Introduction to Experimental Research

Lawrence R. Gordon

Psychology Research Methods I

From last class…Descriptive Stats DISPLAYING DATA -- distributions, graphs,

…”pictures”Properties of distributions – symmetry, modality,

skewness

Continuing today…

SUMMARIZING DATA – measures of central tendency & variability, …”numbers”

Descriptive Statistics

Name some you know of...

What can they do for us?– Tell us more about our data -- Location– Tell us more about our data -- Spread– Help us communicate these to others!

• Highly summarized• Basis of results and tables in reports of studies

Measures of Central Tendency

Mode– the “typical” score– the peak(s) of the frequency distribution

Median– the “center” score– splits distribution into two halves (by area)

Mean– the (arithmetic) “average” of the scores– the balance point of the distribution

(“seesaw”)

Central Tendency, contd.

Pros and Cons --– Mode– Median– Mean

Relationships to distribution shapes --– Symmetric: Mode = Median = Mean– Skewed: Pos (rgt)- Mo < Md < Mn

Neg (lft)- Mn < Md < Mo

Variability

Range– Hi - Lo score– “Goes with” Mode

Interquartile range (IQR)– 75th-%ile - 25th-%ile scores– “Goes with” Median (50th-%ile score)

Standard Deviation (SD)– Sqrt of average of sqrd deviations around Mn– “Goes with” Mean [Handout for reference]

Real Data

First Hour Exam Scores

FIRST HOUR EXAM: Psyc 109, Fall 02

Number Correct out of 50

47.545.042.540.037.535.032.530.027.525.0

FIRST EXAM GRADE (of 50)

Psyc 109 9/26/02

Freq

uenc

y

70

60

50

40

30

20

10

0

Std. Dev = 4.52

Mean = 38.0

N = 233.00

234

1

37.9829

38.0000

37.00

4.51128

20.35164

24.00

24.00

48.00

35.0000

38.0000

41.0000

Valid

Missing

N

Mean

Median

Mode

Std. Deviation

Variance

Range

Minimum

Maximum

25

50

75

Percentiles

Exam I, 9/26/02

Real Data

Baseball salaries revisited

BASEBALL SALARIES 1994

SALARY94

BASEBALL SALARIES 1994

Freq

uenc

y

300

200

100

0

Std. Dev = 1390922

Mean = 1183416.7

N = 747.00

BASEBALL 1994 SALARIES --- Statistics

SALARY94747

0

1183416.68

500000.00

109000

1390921.93

1.93466E+12

1.317

.089

6191000

109000

6300000

170000.00

500000.00

2000000.00

Valid

Missing

N

Mean

Median

Mode

Std. Deviation

Variance

Skewness

Std. Error of Skewness

Range

Minimum

Maximum

25

50

75

Percentiles

Real Data

109 Questionnaire - Scales (briefly!)

COURSE QUESTIONNAIRE CFC SCALE“Concern for Future Consequences” ScaleDescriptive Statistics

Statistics

NC Scale (Range 18 - 90)187

9

62.6390

63.0000

63.00

11.6460

135.6284

-.337

.178

64.00

26.00

90.00

56.0000

63.0000

71.0000

Valid

Missing

N

Mean

Median

Mode

Std. Deviation

Variance

Skewness

Std. Error of Skewness

Range

Minimum

Maximum

25

50

75

Percentiles

CFC Scale (Range 12 - 60)

60.055.050.045.040.035.030.025.020.015.0

CFC Scale (Range 12 - 60)

Freq

uenc

y

60

50

40

30

20

10

0

Std. Dev = 7.26

Mean = 40.9

N = 174.00

Statistics

CFC Scale (Range 12 - 60)174

22

40.9339

41.0000

40.00

7.2553

52.6387

-.325

.184

43.00

17.00

60.00

37.0000

41.0000

46.0000

Valid

Missing

N

Mean

Median

Mode

Std. Deviation

Variance

Skewness

Std. Error of Skewness

Range

Minimum

Maximum

25

50

75

Percentiles

COURSE QUESTIONNAIRE: NC SCALE“Need for Cognition” Scale

Descriptive Statistics

NC Scale Scores

90.0

85.0

80.0

75.0

70.0

65.0

60.0

55.0

50.0

45.0

40.0

35.0

30.0

25.0

NC Scale (Range 18 - 90)

Freq

uenc

y

40

30

20

10

0

Std. Dev = 11.65

Mean = 62.6

N = 187.00

Statistics

NC Scale (Range 18 - 90)187

9

62.6390

63.0000

63.00

11.6460

135.6284

-.337

.178

64.00

26.00

90.00

56.0000

63.0000

71.0000

Valid

Missing

N

Mean

Median

Mode

Std. Deviation

Variance

Skewness

Std. Error of Skewness

Range

Minimum

Maximum

25

50

75

Percentiles

Real Data

My dissertation data A NOTE TO END ON: not everything

interesting in data is captured by a single statistic! We must get to know data well, from many angles, to find its message!

NOW…on to our current topic, Experimental Research...

NOW, RESUMING…

Intro to Experimental Research, A “pseudo-example”… “Time flies when you’re having fun”!

– DOES IT?

A Simple Experiment: “Time Flies”

EXAMPLE: “Time flies when you’re having fun”

Hypothesis: IF one is “having more fun”, THEN time will seem to pass more quickly

Design: • IV: 100 persons randomly assigned to two groups:

– 1: “Having more fun”

– 2: “Having less fun”

• DV: Estimate of a standard 10 minute interval

Procedure: manipulation of cartoon captions

A Simple Experiment, cont.

EXAMPLE: “Time flies when you’re having fun” (cont..)

Results– “Raw data”

– Organized by “frequency distribution”

– Graphs of data• Group “dotplots”

• Group histograms

Quickie summary of results: “More fun” group gave shorter estimates on average than “Less fun” group.

A Simple Experiment, cont.

RESULTS– How describe?

• List of scores

• A picture

• A single number or two?– LOCATION = “central tendency”

– SPREAD = “variability”

“Having Fun” Data

1 6.1 1 10.9 2 13.7 2 13.8 2 9.2 2 14.3 1 15.3 1 9.1 1 8.5 1 10.4 2 8.1 2 8 1 10.5 2 9.7 2 15.7 2 16.5 2 15.5 2 11.5 2 7.1 1 6.5 2 15 1 11.5 1 8 1 11.2 2 9.3 2 12.2 2 13.6

2 12.5 1 10.4 1 7.1 2 14.4 1 11.4 2 13.4 1 6.3 1 7.5 1 9.5 2 17.7 2 10.9 1 7.5 2 6.9 2 11.2 2 21.8 1 6.4 2 13.9 2 11 1 5.8 2 13.2 2 13 1 10.1 1 5.4 2 13 2 4.9 1 10.2 1 8.6

1 11.9 2 13.2 1 8.4 1 8.8 2 10.3 2 12.4 2 12.1 2 8.7 1 11.5 1 6.1 1 10.2 1 4.1 2 13.6 2 13.2 2 14.2 2 16.1 2 18.2 2 15.5 1 10.2 2 11.2 1 7 1 6.2 1 6.7 2 14.3 2 12.8 1 11.3 1 7.8

2 17.1 1 11.4 2 5.3 1 8.5 1 10 2 10.3 1 7.7 1 0.4 1 9.2 1 11.4 1 8.9 1 3.1 1 12.3 2 10.4 1 5.8 1 5.3 2 15.3 2 9 1 11.8

Estimate of 10 minute interval

COND: 2 'Less fun' (No Captions)10

8

6

4

2

0

Std. Dev = 3.35 Mean = 12.5N = 50.00

Estimate of 10 minute interval

COND: 1 'More fun' (Captions)10

8

6

4

2

0

Std. Dev = 2.72 Mean = 8.6N = 50.00

“HAVING FUN” DESCRIPTIVE STATISTICS: HISTOGRAMS W/ LEGENDS

“HAVING FUN” DESCRIPTIVE STATISTICS: TABLES

'More fun' (Captions)Statisticsb

Estimate of 10 minute interval50

0

8.604

8.700

10.2a

2.722

7.408

-.421

.337

14.9

.4

15.3

6.475

8.700

10.600

Valid

Missing

N

Mean

Median

Mode

Std. Deviation

Variance

Skewness

Std. Error of Skewness

Range

Minimum

Maximum

25

50

75

Percentiles

Multiple modes exist. The smallest value is showna.

Experimental Conditions = 'More fun' (Captions)b.

'Less fun' (No Captions)Statisticsa

Estimate of 10 minute interval50

0

12.484

13.000

13.2

3.353

11.240

-.017

.337

16.9

4.9

21.8

10.300

13.000

14.325

Valid

Missing

N

Mean

Median

Mode

Std. Deviation

Variance

Skewness

Std. Error of Skewness

Range

Minimum

Maximum

25

50

75

Percentiles

Experimental Conditions = 'Less fun' (No Captions)a.

A Simple Experiment, cont.

Results (cont.)– Group 1 = “More fun”

• Mean = 8.60, SD = 2.72, N = 50

– Group 2 = “Less fun”• Mean = 12.48, SD = 3.35, N = 50

– Quickie summary of results: the “More fun” group gave shorter estimates of the 10-minute interval, on average, than the “Less fun” group.

NOTE on the Mean & the SD

Most frequently used -- whenever possible Often called “location” and “scale” -- why? Examples of use with NORMAL curve (the

“bell” curve) ---– Why used frequently?– Various commonly used “standard” scales

THAT’S ALL, FOLKS!