................................... 74 16-5 .......................................................................................................................................................... 74

Chapter 18: Reliability Analysis .............................................................................................................. 75 18-1 .......................................................................................................................................................... 77 18-2 .......................................................................................................................................................... 78 18-14 ........................................................................................................................................................ 79

Chapter 23: MANOVA and MANCOVA ............................................................................................... 80 23-1 .......................................................................................................................................................... 82 23-2 .......................................................................................................................................................... 83 23-4 .......................................................................................................................................................... 83 23-6 .......................................................................................................................................................... 84

Chapter 24: Repeated-Measures MANOVA .......................................................................................... 87 24-1 .......................................................................................................................................................... 89 24-2 .......................................................................................................................................................... 89 24-4 .......................................................................................................................................................... 90 24-6 .......................................................................................................................................................... 92

IBM SPSS Statistics 26 Step by Step Answers to Selected Exercises 1

General Notes The following answers are in some cases complete. In other cases, only portions of the answer are in-cluded.

The data files used are available for download at http://www.spss-step-by-step.net.

Check with your instructor to find exactly what she or he wants you to turn in.

We list the questions from each chapter first, followed by answers to selected exercises.

http://www.spss-step-by-step.net/

2 IBM SPSS Statistics 25 Step by Step Answers to Selected Exercises

Chapter 3: Creating and Editing a Data File

1. Set up the variables described above for the grades.sav file, using appropriate variable names, variable labels, and variable values. Enter the data for the first 20 students into the data file.

2. Perhaps the instructor of the classes in the grades.sav dataset teaches these classes at two differ-

ent schools. Create a new variable in this dataset named school, with values of 1 and 2. Create variable labels, where 1 is the name of a school you like, and 2 is the name of a school you don’t like. Save your dataset with the name gradesme.sav.

3. Which of the following variable names will SPSS accept, and which will SPSS reject? For

those that SPSS will reject, how could you change the variable name to make it “legal”? age firstname @edu sex. grade not anxeceu date iq

4. Using the grades.sav file, make the gpa variable values (which currently have two digits after

the decimal point) have no digits after the decimal point. You should be able to do this without retyping any numbers. Note that this won’t actually round the numbers, but it will change the way they are displayed and how many digits are displayed after the decimal point for statistical analyses you perform on the numbers.

5. Using grades.sav, search for a student with 121 total points. What is his or her name?

6. Why is each of the following variables defined with the measure listed? Is it possible for

any of these variables to be defined as a different type of measure? ethnicity Nominal extrcred Ordinal quiz4 Scale grade Nominal

7. Ten people were given a test of balance while standing on level ground, and ten other peo-ple were given a test of balance while standing on a 30° slope. Their scores follow. Set up the appropriate variables, and enter the data into SPSS. Scores of people standing on level ground: 56, 50, 41, 65, 47, 50, 64, 48, 47, 57 Scores of people standing on a slope: 30, 50, 51, 26, 37, 32, 37, 29, 52, 54

8. Ten people were given two tests of balance, first while standing on level ground and then while standing on a 30° slope. Their scores follow. Set up the appropriate variables, and enter the da-ta into SPSS.

Participant: 1 2 3 4 5 6 7 8 9 10

Score standing on level ground: 56 50 41 65 47 50 64 48 47 57

Score standing on a slope: 38 50 46 46 42 41 49 38 49 55


3-2 The variable view screen might look something like this once the new variable is set up:

3-3

Variable Name

SPSS will…

What could be changed?

Age Accept

sex. Reject Variable names can’t include a “.” so just use “sex” without a period.

3-5 Dawne Rathbun received a score of 121 for the course. No one received a score of 121 on the final exam.

3-6 Variable Currently de-

fined as Could also be defined as

ethnicity Nominal Ethnicity will generally be defined as a nominal variable. The only excep-tions might be if, for example, you were examining the relative size of dif-ferent ethnicities in a certain population. In that case, where ethnicity has other theoretical meaning, ethnicity could be defined as an ordinal varia-ble.

3-7 The variable view should look something like this, with one variable identifying whether the person was standing on level or sloped ground and a second variable identifying each person’s balance score:


Once the data is entered, the data view should look something like this:

3-8 Note that, because each person took the balance test both on level ground and on a slope, there are ten rows (one for each person) rather than twenty rows (one for each time the balance test was given).


Chapter 4: Managing Data Some of the exercises that follow change the original data file. If you wish to leave the data in their original form, don’t save your changes. Case Summaries

1. Using the grades.sav file, list variables (in the original order) from id to quiz5, first 30 stu-dents consecutive, fit on one page by editing.

2. Using the helping3.sav file, list variables hclose, hseveret, hcontrot, angert, sympathi, worry, obligat, hcopet, first 30 cases, fit on one page by editing.

3. List ID, lastname, firstname, gender for the first 30 students in the grades.sav file, with the lower division students listed first, followed by upper division students (lowup variable). Edit output to fit on one page.

Missing Values 4. Using the grades.sav file delete the quiz1 scores for the first 20 subjects. Replace the (now)

missing scores with the average score for all other students in the class. Print out lastname, firstname, quiz1 for the first 30 students. Edit to fit on one page.

Computing Variables

5. Using the grades.sav file calculate total (the sum of all five quizzes and the final) and per-cent (100 times the total divided by possible points, 125). Since total and percent are already present, name the new variables total1 and percent1. Print out id, total, total1, percent, per-cent1, first 30 subjects. Total and total1; percent and percent1 should be identical.

6. Using the divorce.sav file compute a variable named spirit (spirituality) that is the mean of sp8 through sp57 (there should be 18 of them). Print out id, sex, and the new variable spirit, first 30 cases, edit to fit on one page.

7. Using the grades.sav file, compute a variable named quizsum that is the sum of quiz1 through quiz5. Print out variables id, lastname, firstname, and the new variable quizsum, first 30, all on one page.

Recode Variables 8. Using the grades.sav file, compute a variable named grade1 according to the instructions on

page 73. Print out variables id, lastname, firstname, grade and the new variable grade1, first 30, edit to fit all on one page. If done correctly, grade and grade1 should be identical.

9. Using the grades.sav file; recode a passfail1 variable so that D’s and F’s are failing, and A’s, B’s, and C’s are passing. Print out variables id, grade, passfail1, first 30, edit to fit all on one page.

10. Using the helping3.sav file, redo the coding of the ethnic variable so that Black = 1, His-panic = 2, Asian = 3, Caucasian = 4, and Other/DTS = 5. Now change the value labels to be consistent with reality (that is the coding numbers are different but the labels are con-sistent with the original ethnicity). Print out the variables id and ethnic, (labels, not val-ues) first 30 cases, fit on one page.


Selecting Cases 11. Using the divorce.sav file select females (sex = 1); print out id and sex, first 30 subjects,

numbered, fit on one page.

12. Select all the students in the grades.sav file with previous GPA less than 2.00, and percent-ages for the class greater than 85. Print id, GPA, and percent on one page.

13. Using the helping3.sav file, select females (gender = 1) who spend more than the average amount of time helping (thelplnz > 0). Print out id, gender, thelplnz, first 30 subjects, numbered, fit on one page.

Sorting Cases 14. Alphabetize the grades.sav file by lastname, firstname, Print out lastname, firstname, first

30 cases, edit to fit on one page.

15. Using the grades.sav file, sort by id (ascending order). Print out id, total, percent, and grade, first 30 subjects, fit on one page.


4-2

. . .


4-3 Case Summaries lastname firstname Lower or upper division Lower 1 VILLARRUZ ALFRED 2 OSBORNE ANN 3 LIAN JENNY 4 MISCHKE ELAINE 5 WU VIDYUTH 6 TORRENCE GWEN 7 CARPIO MARY 8 SAUNDERS TAMARA Total N 8 8 Upper 1 VALAZQUEZ SCOTT 2 GALVEZ JACKIE 3 GUADIZ VALERIE 4 RANGIFO TANIECE 5 TOMOSAWA DANIEL 6 BAKKEN KREG 7 LANGFORD DAWN 8 VALENZUELA NANCY 9 SWARM MARK 10 KHOURY DENNIS 11 AUSTIN DERRICK 12 POTTER MICKEY 13 LEE JONATHAN 14 DAYES ROBERT 15 STOLL GLENDON 16 CUSTER JAMES 17 CHANG RENE 18 CUMMINGS DAVENA 19 BRADLEY SHANNON 20 JONES ROBERT 21 UYEYAMA VICTORINE 22 LUTZ WILLIAM Total N 22 22 Total N 30 30

a Limited to first 30 cases.


4-5 Follow sequence steps 5c and 5c’ to complete this calculation.

4-6

Case Summariesa

id sex Spirituality

1 1 female 3.72

2 2 female 5.28

3 3 female 5.83

4 4 female 5.89

5 5 female 5.44

6 6 male 5.39

7 7 male 5.56

8 8 female 5.39

9 9 male 4.89

10 10 female 6.06

11 11 female 5.61

12 12 female 6.28

13 13 male 6.28

14 14 male 5.28

15 15 male 4.83

16 16 female 5.11

17 17 male 5.72

18 18 male 5.78

19 19 female 5.00

20 20 female 6.28

21 21 female 4.72

22 22 female 4.72

23 23 female 5.56

24 24 male 5.00

25 25 male 5.83

26 26 female 5.61

27 27 male 4.78

28 28 female 5.94

29 29 male 4.83

30 30 female 4.33

Total N 30 30 30

a. Limited to first 30 cases.


4-8 Case Summaries ID LASTNAME FIRSTNAME GRADE GRADE2 1 106484 VILLARRUZ ALFRED D D 2 108642 VALAZQUEZ SCOTT C C 3 127285 GALVEZ JACKIE C C 4 132931 OSBORNE ANN B B 5 140219 GUADIZ VALERIE B B a Limited to first 30 cases.

4-9 Follow sequence step 5d’ but use a range of 70 to 100 for “P”, and 0 to 69.9 for “F”.

4-11

Case Summariesa

id sex

1 1 female

2 2 female

3 3 female

4 4 female

5 5 female

4-12

Case Summaries id gpa percent

1 140219 1.84 86

2 417003 1.91 87

Total N 2 2 2

4-14 ID LASTNAME FIRSTNAME 1 779481 AHGHEL BRENDA 2 777683 ANDERSON ERIC 3 211239 AUSTIN DERRICK 4 420327 BADGER SUZANNA 5 157147 BAKKEN KREG


4-15 Case Summaries(a) id total percent grade 1 106484 80 64 D 2 108642 96 77 C 3 127285 98 78 C 4 132931 103 82 B 5 140219 108 86 B 6 142630 122 98 A 7 153964 112 90 A 8 154441 120 96 A 9 157147 123 98 A 10 164605 124 99 A 11 164842 97 78 C 12 167664 118 94 A 13 175325 111 89 B 14 192627 84 67 D 15 211239 79 63 D 16 219593 94 75 C 17 237983 92 74 C 18 245473 88 70 C 19 249586 98 78 C 20 260983 106 85 B 21 273611 78 62 D 22 280440 114 91 A 23 287617 98 78 C 24 289652 109 87 B 25 302400 65 52 F 26 307894 90 72 C 27 337908 108 86 B 28 354601 120 96 A 29 378446 81 65 D 30 380157 118 86 B 31 390203 97 78 C 32 392464 103 82 B 33 414775 96 77 C 34 417003 109 87 B 35 419891 92 74 C 36 420327 103 82 B


id total percent grade 37 434571 98 78 C 38 436413 96 77 C 39 447659 99 79 C 40 463276 123 98 A Total N 40 40 40 40

a Limited to first 40 cases.


Chapter 5: Graphs All of the following exercises use the grades.sav sample data file.

1. Using a bar chart, examine the number of students in each section of the class along with whether or not students attended the review session. Does there appear to be a relation between these vari-ables?

2. Using a line graph, examine the relationship between attending the review session and section on the final exam score. What does this relationship look like?

3. Create a boxplot of quiz 1 scores. What does this tell you about the distribution of the quiz scores? Create a boxplot of quiz 2 scores. How does the distribution of this quiz differ from the distribu-tion of quiz 1? Which case number is the outlier?

4. Create an error bar graph highlighting the 95% confidence interval of the mean for each of the three

sections’ final exam scores. What does this mean? 5. Based on the examination of a histogram, does it appear that students’ previous GPA’s are normal-

ly distributed? 6. Create the scatterplot described in Step 5f (page 98). What does the relationship appear to be be-

tween gpa and academic performance (total)? Add a regression lines for both men and women to this scatterplot. What do these regression lines tell you?

7. By following all steps on pages 88 and 89, reproduce the bar graph shown on page 89. 8. By following all steps on pages 90 and 91, reproduce the line graph shown on page 91. 9. By following all steps on pages 92, reproduce the pie chart shown on page 92. 10. By following all steps on pages 93 and 94, reproduce the Boxplot shown on page 94. 11. By following all steps on pages 95, reproduce the Error Bar Chart shown on page 95. Note that the

edits are not specified on page 95. See if you can perform the edits that produce an identical chart. 12. By following all steps on pages 96 and 97, reproduce the histogram shown on page 97. 13. By following all steps on page 98, reproduce the scatterplot shown on page 99.


5-1 There does appear to be a relationship (though we don’t know if it’s significant or not): People in Sec-tion 3 were somewhat more likely to skip the review session than in sections 1 or 2, and most people who attended the review sessions were from Section 2, for example. This relationship may be clearer with stacked rather than clustered bars, as there aren’t the same number of people in each section:

5-2

Although it looks like attending the review sessions was helpful for all students, it seems to have been particularly helpful for students in Section 1. For this graph, we have modified the Y-axis to range from 55 to 65; the default is a much more compressed graph.

5-4 This is a good example of why we need to run statistical tests. The lower error bar or section 1, for ex-ample, overlaps the upper error bar for section 3 by more than a half of a one-sided error bar (and vice versa). So, the population mean for section 1 is probably not statistically significant. Because the error bars aren’t quite the same length, though, it may still be worth running a test to see if they are signifi-cantly different.


5-5

1. Note that the GPA’s below the median appear fairly normal, but those above the median do not.

gpa4.003.503.002.502.001.501.00

Freq

uenc

y20

15

10

5

0

Mean =2.7789Std. Dev. =0.7638

N =105


Chapter 6: Frequencies Notice that data files other than the grades.sav file are being used here.

1. Using the divorce.sav file display frequencies for sex, ethnic, and status. Print output to show fre-quencies for all three; edit output so it fits on one page. On a second page, include three bar graphs of these data and provide labels to clarify what each one means.

2. Using the graduate.sav file display frequencies for motive, stable, and hostile. Print output to show frequencies for all three; edit output so it fits on one page. Note: this type of procedure is typically done to check for accuracy of data. Motivation (motive), emotional stability (stable), and hostility (hos-tile) are scored on 1- to 9-point scales. You are checking to see if you have, by mistake, entered any 0s or 99s.

3. Using the helping3.sav file compute percentiles for thelplnz (time helping, measured in z scores), and tqualitz (quality of help measured in z scores). Use percentile values 2, 16, 50, 84, 98. Print output and circle values associated with percentiles for thelplnz; box percentile values for tqualitz. Edit out-put so it fits on one page.

4. Using the helping3.sav file compute percentiles for age. Compute every 10th percentile (10, 20, 30, etc.). Edit (if necessary) to fit on one page.

5. Using the graduate.sav file display frequencies for gpa, areagpa, grequant. Compute quartiles for these three variables. Edit (if necessary) to fit on one page.

6. Using the grades.sav file create a histogram for final. Include the normal curve option. Create a title for the graph that makes clear what is being measured. Perform the edits on page 97 so the borders for each bar are clear.

7. Using the grades.sav file, use the Frequencies command to calculate how many people are in each year in school. Report your answer in both number of people, and percentage of total people.

8. In the grades.sav file, what percentage of students did the extra credit?

9. In the grades.sav file, how many people got As, Bs, Cs, Ds, or Fs? See if you can answer so that your sentences still make sense if you skip the numbers, and report frequencies in APA style.


6-1

sex

Frequency Percent Valid Percent

Cumulative Per-

cent

Valid female 119 52.0 52.0 52.0

male 110 48.0 48.0 100.0

Total 229 100.0 100.0

6-3

Statistics

537 5370 0

-2.0966 -2.1701-.9894 -.8144.0730 .1351.9218 .9481

1.7643 1.4766

ValidMissing

N

216508498

Percentiles

MEAN OFHELPER/

RECIPIENTLNZHELP

MEAN OFHELPER/

RECIPIENTZQUALITY

HELP


6-4

Statistics AGE N Valid 537 Missing 0 Percentiles 10 20.00

6-6

806040

20

15

10

5

0

Freq

uenc

y

Mean =61.48Std. Dev. =7.943

N =105

Distribution of Final Exam Scores


6-7 Minimal answer provided for students.

Year in school

Frequency Percent Valid Percent

Cumulative Per-

cent

Valid Frosh 3 2.9 2.9 2.9 . . . There were 3 Freshmen (2.9%), …


Chapter 7: Descriptive Statistics 1. Using the grades.sav file select all variables except lastname, firstname, grade, passfail. Compute

descriptive statistics including mean, standard deviation, kurtosis, skewness. Edit so that you eliminate Std. Error (Kurtosis) and Std. Error (Skewness) making your chart easier to interpret. Edit the output to fit on one page.

• Draw a line through any variable for which descriptives are meaningless (either they are cate-gorical or they are known to not be normally distributed).

• Place an “*” next to variables that are in the ideal range for both skewness and kurtosis.

• Place an X next to variables that are acceptable but not excellent.

• Place a ψ next to any variables that are not acceptable for further analysis.

2. Using the divorce.sav file select all variables except the indicators (for spirituality, sp8 – sp57, for

cognitive coping, cc1 – cc11, for behavioral coping, bc1 – bc12, for avoidant coping, ac1 – ac7, and for physical closeness, pc1 – pc10). Compute descriptive statistics including mean, standard deviation, kurtosis, skewness. Edit so that you eliminate Std. Error (Kurtosis) and Std. Error (Skewness) and your chart is easier to interpret. Edit the output to fit on two pages.

• Draw a line through any variable for which descriptives are meaningless (either they are cate-gorical or they are known to not be normally distributed).

• Place an “*” next to variables that are in the ideal range for both skewness and kurtosis.

• Place an X next to variables that are acceptable but not excellent.

• Place a ψ next to any variables that are not acceptable for further analysis.

3. Create a practice data file that contains the following variables and values:

• VAR1: 3 5 7 6 2 1 4 5 9 5

• VAR2: 9 8 7 6 2 3 3 4 3 2

• VAR3: 10 4 3 5 6 5 4 5 2 9

Compute: the mean, the standard deviation, and variance and print out on a single page.

4. What are the mean, variance, and standard deviation for the following numbers? 41, 46, 32, 35, 60, 57, 56, 50, 41. 65. Report your results using appropriate APA style.

5. For the numbers in the previous problem, what are the skewness and kurtosis? Would these values be considered close to normal?

6. Calculate the mean, standard deviation, skewness, and kurtosis for the following numbers: 5, 6, 7, 8, 9, 30, 31, 32, 33, 34. Would these values be considered close to normal?


7-1

Descriptive Statistics

N Mean Std. Deviation Skewness Kurtosis

Statistic Statistic Statistic Statistic Statistic

id 105 571366.67 277404.129 -.090 -1.299

gender 105 1.39 .490 .456 -1.828

ethnicity 105 3.35 1.056 -.451 -.554 Year in school 105 2.94 .691 -.460 .553

Lower or upper division 105 1.79 .409 -1.448 .099

section 105 2.00 .797 .000 -1.419

gpa 105 2.7789 .76380 -.052 -.811

Did extra credit project? 105 1.21 .409 1.448 .099

Attended review sessions? 105 1.67 .474 -.717 -1.515

quiz1 105 7.47 2.481 -.851 .162

quiz2 105 7.98 1.623 -.656 -.253 X quiz3 105 7.98 2.308 -1.134 .750

quiz4 105 7.80 2.280 -.919 .024

quiz5 105 7.87 1.765 -.713 .290

final 105 61.48 7.943 -.335 -.332

total 105 100.57 15.299 -.837 .943

percent 105 80.34 12.135 -.834 .952

Valid N (listwise) 105

7-2


N Mean Std. Deviation Skewness Kurtosis Statistic Statistic Statistic Statistic Statistic

id 229 116.32 66.903 -.007 -1.202

sex 229 1.48 .501 .079 -2.011

* age 229 41.90 9.881 .679 .910 . . .

7-4 M = 48.30, SD = …


7-5 The skewness is normal (skewness = -0.01), but …


Chapter 8: Crosstabulation and χ2 Analyses For each of the chi-square analyses computed below:

1. Circle the observed (actual) values. 2. Box the expected values. 3. Put an * next to the unstandardized residuals. 4. Underline the significance value that shows whether observed and expected values differ signif-

icantly. 5. Make a statement about independence of the variables involved. 6. State the nature of the relationship. #5 identifies whether there is a relationship, now you need

to indicate what that relationship is. Example: Men tend to help more with goal-disruptive problems whereas women tend to help more with relational problems.

7. Is there a significant linear association? 8. Does linear association make sense for these variables? 9. Is there a problem with low-count cells? 10. If there is a problem, what would you do about it?

1. File: grades.sav. Variables: gender by ethnic. Select: observed count, expected count, un-standarized residuals. Compute: Chi-square, Phi and Cramer’s V. Edit to fit on one page, print out, then perform the 10 operations listed above.

2. File: grades.sav. Variables: gender by ethnic. Prior to analysis, complete the procedure shown in Step 5c (page 129) to eliminate the “Native” category (low-count cells). Select: observed count, ex-pected count, unstandarized residuals. Compute: Chi-square, Phi and Cramer’s V. Edit to fit on one page, print out, then perform the 10 operations listed above.

3. File: helping3.sav. Variables: gender by problem. Select: observed count, expected count, un-standarized residuals. Compute: Chi-square, Phi and Cramer’s V. Edit to fit on one page, print out, then perform the 10 operations listed above.

4. File: helping3.sav. Variables: school by occupat. Prior to analysis, select cases: “school > 2 & occu-pat < 6”. Select: observed count, expected count, unstandarized residuals. Compute: Chi-square, Phi and Cramer’s V. Edit to fit on one page, print out, then perform the 10 operations listed above.

5. File: helping3.sav. Variables: marital by problem. Prior to analysis, eliminate the “DTS” category (marital < 3). Select: observed count, expected count, unstandarized residuals. Compute: Chi-square, Phi and Cramer’s V. Edit to fit on one page, print out, then perform the 10 operations listed above.

6. Using the grades.sav file, run a crosstabulation on whether people attended the review session, and whether they did the extra credit. How many people both attended the review session and did extra credit, attended the review session but did not do extra credit, did not attend the re-view session but did extra credit, or neither attended the review session nor did extra credit?


Can you confidently say that there is a relationship between attending the review session and getting extra credit? Report your χ2 value, p value, and effect size measure (φ) in APA style.

7. The following table shows how many people in the town of Grover’s Corners are happy or unhappy, along with whether their socioeconomic status is lower, middle, or upper class. Is there a relationship between social class and happiness, or are they independent? If there is a relationship, how large is this effect and what does it look like?

Happy? Socioeconomic Status Number of People

Yes Lower 3630

Yes Middle 4992

Yes Upper 5196

No Lower 5567

No Middle 5105

No Upper 5190

8. Professor Rteneggg predits that timid creativity is associated with cerebrosolution levels. He finds that, among people with high levels of cerebrosolution, 25 have timid creativity and 55 do not have timid creativity. Among those with low levels of cerebrosolution, 46 have timid creativity and 44 do not have timid creativity. Is Rteneggg’s prediction supported by your da-ta? How do your results support this conclusion?


8-1

5. Ethnicity and gender are independent of each other.

6. There is no difference of gender balance across different ethnic groups.

or, Across different ethnic groups there is no difference in the balance of men and women.

7. No

8. No

9. Yes, there are 30% of cells with an expected value of less than 5. Acceptable is less than 25%.

10. Delete the category which most contributes to the low cell counts, the “Native” category in this case.


8-2

Symmetric Measures

Value

Approximate

Significance

Nominal by Nominal Phi .062 .942

Cramer's V .062 .942

N of Valid Cases 100

5. Ethnicity and gender are independent of each other.

8-3 5. Gender and problem type are dependent, that is, which problems receive the most attention is de-pendent upon the gender of the helper.

6. While there are no significant gender differences in the likelihood of helping with illness or cata-strophic problems, women are significantly more likely to help with relational problems whereas men are significantly more likely to help with goal-disruptive problems.

7. No

8. No

9. No, there are no cells with an expected value of less than 5. Acceptable is less than 25%.

10. Delete the category which most contributes to the low cell counts. There are none here.

8-8

Cerebrosolution * TimidCreativity Crosstabulation Count

TimidCreativity

Total Have Don't Have

Cerebrosolution Low 46 44 90

High 25 55 80

Total 71 99 170


Chi-Square Tests

Value df

Asymptotic Sig-

nificance (2-

sided)

Exact Sig. (2-

sided)

Exact Sig. (1-

sided)

Pearson Chi-Square 6.869a 1 .009 Continuity Correctionb 6.077 1 .014 Likelihood Ratio 6.941 1 .008 Fisher's Exact Test .012 .007

Linear-by-Linear Association 6.829 1 .009 N of Valid Cases 170 a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 33.41.

b. Computed only for a 2x2 table

Symmetric Measures

Value

Approximate

Significance

Nominal by Nominal Phi .201 .009

Cramer's V .201 .009

N of Valid Cases 170

Cerebrosolution levels are associated with the presence or absence of timid creativity (χ2(1) = 6.87, p = .009, φ = .20). People with low levels of cerebrosolution are about equally likely to have (n = 46) or not have (n = 44) timid creativity, but people with high levels of cerebrosolution are less likely to have (n = 25) than not have (n = 55) timid creativity. Or: People with timid creativity are more likely to have low (n = 46) than high (n = 25) levels of cerebrosolution, but people without timid creativity are more likely to have high (n = 55) than low (n = 44) levels of cerebrosolution.


Chapter 9: The Means Procedure

1. Using the grades.sav file use the Means procedure to explore the influence of ethnic and section on total. Print output, fit on one page, in general terms describe what the value in each cell means.

2. Using the grades.sav file use the Means procedure to explore the influence of year and section on final. Print output, fit on one page, in general terms describe what the value in each cell means.

3. Using the divorce.sav file use the Means procedure to explore the influence of gender (sex) and mar-ital status (status) on spiritua (spirituality—high score is spiritual). Print output and, in general terms, describe what the value in each cell means.

4. Using the grades.sav file and the Means procedure, examine the difference in total points between students who did or did not do the extra credit (extrcredit) project. Can you confidently say that doing the extra credit project helped student grades? Report the means (M), F, p, and η or η2 using APA style.

5. Using the grades.sav file and the Means procedure, examine the difference in total points between students who did or did not attend review sessions. Can you confidently say attending review ses-sions helped student grades?

6. Dr. Toob believes that people who meditate regularly are less jealous. She has ten participants medi-tate for a week, and ten participants not meditate for a week. After she measures level of jealousy for her participants, she uses the means procedure to determine whether her hypothesis is supported. People who meditated scored 45, 38, 34, 40, 30, 41, 37, 32, 28, and 29. People who did not meditate scored 27, 23, 27, 25, 27, 13, 13, 20, 37, and 23. Perform this analysis. Is her hypothesis supported? How confident can you be?


9-1

Report total ethnicity section Mean N Std. Deviation

Native 2 90.25 4 15.042

3 115.00 1 .

Total 95.20 5 17.094

Asian 1 108.00 7 12.423

2 97.78 9 14.394

3 105.50 4 6.351

Total 102.90 20 12.876

Black 1 105.14 7 12.185

2 105.00 7 11.547

3 93.10 10 16.509

Total 100.08 24 14.714

White 1 105.75 16 17.628

2 100.00 18 10.123

3 100.91 11 16.736

Total 102.27 45 14.702

Hispanic 1 94.67 3 27.154

2 104.00 1 .

3 90.57 7 21.816

Total 92.91 11 21.215

Total 1 105.09 33 16.148

2 99.49 39 12.013

3 97.33 33 17.184

Total 100.57 105 15.299 The ETHNICITY column identifies the ethnic group for which data are entered.

The SECTION column identifies which of the three sections individuals of a particular ethnic group are enrolled.

The MEAN column identifies the mean total points for the individuals in each cell of the table.

The N column identifies how many individuals are in each group.

The STD. DEVIATION column identifies the standard deviation for the values in each catego-ry.


9-3

• The SEX column identifies the gender of the subjects. • The STATUS column identifies the marital status (4 levels) of women (first) then men. • The MEAN column identifies the mean total points for the individuals in each cell of the ta-

ble. • The N column identifies how many individuals are in each group. • The STD. DEVIATION column identifies the standard deviation for the values in each cat-

egory.

9-4

Report total Did extra credit project? Mean N Std. Deviation

No 98.24 83 15.414

Yes 109.36 22 11.358

Total 100.57 105 15.299

ANOVA Table

Sum of Squares df Mean Square F Sig.

total * Did extra credit project? Between Groups (Combined) 2151.443 1 2151.443 9.985 .002

Within Groups 22192.272 103 215.459 Total 24343.714 104

Measures of Association

Eta Eta Squared

total * Did extra credit project? .297 .088

Students who did the extra credit did have higher total points (M = 109.36, SD = 11.36) than students who did not do the extra credit (M = 98.24, SD = 15.41), p = .002.

9-5

ANOVA Table


total * Attended review sessions? Between Groups (Combined) 499.886 1 499.886 2.159 .145



9-6

Report Jealousy Meditate Mean N Std. Deviation

Meditate 35.40 10 5.700

No Meditate 23.50 10 7.106

Total 29.45 20 8.751

ANOVA Table


Jealousy * Meditate Between Groups (Combined) 708.050 1 708.050 17.064 .001


Measures of Association

Eta Eta Squared

Jealousy * Meditate .698 .487

Dr. Toob’s hypothesis was not supported. People who meditated reported more jealousy (M = 35.40, SD = 5.70) than people who did not meditate (M =23.50, SD = 7.11), p < .001.


Chapter 10: Bivariate Correlation

1. Using the grades.sav file create a correlation matrix of the following variables; id, ethnic, gender, year, section, gpa, quiz1, quiz2, quiz3, quiz4, quiz5, final, total; select one-tailed significance; flag sig-nificant correlations. Print out results on a single page.

• Draw a single line through the columns and rows where the correlations are meaningless.

• Draw a double line through cells where correlations exhibit linear dependency.

• Circle the 1 “largest” (greatest absolute value) NEGATIVE correlation (the p value will be less than .05) and explain what it means.

• Box the 3 largest POSITIVE correlations (each p value will be less than .05) and explain what they mean.

• Create a scatterplot of gpa by total and include the regression line. (see Chapter 5, page 97-98 for instructions).

2. Using the divorce.sav file create a correlation matrix of the following variables; sex, age, sep, mar, status, ethnic, school, income, avoicop, iq, close, locus, asq, socsupp, spiritua, trauma, lsatisy; select one-tailed significance; flag significant correlations. Print results on a single page. Note: Use Data Files descriptions (p. 389) for meaning of variables.

• Draw a single line through the columns and rows where the correlations are meaningless.

• Draw a double line through the correlations where there is linear dependency

• Circle the 3 “largest” (greatest absolute value) NEGATIVE correlations (each p value will be less than .05) and explain what they mean.

• Box the 3 largest POSITIVE correlations (each p value will be less than .05) and explain what they mean.

• Create a scatterplot of close by lsatisy and include the regression line. (see Chapter 5, page 97-98 for instructions).

• Create a scatterplot of avoicop by trauma and include the regression line.

3. What is the correlation between GPA and percent in the class? Can you be confident of that this cor-relation is different than zero? If so, how large is the correlation? Report the correlation and p value in APA style.


4. Romantic couples take a Big 5 personality test. The extroversion scores for the individuals in each couple are:

Person 1 Person 2

1274 1413

1319 1145

844 928

1237 1211

531 714

979 1230

983 1055

1087 885

724 678

1023 741

What is the correlation between extroversion for these couples? Can you be confident that this correla-tion is larger than zero? If so, how large is the correlation?

5. Agreeableness scores for the same couples as the previous question are listed below. What is the cor-relation? Can you be confident that it is different than zero? How strong is it?

Person 1 916 622 628 1279 943

Person 2 976 706 835 694 1354

Person 1 1531 1303 901 1096 778

Person 2 1489 1294 667 847 1138


10-1 • r = -.21, p = .014: Students in lower numbered sections (e.g. sections 1 and 2) tend to score higher on quiz 1 than students in lower

numbered sections. • r = .86, p < .001: Those who score higher on quiz 1 tend to score higher on quiz 3. • r = .83, p < .001: Those who score higher on quiz 1 tend to score higher on quiz 4. • r = .80, p < .001: Those who score higher on quiz 3 tend to score higher on quiz 4.


10-3

Correlations gpa percent

gpa Pearson Correlation 1 .440**

Sig. (2-tailed) .000

N 105 105

percent Pearson Correlation .440** 1

Sig. (2-tailed) .000 N 105 105

**. Correlation is significant at the 0.01 level (2-tailed).

We can be quite confident (p < .001) that GPA is somewhat positively correlated with percent in the class (r = .44).

10-4 We can be reasonably certain (p = .012) that extroversion is …

10-5

Correlations Person 1 Person 2

Person 1 Pearson Correlation 1 .499

Sig. (2-tailed) .142

N 10 10

Person 2 Pearson Correlation .499 1

Sig. (2-tailed) .142 N 10 10


Chapter 11: The T Test Procedure

For questions 1- 7, perform the following operations:

a) Print out results b) Circle the two mean values that are being compared. c) Circle the appropriate significance value (be sure to consider equal or unequal variance).

d) For statistically significant results (p < .05) write up each finding in standard APA format.

1. Using the grades.sav file, compare men with women (gender) for quiz1, quiz2, quiz3, quiz4, quiz5, final, total.

2. Using the grades.sav file, determine whether the following pairings produce significant differences: quiz1 with quiz2, quiz1 with quiz3, quiz1 with quiz4, quiz1 with quiz5.

3. Using the grades.sav file, compare the GPA variable (gpa) with the mean GPA of the university of 2.89.

4. Using the divorce.sav file, compare men with women (sex) for lsatisfy, trauma, age, school, cog-cope, behcope, avoicop, iq, close, locus, asq, socsupp, spiritua.

5. Using the helping3.sav file, compare men with women (gender) for age, school, income, hclose, hcontrot, sympathi, angert, hcopet, hseveret, empathyt, effict, thelplnz, tqualitz, tothelp. See the Data Files section (page 385) for meaning of each variable.

6. Using the helping3.sav file, determine whether the following pairings produce significant differ-ences: sympathi with angert, sympathi with empathyt, empahelp with insthelp, empahelp with infhelp, insthelp with infhelp.

7. Using the helping3.sav file, compare the age variable (age) with the mean age for North Americans (33.0).

8. In an experiment, 10 participants were given a test of mental performance in stressful situations. Their scores were 2, 2, 4, 1, 4, 3, 0, 2, 7, and 5. Ten other participants were given the same test after they had been trained in stress-reducing techniques. Their scores were 4, 4, 6, 0, 6, 5, 2, 3, 6, and 4. Do the appropriate t test to determine if the group that had been trained had different mental performance scores than the group that had not been trained in stress reduction tech-niques. What do these results mean? Report your results using APA style.

9. In a similar experiment, ten participants who were given a test of mental performance in stress-ful situations at the start of the study, were then trained in stress reduction techniques, and were finally given the same test again at the end of the study. In an amazing coincidence, the participants received the same scores as the participants in question 8: The first two people in the study received a score of 2 on the pretest, and a score of 4 on the posttest; the third person received a score of 4 on the pretest and 6 on the posttest; and so on. Do the appropriate t test to determine if there was a significant difference between the pretest and posttest scores. What do


these results mean? How was this similar and how was this different than the results in ques-tion 1? Why?

10. You happen to know that the population mean for the test of mental performance in stressful situations is exactly three. Do a t test to determine whether the post-test scores in #9 above (the same numbers as the training group scores in #8) is significantly different than three. What do these results mean? How was this similar and how was this different than the results in ques-tion 9? Why?

11. You are studying whether high- and low-gestaltists differ in number of hours of sleep per night; you think that high-gestaltists get more sleep than low-gestaltists. In your data, high ge-staltists slept for the following number of hours: 6, 7.3, 7, 6.9, 4.6, 4.8, 6.9, 9.9, 7.1, and 6.9. Low gestaltists slept for the following number of hours: 5.1, 5.9, 6, 5.5, 3.5, 4.1, 5.1, 8.8, 6.1, and 5.6. Is the hypothesis supported? If so, how large is the effect?

12. You expose 10 participants to red and blue rooms (in a counterbalanced order), and in each room you measure their levels of humility. You are exploring the possibility that people ex-posed to red rooms will be more humble than people exposed to blue rooms. Data are present-ed below; is there a relationship between humility and room color?

Person Red Room Blue Room

1 60 51

2 73 49

3 70 60

4 69 55

5 46 35

6 48 41

7 69 51

8 99 88

9 71 61

10 69 56


11-1

Group Statistics

gender N Mean

Std. Devia-

tion

Std. Error Mean

quiz1 1 Female 64 7.72 2.306 .288

2 Male 41 7.07 2.715 .424

quiz2 1 Female 64 7.98 1.548 .194

2 Male 41 7.98 1.753 .274

quiz3 1 Female 64 8.19 2.130 .266

2 Male 41 7.66 2.555 .399

quiz4 1 Female 64 8.06 2.181 .273

2 Male 41 7.39 2.397 .374

quiz5 1 Female 64 7.88 1.638 .205

2 Male 41 7.85 1.969 .308

final 1 Female 64 62.36 7.490 .936

2 Male 41 60.10 8.514 1.330

total 1 Female 64 102.03 13.896 1.737

2 Male 41 98.29 17.196 2.686


Independent Samples Test Levene's Test for

Equality of Vari-ances t-test for Equality of Means

F Sig. t df Sig. (2-tailed)

Mean Dif-ference

Std. Error Difference

95% Confidence Interval of the

Difference Lower Upper quiz1 Equal variances assumed 2.180 .143 1.305 103 .195 .646 .495 -.335 1.627

Equal variances not assumed 1.259 75.304 .212 .646 .513 -.376 1.667 quiz2 Equal variances assumed 1.899 .171 .027 103 .979 .009 .326 -.638 .656

Equal variances not assumed .026 77.634 .979 .009 .335 -.659 .676 quiz3 Equal variances assumed 3.436 .067 1.147 103 .254 .529 .461 -.385 1.443

Equal variances not assumed 1.103 74.189 .274 .529 .480 -.427 1.485 quiz4 Equal variances assumed .894 .347 1.482 103 .141 .672 .454 -.227 1.572

Equal variances not assumed 1.452 79.502 .151 .672 .463 -.249 1.594 quiz5 Equal variances assumed 4.103 .045 .060 103 .952 .021 .355 -.682 .725

Equal variances not assumed .058 74.071 .954 .021 .369 -.715 .757 final Equal variances assumed .093 .761 1.431 103 .156 2.262 1.581 -.874 5.397

Equal variances not assumed 1.391 77.417 .168 2.262 1.626 -.976 5.500 total Equal variances assumed 2.019 .158 1.224 103 .224 3.739 3.053 -2.317 9.794

Equal variances not assumed 1.169 72.421 .246 3.739 3.198 -2.637 1.011E1

No results are statistically significant


11-2 Paired Samples Statistics

Mean N Std. Deviation Std. Error

Mean Pair 1 quiz1 7.47 105 2.481 .242

quiz2 7.98 105 1.623 .158 Pair 2 quiz1 7.47 105 2.481 .242

quiz3 7.98 105 2.308 .225 Pair 3 quiz1 7.47 105 2.481 .242

quiz4 7.80 105 2.280 .223 Pair 4 quiz1 7.47 105 2.481 .242

quiz5 7.87 105 1.765 .172

Paired Samples Test

Paired Differences

t df Sig. (2-tailed) Mean Std. Deviation Std. Error

Mean

95% Confidence Interval of the Difference

Lower Upper Pair 1 quiz1 - quiz2 -.514 1.835 .179 -.869 -.159 -2.872 104 .005 Pair 2 quiz1 - quiz3 -.514 1.287 .126 -.763 -.265 -4.095 104 .000 Pair 3 quiz1 - quiz4 -.333 1.405 .137 -.605 -.061 -2.431 104 .017 Pair 4 quiz1 - quiz5 -.400 2.204 .215 -.827 .027 -1.860 104 .066

1. Students scored significantly higher on quiz 2 (M = 7.98, SD = 1.62) than on quiz 1 (M = 7.47, SD = 2.48), t(104) = -2.87, p = .005.

2. Students scored significantly higher on quiz 3 (M = 7.98, SD = 2.31) than on quiz 1 (M = 7.47, SD = 2.48), t(104) = -4.10, p < .001.

[Notice that the mean values are identical with the first comparison but quiz 1 with quiz 3 pairing produces a much stronger result. This is due to a much narrower standard deviation for the second comparison (1.29) than for the first (1.84)]

3. Students scored significantly higher on quiz 4 (M = 7.80, SD = 2.28) than on quiz 1 (M = 7.47, SD = 2.48), t(104) = -2.43, p = .017.


11-3 The values do not differ significantly.

11-4 Women (M = 4.53, SD = .88) are significantly more likely to practice cognitive coping than men (M = 4.28, SD = 4.28), t(227) = 2.08, p = .038.

Men (M = 2.92, SD = .96) are significantly more likely to practice avoidant coping than women (M = 2.55, SD = .84), t(227) = -3.13, p = .002.

Women (M = 3.51, SD = .94) are significantly more likely to experience non-sexual physical closeness than men (M = 3.23, SD = .93), t(227) = 2.26, p = .025.

Women (M = 3.44, SD = 2.74) are significantly more likely to have a positive attributional style than men (M = 2.62, SD = 2.69), t(227) = 2.24, p = .023.

Women (M = 3.67, SD = .96) are significantly more likely to receive social support than men (M = 3.37, SD = .78), t(227) = 2.36, p = .009.

Women (M = 4.80, SD = 1.08) have significantly higher personal spirituality than men (M = 4.14, SD = 1.29), t(227) = 4.20, p < .001.


11-8

There was not a significant difference between the mean for the treatment group (M = 4.00, SD = 1.94) and the control group (M = 3.00, SD = 2.06), t(18) = 1.12, p = .28, d = .25).

11-9 Although the mean for the treatment condition (M = 4.00, SD = 1.94) appeared to be higher than the mean for the control condition (M = 3.00, SD = 2.06), this difference was not statistically significant (t(9) = 2.24, p > .05).

Group Statistics

10 3.00 2.055 .65010 4.00 1.944 .615

CONDITIOControlTreatment (training)

PERFORMAN Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

.134 .718 -1.118 18 .278 -1.00 .894 -2.879 .879

-1.118 17.945 .278 -1.00 .894 -2.880 .880

Equal variancesassumedEqual variancesnot assumed

PERFORMAF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means


Chapter 12: The One-Way ANOVA Procedure For Questions 1-6 below: Perform one-way ANOVAs. If there are significant findings write them up in APA format (or in the professional format associated with your discipline).

1. File: grades.sav; dependent variable: quiz4; factor: ethnic (2,5); use LSD procedure for post hoc comparisons, compute two planned comparisons. This problem asks you to reproduce the output on pages 170-172. Note that you will need to perform a select-cases procedure (see page 166) to delete the “1 = Native” category.

2. File: divorce.sav; dependent variable: behcope (behavioral coping); factor: status (1, 5); use LSD pro-cedure for post hoc comparisons; compute two planned comparisons. Note: status is marital status with five levels: 1 = married, 2 = separated, 3 = divorced, 4 = widowed, 5 = cohabiting.

3. File: divorce.sav; dependent variable: spiritua (spirituality); factor: status (1, 4); use LSD procedure for post hoc comparisons; compute two planned comparisons. Note: status is marital status with four levels: 1 = married, 2 = separated, 3 = divorced/single, 4 = cohabiting.

4. File: divorce.sav; dependent variable: close (amount of non-sexual closeness experienced); factor: employ (1, 2, 3, 4, 6); use LSD procedure for post hoc comparisons; compute two planned comparisons. Note: employ refers to type of employment: 1 = management, 2 = own business, 3 = employed, 4 = self-employed, 6 = unemployed. Important: the employ variable has 7 levels. We are deleting levels 5 and 7 due to low N. In the select-cases option, enter as the selection criteria: “employ < 5 | employ = 6”.

5. File: divorce.sav; dependent variable: socsupp (amount of social support); factor: employ (1, 2, 3, 4, 6); use LSD procedure for post hoc comparisons; compute two planned comparisons. Note: employ refers to type of employment: 1 = management, 2 = own business, 3 = employed, 4 = self-employed, 6 = unemployed. Important: the employ variable has 7 levels. We are deleting levels 5 and 7 due to low N. In the select-cases option, enter the selection criteria: “employ < 5 | employ = 6”.

6. File: divorce.sav; dependent variable: lsatisy (life satisfaction); factor: employ (1, 2, 3, 4, 6); use LSD procedure for post hoc comparisons; compute two planned comparisons. Note: employ refers to type of employment: 1 = management, 2 = own business, 3 = employed, 4 = self-employed, 6 = unemployed. Important: the employ variable has 7 levels. We are deleting levels 5 and 7 due to low N. In the select-cases option, enter as the selection criteria: “employ < 5 | employ = 6”.

7. You are studying whether people who have been exposed to red, green, or blue rooms differ in hu-mility. You expose some people to red, some to green, and some to blue rooms. After two hours of con-templating the room, you measure their levels of humility. Is there a difference between the groups? If so, what does it look like?

• Humility scores for red group: 46, 36, 34, 36, 47, 29, 31, 38, 29, 51 • Humility scores for green group: 30, 25, 35, 23, 13, 45, 11, 21, 41, 25 • Humility scores for blue group: 6, 19, 0, 46, 22, 0, 20, 0, 26, 55

8. You are exploring whether chromatid levels influence intrigued hesitancy. You inject participants with either high levels of chromatids, medium levels, low levels, or a placebo. Data are presented be-


low. Do chromatid levels influence intrigued hesitancy? If so, how large is this effect and what does it look like?

• Placebo group scores: 69, 71, 111, 107, 89, 157, 136, 112, 101 • Low chromatid group scores: 285, 297, 465, 407, 246, 429, 444, 420, 476, 415, 306 • Medium chromatid group scores: 301, 432, 444, 549, 622, 571, 438, 444, 540, 521 • High chromatid group scores: 663, 515, 674, 646, 640, 677, 577, 548, 640, 482, 519, 600


12-1

Descriptives

quiz4

N Mean Std. Deviation Std. Error

95% Confidence Interval for Mean

Minimum Maximum Lower Bound Upper Bound

Asian 20 8.35 1.531 .342 7.63 9.07 6 10

Black 24 7.75 2.132 .435 6.85 8.65 4 10

White 45 8.04 2.256 .336 7.37 8.72 2 10

Hispanic 11 6.27 3.319 1.001 4.04 8.50 2 10

Total 100 7.84 2.286 .229 7.39 8.29 2 10

ANOVA

quiz4 Sum of Squares df Mean Square F Sig.

Between Groups (Combined) 34.297 3 11.432 2.272 .085

Linear Term Unweighted 26.464 1 26.464 5.258 .024

Weighted 14.484 1 14.484 2.878 .093

Deviation 19.813 2 9.906 1.968 .145


Contrast Coefficients

Contrast

ethnicity

Asian Black White Hispanic

1 1 1 -1 -1

2 1 1 1 -3

Contrast Tests

Contrast Value of Contrast Std. Error t df Sig. (2-tailed)

quiz4 Assume equal variances 1 1.78 1.015 1.756 96 .082

2 5.33 2.166 2.459 96 .016

Does not assume equal variances 1 1.78 1.192 1.495 19.631 .151

2 5.33 3.072 1.734 10.949 .111


Post Hoc Tests Multiple Comparisons

Dependent Variable: quiz4 LSD

(I) ethnicity (J) ethnicity Mean Difference (I-J) Std. Error Sig.

95% Confidence Interval

Lower Bound Upper Bound

Asian Black .600 .679 .379 -.75 1.95

White .306 .603 .613 -.89 1.50

Hispanic 2.077* .842 .015 .41 3.75

Black Asian -.600 .679 .379 -1.95 .75

White -.294 .567 .605 -1.42 .83

Hispanic 1.477 .817 .074 -.14 3.10

White Asian -.306 .603 .613 -1.50 .89

Black .294 .567 .605 -.83 1.42

Hispanic 1.772* .755 .021 .27 3.27

Hispanic Asian -2.077* .842 .015 -3.75 -.41

Black -1.477 .817 .074 -3.10 .14

White -1.772* .755 .021 -3.27 -.27

*. The mean difference is significant at the 0.05 level.

A one-way ANOVA revealed marginally significant ethnic differences for scores on Quiz 4, F(3, 96) = 2.27, p = .085. Post hoc comparisons using the LSD procedure with an alpha value of .05 found that Whites (M = 8.04) and Asians (M = 8.35) scored significantly higher than Hispanics (M = 6.27).

12-2

ANOVA behcope Sum of Squares df Mean Square F Sig.

Between Groups 11.438 4 2.859 2.571 .039


Contrast Coefficients

Contrast

current marital status

marred separated divorced or DTS widowed cohabit

1 4 -1 -1 -1 -1

2 1.5 -1 -1 -1 1.5


Contrast Tests

Contrast

Value of Con-

trast Std. Error t df Sig. (2-tailed)

behcope Assume equal variances 1 -1.5050 .88406 -1.702 224 .090

2 -1.6262 .74771 -2.175 224 .031

Does not assume equal

variances

1 -1.5050 .78172 -1.925 19.858 .069

2 -1.6262 .62944 -2.584 9.054 .029

Multiple Comparisons

Dependent Variable: behcope LSD

(I) current marital status (J) current marital status

Mean Differ-

ence (I-J) Std. Error Sig.



marred separated -.46589* .23009 .044 -.9193 -.0125

divorced or DTS -.43981* .17366 .012 -.7820 -.0976

widowed -.64781 .62532 .301 -1.8801 .5845

cohabit .04848 .25440 .849 -.4528 .5498

separated marred .46589* .23009 .044 .0125 .9193

divorced or DTS .02609 .20652 .900 -.3809 .4331

widowed -.18192 .63523 .775 -1.4337 1.0699

cohabit .51438 .27787 .065 -.0332 1.0620

divorced or DTS marred .43981* .17366 .012 .0976 .7820

separated -.02609 .20652 .900 -.4331 .3809

widowed -.20800 .61704 .736 -1.4239 1.0079

cohabit .48829* .23330 .037 .0286 .9480

widowed marred .64781 .62532 .301 -.5845 1.8801

separated .18192 .63523 .775 -1.0699 1.4337

divorced or DTS .20800 .61704 .736 -1.0079 1.4239

cohabit .69630 .64444 .281 -.5736 1.9662

cohabit marred -.04848 .25440 .849 -.5498 .4528

separated -.51438 .27787 .065 -1.0620 .0332

divorced or DTS -.48829* .23330 .037 -.9480 -.0286

widowed -.69630 .64444 .281 -1.9662 .5736


A one-way ANOVA revealed significant effect of marital status on behavioral coping (F(4, 224) = 2.57, p = .039). Post hoc comparisons using the LSD procedure found that married people had lower levels of behavioral coping (M = 4.09, SD = 1.06) than separated people (M = 4.56, SD = 1.23; p = .044), and lower levels of behavioral coping than divorced people (M = 5.53, SD = 1.01; p = .012). Similarly, cohab-iting people had lower levels of behavioral coping (M = 4.04, SD = 1.16) than divorced people (p = .037).


12-3 A one-way ANOVA revealed a significant effect of marital status on spirituality, F(4, 224) = 3.63, p = .007, η = .25. Post hoc comparisons using the LSD procedure found that cohabiting people were lower in spirituality (M = 3.72, SD = .96) than married (M = 4.70, SD = 1.16; p = .001), separated (M = 4.50, SD = 1.21; p = .015), or divorced (M = 4.57, SD = 1.26; p = .002) people.

12-4 A one-way ANOVA revealed a significant effect of employment status on the amount of physical close-ness, F(4, 205) = 2.62, p = .036. Post hoc comparisons using the LSD procedure found…

12-8

Descriptives Intrigued Hesitancy

N Mean Std. Deviation Std. Error

95% Confidence Interval for

Mean

Minimum Maximum Lower Bound Upper Bound

Placebo 9 105.89 28.440 9.480 84.03 127.75 69 157

Low 11 380.91 81.135 24.463 326.40 435.42 246 476

Medium 10 486.20 92.378 29.213 420.12 552.28 301 622

High 12 598.42 68.492 19.772 554.90 641.93 482 677

Total 42 409.19 192.950 29.773 349.06 469.32 69 677

ANOVA

Intrigued Hesitancy Sum of Squares df Mean Square F Sig.

Between Groups 1325708.162 3 441902.721 83.666 .000


Multiple Comparisons

Dependent Variable: Intrigued Hesitancy LSD

(I) Chromatid Level (J) Chromatid Level

Mean Difference

(I-J) Std. Error Sig.



Placebo Low -275.020* 32.665 .000 -341.15 -208.89

Medium -380.311* 33.392 .000 -447.91 -312.71

High -492.528* 32.047 .000 -557.40 -427.65

Low Placebo 275.020* 32.665 .000 208.89 341.15

Medium -105.291* 31.754 .002 -169.57 -41.01

High -217.508* 30.337 .000 -278.92 -156.09


Medium Placebo 380.311* 33.392 .000 312.71 447.91

Low 105.291* 31.754 .002 41.01 169.57

High -112.217* 31.118 .001 -175.21 -49.22

High Placebo 492.528* 32.047 .000 427.65 557.40

Low 217.508* 30.337 .000 156.09 278.92

Medium 112.217* 31.118 .001 49.22 175.21


Chromatid levels strongly influenced intrigued hesitancy (F(3, 38) = 83.67, p < .001, η2 = .87). Higher levels of chromatids were consistently associated with higher levels of intrigued hesitancy. [If all means and SDs should be reported, this would be a good place for a table.] [If post hoc tests are desired: Post hoc LSD tests indicated that every condition was significantly different than every other condition, all ps < .002.]


Chapter 14: Three-Way ANOVA For the first five problems below, perform the following:

• Print out the cell means portion of the output.

• Print out the ANOVA results (main effects, interactions, and so forth).

• Interpret and write up correctly (APA format) all main effects and interactions.

• Create multiple-line graphs (or clustered bar charts) for all significant interactions.

1. File: helping3.sav; dependent variable: tothelp; independent variables: gender, problem.

2. File: helping3.sav; dependent variable: tothelp; independent variables: gender, income.

3. File: helping3.sav; dependent variable: hseveret; independent variables: ethnic, problem.

4. File: helping3.sav; dependent variable: thelplnz; independent variables: gender, problem; covari-ate: tqualitz.

5. File: helping3.sav; dependent variable: thelplnz; independent variables: gender, income, marital.

6. In an experiment, participants were given a test of mental performance in stressful situations. Some participants were given no stress-reduction training, some were given a short stress-reduction train-ing session, and some were given a long stress-reduction training session. In addition, some partici-pants who were tested had a low level of stress in their lives, and others had a high level of stress in their lives. Perform an ANOVA on these data (listed below). What do the results mean?

Training: None Short Life Stress: High Low High

Performance Score: 5 4 2 5 4 4 4 6 6 2 6 4 5 4 3

Training: Short Long Life Stress: Low High Low

Performance Score: 7 6 6 5 7 5 5 5 3 5 7 7 9 9 8

7. In an experiment, participants were given a test of mental performance in stressful situations. Some participants were given no stress-reduction training, and some were given a stress-reduction train-ing session. In addition, some participants who were tested had a low level of stress in their lives, and others had a high level of stress in their lives. Finally, some participants were tested after a full night's sleep, and some were tested after an all-night study session on three-way ANOVA. Perform an ANOVA on these data (listed below question 8; ignore the "caffeine" column for now). What do these results mean?


8. In the experiment described in problem 7, data were also collected for caffeine levels. Perform an

ANOVA on these data (listed below). What do these results mean? What is similar to and different than the results in question 7?

Training? Stress Level Sleep/Study Performance Caffeine No Low Sleep 8 12 No Low Sleep 9 13 No Low Sleep 8 15

No Low Study 15 10 No Low Study 14 10 No Low Study 15 11

No High Sleep 10 14 No High Sleep 11 15 No High Sleep 11 16

No High Study 18 11 No High Study 19 10 No High Study 19 11

Yes Low Sleep 18 11 Yes Low Sleep 17 10 Yes Low Sleep 18 11

Yes Low Study 10 4 Yes Low Study 10 4 Yes Low Study 11 4

Yes High Sleep 22 14 Yes High Sleep 22 14 Yes High Sleep 23 14

Yes High Study 13 5 Yes High Study 13 5 Yes High Study 12 4

9. Dr. Toob believes that people who meditate regularly are less jealous, but that this effect is larger for people who are religious than people who are not. She has 20 participants meditate for a week, and 20 participants not meditate for a week. After she measures level of jealousy for her participants, she hires you to determine whether her hypothesis is supported. Is it? What do the results mean?

Meditate? Religious? Jealousy

Yes Yes 2

Yes Yes 3

Yes Yes 4

Yes Yes 1

Yes Yes 4

Yes Yes 3



Yes Yes 7

Yes Yes 5

Yes Yes -1

Yes Yes 2

Yes No 1

Yes No 2

Yes No 2

Yes No 4

Yes No 4

Yes No 3

Yes No 3

Yes No 4

Yes No 1

Yes No 2

No Yes 5

No Yes 4

No Yes 7

No Yes 4

No Yes 4

No Yes 6

No Yes 3

No Yes 5

No Yes 8

No Yes 5



No No 9

No No 6

No No 7

No No 6

No No 7

No No 5

No No 8

No No 6

No No 9

No No 5

10. You are exploring whether the effect of chromatid levels on intrigued hesitancy is moderated by electrolyte levels. You inject participants with either high levels of chromatids, medium levels, low lev-els, or a placebo; you either have them drink lots of sports drink (high electrolyte group) or a diuretic (low electrolyte group). Data are presented below Question 12. Is the effect of chromatid levels on in-trigued hesitancy moderated by electrolyte levels? If so, describe this interaction along with the main effect(s) if present.

11. In a follow-up study to the previous question, you measure saltiness (that you think may also be correlated with intrigued hesitancy). Data are presented below Question 12. If you include saltiness as a covariate, do the effects that you found in question 10 get larger or smaller? Does power get larger or smaller? Describe the effect of the covariate, along with the interaction and main effect(s) if present.

12. It occurs to you that you also recorded participants’ gender in the study described in Question 10. You think that the two-way interaction you found in Question 10 may differ between men and women. Perform a three-way ANOVA on these data. For each main effect, two-way interaction, and three-way interaction, a) describe whether the effect is significant, b) how large the effect is, and c) describe the effect (i.e., differences between the means).

Dataset for Questions 10, 11, and 12:

Chromatid Electrolytes Gender Intrigued Hesitancy Saltiness

Placebo High Female 71 13





Placebo High Male 72 5



Low High Female 328 37



Low High Male 369 38



Medium High Female 396 38



Medium High Male 372 42



High High Female 517 53



High High Male 565 61



Placebo Low Female 128 17





Placebo Low Male -20 9

Placebo Low Male -16 10

Placebo Low Male 31 13

Low Low Female 303 35



Low Low Male 199 29

Low Low Male 214 32

Low Low Male 297 40

Medium Low Female 400 40



Medium Low Male 451 42



High Low Female 547 57



High Low Male 582 53




14-1

Between-Subjects Factors

Value Label N

Gender 1 FEMALE 294

2 MALE 199

TYPE OF PROBLEM EXPERI-

ENCED

1 GOAL DISRUP-

TIVE 207

2 RELATIONAL

BREAK 189

3 ILLNESS 84

4 CATASTROPHIC 13


Dependent Variable: COMBINED HELP MEASURE--QUANTITY & QUALITY

gender


ENCED Mean Std. Deviation N

FEMALE GOAL DISRUPTIVE -.0299 .68184 105

RELATIONAL BREAK .1516 .72524 132

ILLNESS .2901 .71572 50

CATASTROPHIC .3449 .62825 7

Total .1149 .71313 294

MALE GOAL DISRUPTIVE -.2752 .77680 102

RELATIONAL BREAK -.0802 .68315 57

ILLNESS -.1298 .82601 34


Total -.1807 .75724 199

Total GOAL DISRUPTIVE -.1507 .73870 207

RELATIONAL BREAK .0817 .71895 189

ILLNESS .1201 .78529 84


Total -.0044 .74478 493


Tests of Between-Subjects Effects

Dependent Variable: COMBINED HELP MEASURE--QUANTITY & QUALITY Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared

Corrected Model 17.019a 7 2.431 4.608 .000 .062

Intercept .510 1 .510 .966 .326 .002

gender 2.785 1 2.785 5.278 .022 .011

problem 5.879 3 1.960 3.714 .012 .022

gender * problem .581 3 .194 .367 .777 .002

Error 255.894 485 .528 Total 272.923 493 Corrected Total 272.913 492

a. R Squared = .062 (Adjusted R Squared = .049) Estimated Marginal Means

1. Grand Mean

Dependent Variable: COMBINED HELP MEASURE--QUANTITY &

QUALITY

Mean Std. Error



.057 .058 -.057 .170

2. gender Dependent Variable: COMBINED HELP MEASURE--QUANTITY & QUALITY

gender Mean Std. Error



FEMALE .189 .077 .038 .341

MALE -.076 .086 -.244 .093

3. TYPE OF PROBLEM EXPERIENCED



ENCED Mean Std. Error



GOAL DISRUPTIVE -.153 .050 -.252 -.053

RELATIONAL BREAK .036 .058 -.077 .149

ILLNESS .080 .081 -.078 .239

CATASTROPHIC .263 .202 -.134 .660


4. gender * TYPE OF PROBLEM EXPERIENCED


gender


ENCED Mean Std. Error



FEMALE GOAL DISRUPTIVE -.030 .071 -.169 .109

RELATIONAL BREAK .152 .063 .027 .276

ILLNESS .290 .103 .088 .492

CATASTROPHIC .345 .275 -.195 .884

MALE GOAL DISRUPTIVE -.275 .072 -.416 -.134

RELATIONAL BREAK -.080 .096 -.269 .109

ILLNESS -.130 .125 -.375 .115

CATASTROPHIC .182 .297 -.401 .765

(The chart (left) is included for demon-stration only. There is no significant in-teraction in the present results.)

A 2-way ANOVA was conducted to de-termine the influence of gender and type of problem on the total amount of help given. Results showed a significant main effect for gender in which women (M = .12) gave slightly more help than men (M = -.18), F(1, 529) = 5.54, p = .019, η2 = .01. There was also a significant (but small) main effect for problem type, F(3, 529) = 1.65, p = .023, η2 = .02. There was no significant gender by problem type interaction.


14-2

A two-way ANOVA was conducted to determine the influence of gender and level of income on the total amount of help given. Results showed a significant main effect for gender in which….There was also a significant main effect for level of income, F(4, 527) = 3.15, p = .014, η2 = .02. Post hoc compari-sons using the LSD procedure revealed that… There was also a significant gender by income interac-tion, F(4, 527) = 2.60, p = .035, η2 = .02. While for all income levels, women helped more than men, for participants making less than 25,000, the gender discrepancy was large, but for participants making more than 25,000, the gender discrepancy was small.

14-3 A two-way ANOVA was conducted to determine the influence of ethnicity and problem type on the severity rating of problems. Problem type had a significant effect on the severity ratings, F(3, 518) = 4.96, p = .002, η2 = .03. Post hoc comparisons using the least significant differences procedure with an alpha value of .05 revealed that the severity rating for goal-disruptive problems (M = 4.58, SD = 1.66) was significantly less than for relational problems (M = 5.15, SD = 1.42), illness problems (M = 5.70, SD = 1.44), or catastrophic problems (M = 6.00, SD = 1.26). Also illness problems were rated more severe than relational problems. There was no significant ethnic by problem type interaction.


14-6

There was a main effect of training: People who had a long training session (M = 6.30, SD = 2.00) per-formed better than people who had a short training session (M = 5.30, SD = 1.34), who in turn did bet-ter than those who had no training session (M = 4.20, SD = 1.40; F(2,24) = 8.17, p = .002, η2 = .41).

There was a main effect of level of life stress: People with low levels of life stress (M = 6.20, SD = 1.90) performed better than people with high levels of life stress (M = 4.33, SD = 1.05; F(1,24) = 19.36, p < .001, η2 = .45).

There was an interaction between training and level of life stress, as displayed in this graph (F(2, 24) = 4.17, p = .028, η2 = .26):


Dependent Variable: PERFORMA

4.00 1.225 54.40 1.673 54.20 1.398 104.40 1.140 56.20 .837 55.30 1.337 104.60 .894 58.00 1.000 56.30 2.003 104.33 1.047 156.20 1.897 155.27 1.780 30

LIFESTREHighLowTotalHighLowTotalHighLowTotalHighLowTotal

TRAININGNone

Short

Long

Total

Mean Std. Deviation N


Dependent Variable: PERFORMA

59.467b 5 11.893 8.810 .000 .647 44.049 .999832.133 1 832.133 616.395 .000 .963 616.395 1.000

22.067 2 11.033 8.173 .002 .405 16.346 .93426.133 1 26.133 19.358 .000 .446 19.358 .98811.267 2 5.633 4.173 .028 .258 8.346 .67832.400 24 1.350

924.000 3091.867 29

SourceCorrected ModelInterceptTRAININGLIFESTRETRAINING * LIFESTREErrorTotalCorrected Total

Type III Sumof Squares df Mean Square F Sig.

Partial EtaSquared

Noncent.Parameter

ObservedPowera

Computed using alpha = .05a.

R Squared = .647 (Adjusted R Squared = .574)b.


Note that for those with low life stress, the amount of training seems to make a big difference. For those with high life stress, the impact of training is minimal.

14-7 • There was a main effect for training: Participants who received training performed better

(M = 15.75, SD = 4.86) than participants who did not receive training (M = 13.08, SD = 4.14), F(1, 16) = 128.00, p < .001, η2 = .89).

• There was a main effect of stress level: Participants with high stress levels performed better (M = 16.08, SD = 4.89) than those with low stress levels (M = 12.75, SD = 3.85), F(1, 16) = 200.00, p < .001, η2 = .93).

• There was main effect on sleeping versus studying all night: People who slept performed somewhat better (M = 14.75, SD = 5.83) than those who didn’t sleep (M = 14.08, SD = 3.23), F(1, 16) = 8.00, p = .012, η2 = .33).

• There was no significant interaction effect between training and stress level (F(1, 16) = .50, p > .05, η2 = .03).

• There was a significant interaction between training and sleeping versus studying (F(1, 16) = 1104.50, p < .001, η2 = .99): For those with no training, people who slept per-formed worse (M = 9.50, SD = 1.38) than those who studied (M = 16.67, SD = 2.25). For those with training, however, people who slept performed better (M = 20.00, SD = 2.61) than people who studied (M = 11.50, SD = 1.38).

• There was no significant interaction between stress level and sleeping versus studying (F(1, 16) = .50, p > .05, η2 = .03).

• There was a significant three-way interaction between training, stress level, and sleeping versus studying (F(1, 16) = 18.00, p = .001, η2 = .53).

• For those who slept, they performed better with high stress levels, and better with training. A post hoc test could determine whether the difference between high and low stress levels was greater in the training condition than in the no training condition.

TrainingLongShortNone

Estim

ated

Mar

gina

l Mea

ns

8

7

6

5

4

LowHigh

Life Stress

Estimated Marginal Means of Performance Score


• For those who didn’t sleep, they performed better with high stress levels and better without training. A post hoc test could determine whether the performance gain for the high stress level participants was greater in the no training condition than in the training condition.

14-10

Tests of Between-Subjects Effects Dependent Variable: IntriguedHesitancy

Source

Type III Sum of

Squares df Mean Square F Sig.

Partial Eta

Squared

Corrected Model 1380330.979a 7 197190.140 82.103 .000 .935

Intercept 5362038.521 1 5362038.521 2232.566 .000 .982

Chromatid 1352379.562 3 450793.187 187.695 .000 .934

Electrolytes 1291.687 1 1291.687 .538 .468 .013

Chromatid * Electrolytes 26659.729 3 8886.576 3.700 .019 .217

Error 96069.500 40 2401.738 Total 6838439.000 48 Corrected Total 1476400.479 47 a. R Squared = .935 (Adjusted R Squared = .924)

1. Grand Mean

Dependent Variable: IntriguedHesitancy

Mean Std. Error



334.229 7.074 319.933 348.525

2. Chromatid


Chromatid Mean Std. Error



Placebo 80.667 14.147 52.074 109.259

Low 303.333 14.147 274.741 331.926

Medium 417.333 14.147 388.741 445.926

High 535.583 14.147 506.991 564.176

3. Electrolytes


Electrolytes Mean Std. Error



Low 329.042 10.004 308.824 349.260


High 339.417 10.004 319.199 359.635

4. Chromatid * Electrolytes


Chromatid Electrolytes Mean Std. Error



Placebo Low 67.500 20.007 27.064 107.936

High 93.833 20.007 53.397 134.269

Low Low 269.333 20.007 228.897 309.769

High 337.333 20.007 296.897 377.769

Medium Low 412.500 20.007 372.064 452.936

High 422.167 20.007 381.731 462.603

High Low 566.833 20.007 526.397 607.269

High 504.333 20.007 463.897 544.769

Electrolyte levels do moderate the effect of chromatid levels on intrigued hesitancy (F(3, 40) = 3.70, p = .019, η2 = .22). In the placebo and low chromatid conditions, higher levels of electrolytes were asso-ciated with higher levels of intrigued hesitancy; for the medium chromatid level condition, there was little difference between levels of electrolytes on intrigued hesitancy. For people in the high chromatid level, however people with high electrolytes had lower levels of intrigued hesitancy than people with low electrolytes. See the figure above.

There was also a main effect of chromatid levels on intrigued hesitancy (F(3, 40) = 187.70, p < .001, η2 = .93), such that people in the high chromatid level had the highest levels of intrigued hesitancy


(M = 535.58, SE = 14.15), followed by the medium chromatid condition (M =417.33, SE = 14.15) , the low chromatid condition (M = 303.33, SE = 14.15), and the placebo condition (M = 80.67, SE = 14.15).

There was no main effect of electrolyte levels on intrigued hesitancy (F(1, 40) = .59, p = .47, η2 = .01).


Chapter 15: Simple Linear Regression 1. Use the anxiety.sav file for exercises that follow.

Perform the 4a - 5a sequences on pages 200 and 201. Include output in as compact a form as is reasonable Write the linear equation for the predicted exam score Write the quadratic equation for the predicted exam score

For subjects numbered 5, 13, 42, and 45 Substitute values into the two equations and solve. Show work on a separate page. Then compare in a small table (shown below and similar to that on page 198)

The anxiety score for each subject Linear equation results, Quadratic equation results, and Actual exam scores for sake of comparison.

subject # anxiety score predicted linear score predicted quadratic score

actual exam score

5

13

42

45

2. Now using the divorce.sav file, test for linear and curvilinear relations between:

physical closeness (close) and life satisfaction (lsatisy) attributional style (asq) and life satisfaction (lsatisy)

Attributional style, by the way, is a measure of optimism—a low score is “pessimistic” and a high score is “optimistic”.

Print graphs and write linear and quadratic equations for both. For each of the three analyses in problems 3 and 4:

Print out the results Box the Multiple R, Circle the R Square, Underline the three (3) B values, and Double underline the three (3) Sig of T values.

In a single sentence (just once, not for each of the 3 problems) identify the meaning of each of the final four (4) bulleted items above. 3. First, perform step 5b (p. 202) demonstrating the influence of anxiety and anxiety squared (anxie-ty2) on the exam score (exam).


4. Now, complete similar procedures for the two relationships shown in problem 2 (from the di-vorce.sav file) and perform the 5 steps bulleted above: Specifically,

• the influence of closeness (close) and closeness squared (close2) on life satisfaction (lsatisy), and

• the influence of attributional style (asq) and the square of attributional style (asq2) on life satisfaction (lsatisy).

5. A researcher is examining the relationship between stress levels and performance on a test of cognitive performance. She hypothesizes that stress levels lead to an increase in performance to a point, and then increased stress decreases performance. She tests ten participants, who have the following levels of stress: 10.94, 12.76, 7.62, 8.17, 7.83, 12.22, 9.23, 11.17, 11.88, and 8.18. When she tests their levels of mental performance, she finds the following cognitive performance scores (listed in the same participant order as above): 5.24, 4.64, 4.68, 5.04, 4.17, 6.20, 4.54, 6.55, 5.79, and 3.17. Perform a linear regression to examine the relationship between these variables. What do these results mean? 6. The same researcher tests ten more participants, who have the following levels of stress: 16, 20, 14, 21, 23, 19, 14, 20, 17, and 10. Their cognitive performance scores are (listed in the same partici-pant order): 5.24, 4.64, 4.68, 5.04, 4.17, 6.20, 4.54, 6.55, 5.79, and 3.17. (Note that in an amazing coinci-dence, these participants have the same cognitive performance scores as the participants in Question 5; this coincidence may save you some typing.) Perform a linear regression to examine the relationship between these variables. What do these results mean?

7. Create a scatterplot (see Chapter 5) of the variables in Question 6. How do results suggest that linear regression might not be the best analysis to perform?

8. Perform curve estimation on the data from Question 6. What does this tell you about the data that you could not determine from the analysis in Question 6?

9. What is different about the data in Questions 5 and 6 that leads to different results? 10. You believe that milk is good for you, and good for creativity. To test your hypothesis, you examine the number of gallons of 2% milk consumed per person in the US from 2000-2009; you think that this will be a good predictor of the number of visual art works copyrighted in those years. Data are listed below; perform a regression to test your hypothesis. Is your hypothesis cor-rect? Report your results including R and R2, B or b (beta), and significance values.

Year Works of visual art copyrighted (US, thou-

sands) Per capita consumption of 2% milk (US; gal-

lons)

2000 85.8 7.1

2001 99.9 7

2002 79.9 7

2003 93.4 6.9


Year Works of visual art copyrighted (US, thou-

sands) Per capita consumption of 2% milk (US; gal-

lons)

2004 107.8 6.9

2005 82.5 6.9

2006 90.7 6.9

2007 89.2 6.9

2008 42.1 7.3

2009 75.2 7.3

11. Emmanuel Lance is trying to predict the cost of potato chips. She collects data for several years on the amount of precipitation in Idaho (the largest potato producer in the US) and the cost of potato chips in the US. Does precipitation in Idaho predict the cost of potato chips? Data is presented on the next page. Data for Question 11 and Chapter 16 Question 5

Year Cost for 1 pound of po-

tato chips Average Precipitation in

Idaho (mm) Number of

Farms Number of

Lawyers

1985 $2.75 1.43 2,293

1986 $2.67 1.80 2,250

1987 $2.70 1.33 2,213

1988 $2.85 1.44 2,201

1989 $2.97 1.50 2,175 725,579

1990 $3.03 1.63 2,146 755,694

1991 $3.12 1.60 2,117 777,119

1992 $3.17 1.27 2,108 799,760

1993 $3.18 1.61 2,202 846,036

1994 $3.33 1.34 2,198 865,614

1995 $3.44 2.16 2,196 896,140

1996 $3.48 2.23 2,191 953,260

1997 $3.47 1.74 2,191 953,260

1998 $3.58 2.00 2,192 985,921


Year Cost for 1 pound of po-

tato chips Average Precipitation in

Idaho (mm) Number of

Farms Number of

Lawyers

1999 $3.35 1.42 2,187 1,000,440

2000 $3.46 1.43 2,167 1,022,462

2001 $3.41 1.33 2,149 1,048,903

2002 $3.65 1.34 2,135 1,049,751

2003 $4.48 1.62 2,127 1,058,662

2004 $4.65 1.66 2,113 1,084,504

2005 $4.74 1.79 2,099 1,104,766


15-1

Dependent Variable: exam

Equation

Model Summary Parameter Estimates

R Square F df1 df2 Sig. Constant b1 b2

Linear .238 22.186 1 71 .000 64.247 2.818 Quadratic .641 62.525 2 70 .000 30.377 18.926 -1.521

The independent variable is anxiety.

Linear: EXAM(pred) = 64.247 + 2.818(ANXIETY)

Quadratic: EXAM(pred) = 30.377 + 18.926(ANXIETY) – 1.521(ANXIETY)2

subject # Anxiety score predicted linear score predicted quadratic score actual score

5 3.0 72.7 73.5 70

13 4.0 75.5 81.7 82

42 6.5 82.6 89.1 98

45 9.0 89.6 77.6 79

anxiety10.08.06.04.02.00.0

100

90

80

70

60

50

40

exam

QuadraticLinearObserved


15-2 Linear: LSATISFY(pred) = 4.571 + .08(ASQ)

Quadratic: LSATISFY(pred) = 4.587 + .051(ASQ) + .004(ASQ)2

15-3 Model Summary

Model R R Square

Adjusted R Square

Std. Error of the Estimate

di

1 .801a .641 .631 8.443

a. Predictors: (Constant), square of anxiety, anxiety

Multiple R: The multiple correlation between the dependent variable and (in this case) the two inde-pendent variables.

15-5

These results suggest that there is a significant relationship between stress and performance (R2 = .399, F(1,8) = 5.31, p = .05). Note, though, that we have tested for a linear relationship—which is not what the research hypothesized.

15-8 Notice that the linear regression information has (within rounding error) the same information as calcu-lated by the linear regression procedure in exercise 5, above. That model doesn’t fit the data well. The quadratic equation, however, fits the data much better (R2 = .69, F(1, 7) = 7.68, p = .017). This tells us that the data is predicted much better from a quadratic equation (which will form an upside-down “U” shape) than a linear one.

15-9 The data in question 4 is (roughly) linear; the data in question 5 is curvilinear.

Model Summary

.632a .399 .324 .82256Model1

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Predictors: (Constant), STRESSa.

ANOVAb

3.594 1 3.594 5.312 .050a

5.413 8 .6779.007 9

RegressionResidualTotal

Model1

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), STRESSa.

Dependent Variable: PERFORMAb.


15-11 The average precipitation in Idaho does not predict the average cost for potato chips in the United States (R2 = .06, F(1, 19) = …).


Chapter 16: Multiple Regression Analysis

Use the helping3.sav file for the exercises that follow.

Conduct the following THREE regression analyses:

Criterion variables:

1. thelplnz: Time spent helping

2. tqualitz: Quality of the help given

3. tothelp: A composite help measure that includes both time and quality

Predictors: (use the same predictors for each of the three dependent variables)

age: range from 17 to 89

angert: Amount of anger felt by the helper toward the needy friend

effict: Helper’s feeling of self-efficacy (competence) in relation to the friend’s problem

empathyt: Helper’s empathic tendency as rated by a personality test

gender: 1 = female, 2 = male

hclose: Helper’s rating of how close the relationship was

hcontrot: helper’s rating of how controllable the cause of the problem was

hcopet: helper’s rating of how well the friend was coping with his or her problem

hseveret: helper’s rating of the severity of the problem

obligat: the feeling of obligation the helper felt toward the friend in need

school: coded from 1 to 7 with 1 being the lowest education, and 7 the highest (> 19 years)

sympathi: The extent to which the helper felt sympathy toward the friend

worry: amount the helper worried about the friend in need

• Use entry value of .06 and removal value of .11. • Use stepwise method of entry.

Create a table (example below) showing for each of the three analyses Multiple R, R2, then each of the variables that significantly influence the dependent variables. Following the R2, List the name of each variable and then (in parentheses) list its β value. Rank order them from the most influential to least influential from left to right. Include only significant predictors.


Depend-ent

Variable Multiple R R2 1st var (β) 2nd var (β 3rd var (β) 4th var (β) 5th var (β) 6th var (β)

Time helping

Help quality

Total help

4. A researcher is examining the relationship between stress levels, self-esteem, coping skills, and per-formance on a test of cognitive performance (the dependent measure). His data are shown below. Perform multiple regression on these data, entering variables using the stepwise procedure. Inter-pret the results.

Stress Self-esteem Coping skills Performance

6 10 19 21

5 10 14 21

5 8 14 22

3 7 13 15

7 14 16 22

4 9 11 17

6 9 15 28

5 9 10 19

5 11 20 16

5 10 17 18

5. Emmanuel Lance is trying to predict the cost of potato chips. She collects data for several years on the amount of precipitation in Idaho (the largest potato producer in the US), the number of farms in the US, and the number of lawyers in the US (because she has anecdotally observed that the three lawyers she knows eat a lot of potato chips). Do these three predictors work to predict the cost of potato chips? How well do they do this? The data for this problem is listed at the end of the previous chapter, page 209. In your answer, be sure to state whether there is causal evidence or if there are possible third vari-ables that explain these relationships.


16-1 Dependent

Variable Multiple

R R2 1st var (β) 2nd var (β) 3rd var (β) 4th var (β) 5th var (β) 6th var

(β)

1. Time help-ing .576 .332 Efficacy

(.330) Severity

(.214) Worry (.153)

Closeness (.113)

Anger (.110)

Gender (-.096)

16-4 Two different models were examined. The first model, Performance = 7.688 + 2.394 x Stress + Residual, fit the data fairly well (R2 = .49, F(1,8) = 7.53, p = .025). Adding self-esteem significantly improved the model, so the second model, Performance = 12.999 + 4.710 x Stress – 1.765 x Self-Esteem + Residual, fit the data even better (R2 = .90, F(2,7) = 14.65, p = .003). So, when stress goes up, performance goes up; but when self-esteem goes up, performance goes down. Coping skills didn’t contribute to make the model better.

16-5 Note: Because the question is worded “…do these three predictors work to predict…” using the “En-ter” method of multiple regression most closely matches the question. The same pattern of results would be found if using “Stepwise” multiple regression, but the write-up would be slightly different as would the statistics supporting the results.

Precipitation in Idaho, the number of farms, and the number of lawyers strongly predict the cost of po-tato chips in the United States (R2 = .81, F(3, 13) = 18.05, p < .001). Examining the standardized coeffi-cients indicates that …


Chapter 18: Reliability Analysis Use the helping3.sav file for the exercises that follow (downloadable at the address shown above). Measure the internal consistency (coefficient alpha) of the following sets of variables. An “h” in front of a variable name, refers to assessment by the help giver; an “r” in front of a variable name refers to assessment by the help recipient.

Compute Coefficient alpha for the following sets of variables, then delete variables until you achieve the highest possible alpha value. Print out relevant results.

1. hsevere1, hsevere2, rsevere1, rsevere2 measure of problem severity

2. sympath1, sympath2, sympath3, sympath4 measure of helper’s sympathy

3. anger1, anger2, anger3, anger4 measure of helper’s anger

4. hcope1, hcope2, hcope3, rcope1, rcope2, rcope3 how well the recipient is coping

5. hhelp1-hhelp15 helper rating of time spent helping

6. rhelp1-rhelp15 recipient’s rating of time helping

7. empathy1-empath14 helper’s rating of empathy

8. hqualit1, hqualit2, hqualit3, rqualit1, rqualit2, rqualit3 quality of help

9. effic1-effic15 helper’s belief of self efficacy

10. hcontro1, hcontro2, rcontro1, rcontro2 controllability of the cause of the problem

From the divorce.sav file:

11. drelat-dadjust (16 items) factors disruptive to divorce recovery

12. arelat-amain2 (13 items) factors assisting recovery from divorce

13. sp8-sp57 (18 items) spirituality measures

14. You are developing a scale to measure focused anger. You draft a five-item scale, with each item an-swered on a 1-9 scale. Data are listed below; calculate Chronbach’s alpha. How reliable is this scale?

Item 1 Item 2 Item 3 Item 4 Item 5

6 7 7 3 5

6 5 8 6 5

7 7 6 7 7

3 4 4 5 3

4 4 4 4 6


Item 1 Item 2 Item 3 Item 4 Item 5

7 6 6 5 7

5 4 4 5 5

5 5 5 4 4

4 5 4 7 5

4 4 3 4 4


18-1

Reliability Statistics

.889 .890 4

Cronbach'sAlpha

Cronbach'sAlpha Based

onStandardized

Items N of Items

Inter-Item Correlation Matrix

1.000 .789 .610 .603

.789 1.000 .588 .647

.610 .588 1.000 .774

.603 .647 .774 1.000

HELPER RATINGOF DISRUPTIONHELPER RATINGOF TRAUMARECIPIENT RATINGOF DISRUPTIONRECIPIENT RATINGOF TRAUMA

HELPERRATING OF

DISRUPTION

HELPERRATING OF

TRAUMA

RECIPIENTRATING OF

DISRUPTION

RECIPIENTRATING OF

TRAUMA

The covariance matrix is calculated and used in the analysis.

Summary Item Statistics

5.082 4.886 5.199 .313 1.064 .019 42.782 2.638 2.944 .306 1.116 .016 4

.668 .588 .789 .201 1.342 .007 4

Item MeansItem VariancesInter-Item Correlations

Mean Minimum Maximum RangeMaximum /Minimum Variance N of Items

The covariance matrix is calculated and used in the analysis.

Item-Total Statistics

15.44 19.157 .754 .655 .859

15.18 19.718 .768 .668 .854

15.23 19.662 .741 .631 .864

15.13 19.459 .766 .655 .855

HELPER RATINGOF DISRUPTIONHELPER RATINGOF TRAUMARECIPIENT RATINGOF DISRUPTIONRECIPIENT RATINGOF TRAUMA

Scale Mean ifItem Deleted

ScaleVariance if

Item Deleted

CorrectedItem-TotalCorrelation

SquaredMultiple

Correlation

Cronbach'sAlpha if Item

Deleted

Scale Statistics

20.33 33.433 5.782 4Mean Variance

Std.Deviation N of Items


18-2 There is a special data file available on the course website for those using the student version of SPSS.

Reliability Statistics

Cronbach's Al-

pha

Cronbach's Al-

pha Based on

Standardized

Items N of Items

.817 .820 3

Inter-Item Correlation Matrix

HELPER RAT-

ING OF COM-

PASSION

HELPER RAT-

ING OF SYM-

PATHY

HELPER RAT-

ING OF MOVED

HELPER RATING OF COM-

PASSION

1.000 .591 .590

HELPER RATING OF SYM-

PATHY

.591 1.000 .626

HELPER RATING OF

MOVED

.590 .626 1.000

Summary Item Statistics

Mean Minimum Maximum Range

Maximum / Min-

imum Variance N of Items

Item Means 5.138 4.732 5.458 .726 1.153 .138 3

Item Variances 2.321 1.857 2.790 .933 1.502 .218 3

Inter-Item Correlations .602 .590 .626 .036 1.061 .000 3

Item-Total Statistics

Scale Mean if

Item Deleted

Scale Variance if

Item Deleted

Corrected Item-

Total Correlation

Squared Multiple

Correlation

Cronbach's Al-

pha if Item De-

leted

HELPER RATING OF COM-

PASSION

9.96 8.291 .655 .429 .768

HELPER RATING OF SYM-

PATHY

10.19 7.333 .683 .467 .733

HELPER RATING OF

MOVED

10.68 6.623 .683 .467 .740


Scale Statistics Mean Variance Std. Deviation N of Items

15.42 15.284 3.910 3

18-14 The focused anger scale is reliable (Chronbach’s α = …).


Chapter 23: MANOVA and MANCOVA 1. Using the grade.sav file, compute and interpret a MANOVA examining the effect of whether or

not students completed the extra credit project on the total points for the class and the previous GPA.

2. Using the grades.sav file, compute and interpret a MANOVA examining the effects of section and lowup on total and GPA.

3. Why would it be a bad idea to compute a MANOVA examining the effects of section and lowup on total and percent?

4. A researcher wishes to examine the effects of high- or low-stress situations on a test of cognitive performance and self-esteem levels. Participants are also divided into those with high- or low-coping skills. The data are shown after question 5 (ignore the last column for now). Perform and interpret a MANOVA examining the effects of stress level and coping skills on both cogni-tive performance and self-esteem level.

5. Coping skills may be correlated with immune response. Include immune response levels (listed below) in the MANOVA performed for Question 4. What do these results mean? In what way are they different than the results in Question 4? Why?

Stress Level Coping Skills Cognitive Performance Self-Esteem Immune Response High High 6 19 21

Low High 5 18 21

High High 5 14 22

High Low 3 8 15

Low High 7 20 22

High Low 4 8 17

High High 6 15 28

High Low 5 7 19

Low Low 5 20 16

Low Low 5 17 18 6. You want to examine the effect of sleep deprivation on state self-esteem and state self-efficacy. You deprive half of your participants of sleep, and measure all of your participants’ self-esteem and self-efficacy. Data are presented below. Perform a MANOVA and describe your results. Are they significant? Describe your results. How large is this (or are these) effect(s)? Does it appear that sleep deprivation causes a change in self-esteem and self-efficacy?

Sleep Depri-vation

State Self-Esteem

State Self-Efficacy

Low 29 37

Low 31 30


Sleep Depri-vation

State Self-Esteem

State Self-Efficacy

Low 24 35

Low 39 35

Low 30 36

High 12 34

High 15 31

High 18 27

High 23 35

High 22 30


23-1

There is a significant effect of whether or not students did the extra credit project and their previous GPA’s/class points (F(2,102) = 5.69, p = .005, η2 = .10).

One-way ANOVA suggest that this effect seems to primarily be related to the total class points (F(1,103) = 9.99, p = .002, η2 = .09) rather than the previous GPA (F(1,103) = .093, p > .05, η2 = .00).

Students who completed the extra credit project had more points (M = 109.36, SD = 11.36) than those who did not complete the extra credit project (M = 98.24, SD = 15.41).

Multivariate Testsc

.971 1733.479b 2.000 102.000 .000 .971 3466.959 1.000

.029 1733.479b 2.000 102.000 .000 .971 3466.959 1.00033.990 1733.479b 2.000 102.000 .000 .971 3466.959 1.00033.990 1733.479b 2.000 102.000 .000 .971 3466.959 1.000

.100 5.686b 2.000 102.000 .005 .100 11.372 .854

.900 5.686b 2.000 102.000 .005 .100 11.372 .854

.111 5.686b 2.000 102.000 .005 .100 11.372 .854

.111 5.686b 2.000 102.000 .005 .100 11.372 .854

Pillai's TraceWilks' LambdaHotelling's TraceRoy's Largest RootPillai's TraceWilks' LambdaHotelling's TraceRoy's Largest Root

EffectIntercept

EXTRCRED

Value F Hypothesis df Error df Sig.Partial EtaSquared

Noncent.Parameter

ObservedPowera


Exact statisticb.

Design: Intercept+EXTRCREDc.


.055b 1 .055 .093 .761 .001 .093 .0612151.443c 1 2151.443 9.985 .002 .088 9.985 .879

543.476 1 543.476 923.452 .000 .900 923.452 1.000749523.786 1 749523.786 3478.731 .000 .971 3478.731 1.000

.055 1 .055 .093 .761 .001 .093 .0612151.443 1 2151.443 9.985 .002 .088 9.985 .879

60.618 103 .58922192.272 103 215.459

871.488 1051086378.000 105

60.673 10424343.714 104

Dependent VariableGPATOTALGPATOTALGPATOTALGPATOTALGPATOTALGPATOTAL

SourceCorrected Model

Intercept

EXTRCRED

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

Partial EtaSquared

Noncent.Parameter

ObservedPowera


R Squared = .001 (Adjusted R Squared = -.009)b.

R Squared = .088 (Adjusted R Squared = .080)c.


2.7671 .78466 832.8232 .69460 222.7789 .76380 105

98.24 15.414 83109.36 11.358 22100.57 15.299 105

EXTRCREDNoYesTotalNoYesTotal

GPA

TOTAL



23-2 • There is not a significant main effect of lower/upper division status on total class points and

previous gpa (F(2, 98) = 1.14, p = .323, η2 = .02). • There is not a significant main effect of class section on total class points and previous GPA

(F(4, 198) = 1.98, p = .10, η2 = .04). • There is a significant interaction between class section and lower/upper division status, on

total class points and previous GPA (F(4, 198) = 4.23, p = .003, η2 = .08). • One-way ANOVA suggest that this interaction takes place primarily in the total class points

(F(2, 99) = 4.60, p = .012, η2 = .09), though the interaction of lower/upper division status and class section on GPA was only somewhat weaker (F(2, 99) = 3.00, p = .055, η2 = .06).

• An examination of means suggests that lower division students had more total points than upper division students in sections 1 (M = 109.86, SD = 9.51 vs. M = 103.81, SD = 17.44) and 3 (M = 107.50, SD = 9.47 vs. M = 95.93, SD = 17.64), but upper division students had more to-tal points (M = 103.18, SD = 9.44) than lower division students (M = 90.09, SD = 13.13) in section 2. Lower division students had higher GPA’s than upper division students is sec-tions 2 (M = 2.84, SD = .99 vs. M = 2.67, SD = .68) and 3 (M = 3.53, SD = .50 vs. M = 2.57, SD = .77), but lower GPA’s (M = 2.72, SD = .99) than upper division students (M = 3.00, SD = .71) in section 1.

23-4 • MANOVA suggests that there is a main effect of stress on cognitive performance and self-

esteem (F(2, 5) = 13.70, p = .009, η2 = .85). One-way ANOVA suggest that this effect is pri-marily centered on the relation between stress and self-esteem (F(1,6) = 32.55, p = .001, η2 = .84) rather than stress and cognitive performance (F(1,6) = 1.37, p > .05, η2 = .19). Those in the low-stress condition had higher self-esteem (M = 18.75, SD = 1.50) than those in the high-stress condition (M = 11.83, SD = 4.88).

• MANOVA also revealed a significant main effect of coping on cognitive performance and self-esteem (F(2,5) = 6.24, p = .044, η2 = .71). One-way ANOVA suggest that this effect is clearly present in the relation between coping and self-esteem (F(1,6) = 13.27, p = .011, η2 = .70), though the relation between coping and cognitive performance was marginally significant as well (F(1,6) = 5.49, p = .058, η2 = .48). Those with high coping skills had higher self-esteem (M = 17.20, SD = 2.59) than those with low coping skills (M = 12.00, SD = 6.04). Those high coping skills may have also had higher cognitive performance (M = 5.80, SD = .84) than those with low coping skills (M = 4.40, SD = .89).

• The interaction effect between coping and stress levels was not significant (F(2,5) = 4.42, p = .079, η2 = .64).


23-6

Multivariate Testsa

Effect Value F

Hypothesis

df

Error

df Sig.

Partial Eta

Squared

Noncent.

Parameter

Observed

Powerc

Intercept Pillai's Trace .995 676.599b 2.000 7.000 .000 .995 1353.198 1.000

Wilks' Lambda .005 676.599b 2.000 7.000 .000 .995 1353.198 1.000

Hotelling's

Trace

193.314 676.599b 2.000 7.000 .000 .995 1353.198 1.000

Roy's Largest

Root

193.314 676.599b 2.000 7.000 .000 .995 1353.198 1.000

SleepDeprivation Pillai's Trace .709 8.530b 2.000 7.000 .013 .709 17.060 .843

Wilks' Lambda .291 8.530b 2.000 7.000 .013 .709 17.060 .843

Hotelling's

Trace

2.437 8.530b 2.000 7.000 .013 .709 17.060 .843

Roy's Largest

Root

2.437 8.530b 2.000 7.000 .013 .709 17.060 .843

a. Design: Intercept + SleepDeprivation

b. Exact statistic

c. Computed using alpha = .05

A MANOVA revealed that sleep deprivation condition did affect self-esteem and self-efficacy (F(2, 7) = 8.53, p = .013, η2 = .71).



Source

Dependent

Variable

Type III

Sum of

Squares df

Mean

Square F Sig.

Partial Eta

Squared

Noncent.

Parameter

Observed

Powerc

Corrected Model State Self-

Esteem

396.900a 1 396.900 15.626 .004 .661 15.626 .932

State Self-

Efficacy

25.600b 1 25.600 2.909 .126 .267 2.909 .324

Intercept State Self-

Esteem

5904.900 1 5904.900 232.476 .000 .967 232.476 1.000

State Self-

Efficacy

10890.000 1 10890.000 1237.500 .000 .994 1237.500 1.000

SleepDeprivation State Self-

Esteem

396.900 1 396.900 15.626 .004 .661 15.626 .932

State Self-

Efficacy

25.600 1 25.600 2.909 .126 .267 2.909 .324

Error State Self-

Esteem

203.200 8 25.400

State Self-

Efficacy

70.400 8 8.800

Total State Self-

Esteem

6505.000 10

State Self-

Efficacy

10986.000 10

Corrected Total State Self-

Esteem

600.100 9

State Self-

Efficacy

96.000 9

a. R Squared = .661 (Adjusted R Squared = .619)

b. R Squared = .267 (Adjusted R Squared = .175)

c. Computed using alpha = .05

Univariate ANOVA revealed that this effect was fairly large and significant for state self-esteem (F(1, 8) = 15.62, p = .004, η2 = .66), but moderately small and not significant for state self-efficacy (F(1, 8) = 2.91, p = .126, η2 = .27).


Descriptive Statistics Sleep Deprivation Mean Std. Deviation N

State Self-Esteem Low 30.60 5.413 5

High 18.00 4.637 5

Total 24.30 8.166 10

State Self-Efficacy Low 34.60 2.702 5

High 31.40 3.209 5

Total 33.00 3.266 10

Participants with high sleep deprivation exhibited lower levels of state self-esteem (M = 18.00, SD = 4.64) than people with low sleep deprivation (M = 30.60, SD = 5.41).


Chapter 24: Repeated-Measures MANOVA 1. Imagine that in the grades.sav file, the five quiz scores are actually the same quiz taken under

different circumstances. Perform repeated-measures ANOVA on the five quiz scores. What do these results mean?

2. To the analysis in exercise 1, add whether or not students completed the extra credit project (ex-trcred) as a between-subjects variable. What do these results mean?

3. A researcher puts participants in a highly stressful situation (say, performing repeated-measures MANCOVA) and measures their cognitive performance. He then puts them in a low-stress situation (say, lying on the beach on a pleasant day). Participant scores on the test of cog-nitive performance are reported below. Perform and interpret a within-subjects ANOVA on these data.

Case Number: 1 2 3 4 5 5 6 7 8 10 High Stress: 76 89 86 85 62 63 85 115 87 85 Low Stress: 91 92 127 92 75 56 82 150 118 114

4. The researcher also collects data from the same participants on their coping ability. They scored (in case number order) 25, 9, 59, 16, 23, 10, 6, 43, 44, and 34. Perform and interpret a within-subjects ANCOVA on these data.

5. The researcher just discovered some more data…in this case, physical dexterity performance in the high-stress and low-stress situations (listed below, in the same case number order as in the previous two exercises). Perform and interpret a 2 (stress level: high, low) by 2 (kind of perfor-mance: cognitive, dexterity) ANCOVA on these data.

Physical dexterity values:

Case Number: 1 2 3 4 5 5 6 7 8 10 High Stress: 91 109 94 99 73 76 94 136 109 94 Low Stress: 79 68 135 103 79 46 77 173 111 109

6. You want to examine the effects of sleep deprivation on state self-efficacy. One week you de-prive your participants of sleep, add another week you do not deprive them of sleep. Each week, you measure their self-efficacy. Data are presented below. Perform an ANOVA and de-scribe your results. How large is this effect?

Sleep Deprived Enough Sleep

13 20

22 33

26 34

20 22

19 34


Sleep Deprived Enough Sleep

20 35

16 22

23 34

20 27

26 38


24-1

These results suggest that there is a significant difference between the five conditions under which the quiz was taken (F(4,101) = 4.54, p = .002, η2 = .15). We can examine the means to determine what that pattern of quiz scores looks like.

24-2 When the condition in which the quiz was taken is examined at the same time that extra credit partici-pation is examined, there is no difference between the conditions on their own (F(4, 412) = .51, p > .05, η2 = .01). There is, however, an interaction effect between the quiz condition and extra credit participa-tion (F(4, 412) = 7.60, p < .001, η2 = .07).

An examination of the means suggests that doing the extra credit helped more for the quiz in condi-tions 1 and 4 (or, not doing the extra credit hurt more in conditions 1 and 4) than in the other condi-tions, with the extra credit affecting the quiz score least in conditions 2 and 5.

There was also a significant main effect of doing the extra credit (F(1, 103) = 10.16, p = .002, η2 = .09) such that people who did the extra credit assignment had higher scores overall (M = 8.86, SE = .37) that those who didn’t do the extra credit assignment (M = 7.54, SE = .19).


7.47 2.481 1057.98 1.623 1057.98 2.308 1057.80 2.280 1057.87 1.765 105

QUIZ1QUIZ2QUIZ3QUIZ4QUIZ5


Multivariate Testsc

.152 4.539b 4.000 101.000 .002 .152 18.156 .934

.848 4.539b 4.000 101.000 .002 .152 18.156 .934

.180 4.539b 4.000 101.000 .002 .152 18.156 .934

.180 4.539b 4.000 101.000 .002 .152 18.156 .934

Pillai's TraceWilks' LambdaHotelling's TraceRoy's Largest Root

EffectCONDITIO

Value F Hypothesis df Error df Sig.Partial EtaSquared

Noncent.Parameter

ObservedPowera


Exact statisticb.

Design: Intercept Within Subjects Design: CONDITIO

c.


24-4 There is a significant difference in cognitive performance between individuals in the high stress (M = 83.30, SD = 14.86) and low stress (M = 99.70, SD = 27.57) conditions, F(1,8) = 10.50, p = .012, η2 = .57.

There is also a significant interaction between stress and coping skills in their effect on cognitive per-formance, F(1,8) = 128.28, p < .001, η2 = .94. Note that to interpret this interaction, we would need to examine scatterplots and/or regressions for the relation between coping and cognitive performance for the high and low stress conditions. An example of this graph is shown here:

Linear Regression

10.00 20.00 30.00 40.00 50.00 60.00

coping

60.00

70.00

80.00

90.00

100.00

110.00

high

st

A

A

AA

AA

A

A

AA

highst = 74.15 + 0.34 * copingR-Square = 0.16


There is also a significant relationship between coping and cognitive performance overall (F(1,8) = 7.26, p = .027, η2 = .48). From the graphs above, it is clear that as coping skills increase, so does performance on the cognitive task.

Linear Regression

10.00 20.00 30.00 40.00 50.00 60.00

coping

60.00

80.00

100.00

120.00

140.00

low

st

AA

A

A

A

A

A

A

AA

lowst = 65.81 + 1.26 * copingR-Square = 0.65


24-6

Tests of Within-Subjects Effects Measure: MEASURE_1

Source

Type III

Sum of

Squares df

Mean

Square F Sig.

Partial Eta

Squared

Noncent.

Parameter

Observed

Powera

SleepCondition Sphericity As-

sumed

441.800 1 441.800 51.505 .000 .851 51.505 1.000

Greenhouse-

Geisser

441.800 1.000 441.800 51.505 .000 .851 51.505 1.000

Huynh-Feldt 441.800 1.000 441.800 51.505 .000 .851 51.505 1.000

Lower-bound 441.800 1.000 441.800 51.505 .000 .851 51.505 1.000

Error(SleepCondition) Sphericity As-

sumed

77.200 9 8.578

Greenhouse-

Geisser

77.200 9.000 8.578

Huynh-Feldt 77.200 9.000 8.578 Lower-bound 77.200 9.000 8.578

a. Computed using alpha = .05

Sleep condition does strongly affect the level of state self-efficacy (F(1, 9) = 51.51, p < .001, η2 = .85).

Descriptive Statistics Mean Std. Deviation N

Sleep Deprived 20.5000 4.06202 10

Enough Sleep 29.9000 6.52261 10

People had higher levels of state self-efficacy when they had enough sleep (M = 29.90, SD = 6.52) than when they were sleep deprived (M = 20.50, SD = 4.06).

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