The SPSS 16 for Windows icon should be on the Start menu. If you are using a computer in a lab, it is common for the icon to be placed in a folder. If you customize your computer, all you have to do to start SPSS is to point to the SPSS 16 icon on the desktop and double click. Then wait while SPSS loads.

Log in to SPSS There are two ways to launch the SPSS program. One is to simply click on the SPSS icon shown in red letters on your desktop. If you cannot find the icon, you can click Start on the bottom of your screen, then Program Files, and then SPSS. Or if you are not sure whether the computer you are using has SPSS, click Start, then Find, then Files or Folders, then type SPSS. When the SPSS window launches, a dialogue box will pop up as shown below. You have several choices; you can either start a tutorial, type in new data, or open an existing file

Basics steps 1-Data entry 2-Define Variables 3-Test for normality 4-statistical analysis 5-significance 6-chart builder 7-interpretation

Input Data If you want to start from scratch and enter data manually in SPSS, select the Type in Data option from the Open dialogue box. A blank window with a spreadsheet appears. You can click on any cell and enter numbers. If you want to enter characters, you need to define the variables as a string first. It is recommended that you define the variables first even if they contain numbers. Note there are two tabson the bottom-left corner of the SPSS window. One is the data spreadsheet and the other is the sheet where users define and annotate variables. To open a file, you can click File, then Open, then Data (File/Open/Data). A dialogue box should appear. You need to do two things to open your file. First, you needto locate the directory of your file. In this example, it is in C:/Program Files/SPSS. Then choose the correct file type, Cars.savthen click Open. You should have a window filled with data.

1.) Creating a data file. Open SPSS: --> Start, Programs, SPSS. The initial window (center of the screen) will be asking you if you want to open an existing file; close that for now by clicking the "Cancel" button.

What you will be looking at is the Data window; one of three windows generally used when working with SPSS. Data View is used to input and access data. The Variable View is used to specify the details of each variable in the data file.

Name is used to type a short or abbreviated name of the variable; this will appear as the column name when in Data View. Type allows you to specify the type of variable this is ((e.g.scale, nominal and ordinal Width refers to the column width this variable will have in.the Data View

Decimals refers to how many places to the right of the decimal you would like displayed in Data View. Label is used to type a description of this variable (i.e. non- abbreviated). The Label will appear in Data View if one holds his or her cursor over the Name at the top of the column. Values are used to assign names to each value of the variable (i.e. what will each number refer to). Missing allows the user to specify how missing values are coded for recognition by SPSS. Columns allows the user to specify more than one column (in Data View) for this variable. Alignment allows the user to specify the left, center, or right alignment of data within the column of this variable. Measurement allows the user to specify the type of variable; here SPSS uses Nominal, Ordinal, and Scale (which refers to both Interval and Ratio). Role can also be used to specify the type of variable (input, target, both, none, partition, split).

An example for creating and setting up a data file. 1. Click on the Variable View tab at the bottom of the spreadsheet. 2. Click on the first row under Name. 3. Type the word ID (this will stand for the Identification number of each participant). 4. Press 5. Click on the cell under the Decimals column and type a zero (0). 6. Click on the cell under the Label column. 7. Type Participant Identification 8. Click on cell below the Measure column and select Nominal. 9. Click on the Name cell of the next variable. 10. Type IV (this will stand for Independent Variable [or condition]). 11. Press 12. Click on the cell under the Decimals column and type a zero (0). 13. Click on the cell under the Label column 14. Type Condition 15. Click on the Values cell.

16. You will have to click the definition button () in the cell. A new window will open. 17. Type 1 in the Value box, and then click on the Value Label box. 18. Type Control and click Add. 19. Repeat steps 17 18 using the value 2 and the value label Experimental. 20. Click okay. 21. Click on the cell under Measure, then select Nominal. 22. Click on the Name cell of the next variable. 23. Type DV (this will stand for Dependent Variable). 24. Click on the cell under the Decimals column and type a zero (0). 25. Click on the cell under the label column. 26. Type Number Correct.

Using the Data View tab will open the data spreadsheet. It is time to enter the data. The variable names that were typed under the Name column in the Variable View should be at the top of the first three columns. In the Data View, each row represents data for one participant. Data should be entered under each variable for each participant. To enter data simply position the cursor in the appropriate cell and type the number. Pressing the enter key will move the highlighted position down one row. Pressing the tab key after entering a value will move the position over one column to the right. So, the user can either enter all the values for one variable at a time by using enter or all the variables for one participant can be entered by using tab.

Now enter the following data for 12 participants with the first 6 in the control condition and the second 6 in the experimental condition. Their number correct (from the top): 10, 8, 14, 12, 11, 13, 22, 23, 22, 19, 20, 24. Notice that when you hold the cursor over the column headings, the Label for that column is displayed.

Also notice that when you click on the Value Labels button (shown below), the Value Labels (names) are displayed instead of the Values (numbers).

An icon next to each variable provides information about data type and level of measurement.

Testing for Normality Click Analyze > Descriptive Statistics > Explore... on the top menu as shown below:

You will be presented with the following screen:

Transfer the variable that needs to be tested for normality into the Dependent List: box by either drag-and- dropping or using the button :Click thebutton. You will be presented with the following screen

Leave the above options unchanged and click thebutton

Click the button. Change the options so that you are presented with the following screen

Click the button . Click thebutton. Output Shapiro-Wilk Test of Normality The above table presents the results from two well-known tests of normality, namely the Kolmogorov-Smirnov Test and the Shapiro- Wilk Test. The Shapiro-Wilk Test is more appropriate for small sample sizes (< 50 samples), but can also handle sample sizes as large as 2000. For this reason, we will use the Shapiro-Wilk test as our numerical means of assessing normality.

We can see from the above table that for the "Beginner", "Intermediate" and "Advanced" Course Group the dependent variable, "Time", was normally distributed. How do we know this? If the Sig. value of the Shapiro-Wilk Test is greater than 0.05, the data is normal. If it is below 0.05, the data significantly deviate from a normal distribution.

Getting descriptive statistics in SPSS. go to Analyze, Descriptive Statistics, and then Descriptives.

Now you should have a smaller window open, highlight/select "Time to Accelerate from 0 to 60 (sec) [accel]" and use the arrow to put it into the variables box.

Next, click on "Options..." and select the descriptive statistics you want (typically mean, standard deviation, variance, range, standard error (S.E.) of the mean, minimum and maximum, as well as kurtosis and skewness). Then click "Continue".

Method 2: go to Analyze, Descriptive Statistics, and then Frequencies...

Now you should have a smaller window open, highlight/select ""Time to Accelerate from 0 to 60 (sec) [accel]" and use the arrow to put it into the variables box.

Next, click on "Statistics..." and select all the statistics specified earlier, as well as quartiles; then click "Continue".

Next, click on "Charts..." and select Histograms and Show normal curve on histogram. Then click "Continue" and then click "OK". You should now see some output similar to that below. You'll notice the output table containing all the descriptive statistics is smaller and easier to read than the one provided by the Descriptive Statistics function above.

You should now see some output similar to that below. You'll notice the output table containing all the descriptive statistics is smaller and easier to read than the one provided by the Descriptive Statistics function above.

There are four benefits to using the Frequencies function for gathering descriptive statistics. First, you can get more descriptive statistics (quartiles), second; you can get a graphical display of the variable (histogram for continuous variables and bar graph for categorical variables). Third, you get a frequencies table; and fourth, the descriptive statistics table is smaller and easier to read with frequencies function.

Method 3: The Explore Function for getting descriptive statistics by group With the Explore Example data file open in the Data window, go to Analyze, Descriptive Statistics, and then Explore...

Next, pick your dependent variable, in this example we'll use the variable "total score on blame scale [bt]". Highlight and move it to the Dependent List: box. Then, pick your independent variable, in this example we'll use the grouping variable "GENDER [sex]". Highlight it and move it to the Factor List: box. Then click on the Statistics... button.

Now we can specify what we want to get. Check Descriptives, M-estimators, Outliers, and Percentiles. Then click the Continue button. Next, click on the Plots button and select Histogram and Normality plots with tests. Then click the Continue button. Then click the OK button.

You should see some output similar to that displayed below.

Parametric tests t-tests in SPSS. The t-tests are used to determine if there exists a significant difference between means. There are traditionally, three types of t-tests. The seldom used one sample t-test, the dependent samples t-test, and the independent samples t- test (1). One sample t-test is used to determine if the sample mean is different from some constant value; typically assumed to be a population mean. First, we'll test whether or not our sample mean (in this case age) is significantly different from zero. Begin by importing the data, then click on Analyze, Compare Means, One- Sample T test...

Next, highlight the Age variable and use the arrow to move it into the Test Variable(s): box. Next, click the OK button to complete the t-test.

The output provides two tables. The first, offers descriptive statistics for the variable we tested (Age), which includes number of cases/observations, mean, standard deviation, and standard error. The second table provides the actual t-test output--where we see that our sample's age (M = 21.04, SD = 1.85) was significantly different from zero, t(53) = 83.440, p < .001. As you might imagine, this is not terribly useful information. A more informative test might include testing whether or not our sample is significantly different from a specified value. SPSS allows us to specify a value in the One Sample T Test dialog.

Again, click on Analyze, Compare Means, One-Sample T test...

Notice the previous run is still specified (i.e. the Age variable is already in the Test Variable(s): box. Next, we want to specify a value, say 20 which might represent the mean of all undergraduate college students. We simply type the value in the Test Value: box. Then click the OK button to complete the t test.

Here, we see that our sample's age (M = 21.04, SD = 1.85) was significantly different from 20, t(53) = 4.113, p < .001.

(2). Dependent samples t-test is used to determine if the difference between two related sample means is different from zero. It is known by many names: dependent samples t test, paired samples t test. Example A new fitness program is devised for obese people. Each participant's weight was measured before and after the program to see if the fitness program is effective in reducing their weights. In this example, our null hypothesis is that the program is not effective, i.e., there is no difference between the weight measured before and after the program. The alternative hypothesis is that the program is effective and the weight measured after is less than the weight measured before the program. In the data, the first column is the weight measured before the program and the second column is the weight after.

Select "Analyze -> Compare Means -> Paired-Samples T Test". A new window pops out. Drag the variable "Before" and "After" from the list on the left to the pair 1 variable 1 and variable 2 respectively, as shown below. Then click "OK".

The results now pop out in the "Output" window.

We can now interpret the result. From A, since the p-value is 0.472, we reject the alternative hypothesis and conclude that the fitness program is not effective at 5% significant level.

Independent samples t-test is used to test whether or not two independent sample means are significantly different from one another. It is the most commonly used of the t tests. For example, suppose one is interested in learning whether differences exist between females and males in mathematics scores. Data for such a comparison are presented below

The first column, labeled Math_Scores contains individual student mathematics scores. The second column, labeled Sex, identifies whether the student is male or female. As noted in Figure 1, females are coded as 1 and males are coded as 2. One may be curious why numbers are used to represent sex when letters such as F and M should suffice. Often statistical programs, such as SPSS, are programmed to work with numbers rather than letters or other symbols. That is the case for the independent samples t-test command in SPSS.

To help users more easily recognize which students are females and males, one may opt to provide Value Labels for the Sex variable. Figure 1 above shows the "Data View" of the SPSS spreadsheet. Note the tab at the bottom of the spreadsheet labeled "Data View." Next to that tab is a second tab labeled "Variable View." Click on "Variable View" to access the variable characteristics section of the spreadsheet.

the label "Female" is added for a Sex value = 1, and the label "Male" will be added for those students with a Sex value = 2. One much click on the "Add" button to complete adding both value labels for sex.

To access the Independent Samples t-test select "Analyze" select "Compare Means" select "Independent Samples t-test"

The Independent Samples t-test pop-up window will appear. Select the dependent variable (the quantitative variable, mathematics scores in this example) and move it to the "Test Variable(s)" box, and move the grouping variable (the categorical independent variable, sex in this example) to the "Grouping Variable" box.

Now the groups must be defined so SPSS correctly compares the two groups of interest (if more than two groups are present in the data). In the current example there are only two groups; to define these click on "Define Groups" button, identify which group will serve as Group 1 (in this case Females--coded 1-- were selected), then identify which group will serve as Group 2 (males coded 2). Click "Continue" then click "OK" to run the t-test and obtain results.

Results Interesting to note is the Levene's Test for Equality of Variances. This tests the assumption that our two groups have approximately equal variances; sometimes called the homogeneity of variance assumption In the current example, the Levene's test indicates we do not have significantly different variances between our two groups, which is what we want to see as this supports the assumption.

Analysis of Variance (ANOVA) in SPSS. The ANOVA family of analysis are used for testing whether or not a significant difference exists between more than two groups. There are many forms of ANOVA which allows it to be used in a variety of situations. The simplest is the oneway ANOVA which is used for testing multiple groups of one independent variable's effect on one continuous or nearly continuous dependent variable. The oneway name implies one independent variable.

dependent variable should be measured at the interval or ratio level (i.e., they are continuous). Examples of variables that meet this criterion include revision time (measured in(hours independent variable should consist of two or more categorical, independent groups

Example A manager wants to raise the productivity at his company by increasing the speed at which his employees can use a particular spreadsheet program. As he does not have the skills in- house, he employs an external agency which provides training in this spreadsheet program. They offer 3 courses: a beginner, intermediate and advanced course. He is unsure which course is needed for the type of work they do at his company, so he sends 10 employees on the beginner course, 10 on the intermediate and 10 on the advanced course. When they all return from the training, he gives them a problem to solve using the spreadsheet program, and times how long it takes them to complete the problem. He then compares the three courses (beginner, intermediate, advanced) to see if there are any differences in the average time it took to complete the problem. In SPSS, we separated the groups for analysis by creating a grouping variable called Course (i.e., the independent variable), and gave the beginners course a value of "1", the intermediate course a value of "2" and the advanced course a value of "3". Time to complete the set problem was entered under the variable name Time (i.e., the dependent variable).

Click Analyze > Compare Means > One-Way ANOVA... on the top menu as shown below.

You will be presented with the following screen: Transfer the dependent variable (Time( into the Dependent List: box and the independent variable (Course( into the Factor: box using the appropriate buttons (or drag-and-drop the variables into the boxes(, as indicted in the diagram below

., Click thebutton. Tick the Tukey checkbox as shown below

Click the button. Click the button. Tick the Descriptive checkbox in the Statisticsarea, as shown below:

Click the button. Click the button. Descriptives Table The descriptives table (see below) provides some very useful descriptive statistics, including the mean, standard deviation and 95% confidence intervals for the dependent variable (Time) for each separate group (Beginners, Intermediate and Advanced), as well as when all groups are combined (Total).

This is the table that shows the output of the ANOVA analysis and whether we have a statistically significant difference between our group means. We can see that the significance level is 0.021 (p = .021), which is below 0.05. and, therefore, there is a statistically significant difference in the mean length of time to complete the spreadsheet problem between the different courses taken. This is great to know, but we do not know which of the specific groups differed. Luckily, we can find this out in the Multiple Comparisons Table which contains the results of post-hoc tests.

Multiple Comparisons Table From the results so far, we know that there are significant differences between the groups as a whole. The table below, Multiple Comparisons, shows which groups differed from each other. The Tukey post-hoc test is generally the preferred test for conducting post-hoc tests on a one-way ANOVA, but there are many others. We can see from the table below that there is a significant difference in time to complete the problem between the group that took the beginner course and the intermediate course (p = 0.046), as well as between the beginner course and advanced course (p = 0.034). However, there were no differences between the groups that took the intermediate and advanced course (p = 0.989).

Reporting the output of the one-way ANOVA There was a statistically significant difference between groups as determined by one-way ANOVA (F(2,27) = 4.467, p = .021). A Tukey post-hoc test revealed that the time to complete the problem was statistically significantly lower after taking the intermediate (23.6 3.3 min, p = .046) and advanced (23.4 3.2 min, p = .034) course compared to the beginners course (27.2 3.0 min). There were no statistically significant differences between the intermediate and advanced groups (p = .989).

Factorial ANOVA The Factorial ANOVA is an extension of the Oneway situation where the design is composed of more than one independent variable, each with two or more groups (sometimes called multi-way ANOVA). The major benefit of factorial ANOVA is the ability to investigate interactions among the independent variables. The Factorial ANOVA is still considered a univariate analysis (as opposed to a multivariate analysis) because, it deals with only one dependent variable (where the multivariate ANOVA deals with multiple dependent variables).

Two-way ANOVA the two-way ANOVA is used when there is more than one independent variable and multiple observations for each independent variable. Example A researcher was interested in whether an individual's interest in politics was influenced by their level of education and gender. They recruited a random sample of participants to their study and asked them about their interest in politics, which they scored from 0 to 100, with higher scores indicating a greater interest in politics. The researcher then divided the participants by gender (Male/Female) and then again by level of education (School/College/University). Therefore, the dependent variable was "interest in politics", and the two independent variables were "gender" and "education".

In SPSS, we separated the individuals into their appropriate groups by using two columns representing the two independent variables, and labelled them Gender and Edu_Level. For Gender, we coded "males" as 1 and "females" as 2, and for Edu_Level, we coded "school" as 1, "college" as 2 and "university" as 3. The participants' interest in politics the dependent variable was entered under the variable name, Int_Politics. The setup for this example can be seen below:

Click Analyze > General Linear Model > Univariate... on the top menu,

You will be presented with the Univariate dialogue box

Transfer the dependent variable, Int_Politics, into the Dependent Variable: box, and transfer both independent variables, Gender and Edu_Level, into the Fixed Factor(s): box. You can do this by drag-and- dropping the variables into the respective boxes or by using the button. If you are using older versions of SPSS you will need to use the latter method. You will end up with a screen similar to that shown below:

Click on the button. You will be presented with the Univariate: Profile Plots dialogue box

Transfer the independent variable, Edu_Level, from the Factors: box into the Horizontal Axis: box, and transfer the other independent variable, Gender, into the Separate Lines: box. You will be presented with the following screen:

Click the button. You will see that "Edu_Level*Gender" has been added to the Plots: box Click the button. This will return you to the Univariate xob eugolaid.

Click the button. You will be presented with the Univariate: Post Hoc Multiple Comparisons for Observed Means.

Transfer Edu_Level from the Factor(s): box to the Post Hoc Tests for: box. This will make the Equal Variances Assumed area become active (lose the "grey sheen") and present you with some choices for which post hoc test to use. For this example, we are going to select Tukey, which is a good, all-round post hoc test. Note: You only need to transfer independent variables that have more than two groups into the Post Hoc Tests for: box. This is why we do not transfer Gender.

Click the button to return to the Univariatexob eugolaid Click the button. This will present you with the Univariate: Options

Transfer Gender, Edu_Level and Gender*Edu_Level from the Factor(s) and Factor Interactions: box into the Display Means for: box. In the Display area, tick the Descriptive Statistics option. Click thebutton to return to the Univariatexob eugolaid

Click the button to generate the output You can find appropriate descriptive statistics for when you report the results of your two- way ANOVA in the aptly named "Descriptive Statistics" table, as shown below: This table is very useful because it provides the mean and standard deviation for each combination of the groups of the independent variables (what is sometimes referred to as each "cell" of the design). In addition, the table provides "Total" rows, which allows means and standard deviations for groups only split by one independent variable, or none at all, to be known. This might be more useful if you do not have a statistically significant interaction.

The actual result of the two-way ANOVA namely, whether either of the two independent variables or their interaction are statistically significant is shown in the Tests of Between-Subjects Effects table The particular rows we are interested in are the "Gender", "Edu_Level" and "Gender*Edu_Level" rows

These rows inform us whether our independent variables (the "Gender" and "Edu_Level" rows) and their interaction (the "Gender*Edu_Level" row) have a statistically significant effect on the dependent variable We can see from the above table that there was no statistically significant difference in mean interest in politics between males and females (p = .207), but there were statistically significant differences between educational levels (p < .0005).

When you have a statistically significant interaction, reporting the main effects If you do not have a statistically significant interaction, you might interpret the Tukey post hoc test results for the different levels of education, which can be found in the Multiple Comparisons table

You can see from the above table that there is some repetition of the results, but regardless of which row we choose to read from, we are interested in the differences between (1) School and College, (2) School and University, and (3) College and University. From the results, we can see that there is a statistically significant difference between all three different educational levels (p < .0005). Reporting the results of a two-way ANOVA A two-way ANOVA was conducted that examined the effect of gender and education level on interest in politics. There was a statistically significant interaction between the effects of gender and education level on interest in politics, F (2, 54) = 4.643, p = .014. From post Hoc males were significantly more interested in politics than females when educated to university level (p = .002), but there were no differences between gender when educated to school (p = .465) or college level (p = .793).

Multivariate analysis of variance It is used when there are two or more dependent variables. Analyze General Linear Model Multivariate

After clicking on Multivariate, the following screen will appear. You will send your dependent variables to the Dependent Variables box and your independent variable to the Fixed Factor box.

Now send the four dependent variables (i.e., Verbal 1 through Verbal 4) over one at a time to the Dependent Variables screen.

Then send over the independent variable, Reading Group Membership, to the Fixed Factor box. Then click on Options.

We will use this screen to obtain descriptive statistics of our four dependent variables for each of our three reading groups

To obtain the information just mentioned, you will need to click on: Descriptive Statistics Estimates of Effect Size Homogeneity tests

After checking the three boxes mentioned, then click on Continue

After clicking on Continue, the following screen will appear. Now click on Post Hoc so that pairwise analyses can be conducted.

Clicking on Post Hoc will then give you the screen below. Click on group and send it to the box labeled Post Hoc Tests and then click Turky bottom

Then click on OK.

Repeated-Measures ANOVA The repeated-measures or within-subjects ANOVA is used when there are multiple measures for each participant

Next well have to define the factor of study. From the table above we have 3 levels of treatment (i.e. time 1,2,3), and well call the factor TIME (instead of factor1). Click Add after giving the name and number of levels:

Now we click Define and were all set. Now on the box well need to highlight our 3 variables of interest (time1-3), and move them over to the Within Subjects Variables area by clicking on the arrow between where the variables are on the left and where theyre going on the right.

Lastly, we are going to select a few options. Click the Options button. Here check the Descriptive Statistics box and the Estimates of effect size box. Click Continue. Click OK. SPSS will produce the output

To perform the repeated-measures ANOVA in SPSS, click on Analyze, then General Linear Model, and then Repeated Measures

Corporation. In the resulting Repeated Measures dialog, you must specify the number of factors and the number of levels for each factor. In this case, the single factor is the time the algebra test was taken, and there are three levels: at the beginning of the course, immediately after the course, and six months after the course. You can accept the default label of factor1, or change it to a more descriptive one. We will use "Time" as the label for our factor, and specify that there are three levels

Non-parametric statistics Refers to comparative properties (statistics) of the data, or population, which do not include the typical parameters, of mean, variance, standard deviation, etc.

Chi-square test. Chi squrare test of association Simple chi square test

In Chi-Square goodness of fit test, sample data is divided into intervals. Then the numbers of points that fall into the interval are compared, with the expected numbers of points in each interval. The Chi-Square test of Independence is used to determine if there is a significant relationship between two nominal (categorical) variables. The frequency of one nominal variable is compared with different values of the second nominal variable.

To test if there is an association between two.nominal variables In SPSS you just indicate that one variable (the independent one) should come in the row, and the other variable (the dependent one) should come in the column of the cross table. Then you ask for row percentages and the Chi-square statistic.

Example Final year psychology students were asked about their career plans. 12 females and 26 males said they would like to work in the field of clinical psychology, while 24 females and 8 males said they preferred the area of organisational psychology. We want to investigate if there is any relationship between gender and career preference. In this example, our null hypothesis is that there is no relationship between gender and career preference. Our alternative hypothesis is that there is a relationship between gender and career preference

Two variables that are ordinal or nominal (categorical data). There are two or more groups in each variable.

Select "Analyze -> Descriptive Statistics -> Crosstab".

It does not matter which variables we select as rows and which as column. For illustration purpose, we select "Gender" as "Row(s)" and "Career_Preference" as "Column(s)".

Now click "Statistics" on the right. A new window pops out. Make sure that the "Chi-square" box at the top is checked. Click "Continue".

Click "Cells" on the right. A new window pops out. You can check the box "Observed", "Expected", "Row", "Column" and "Total" if you want to extract more information from crosstab. Click "Continue". The window will then be closed. Now click "OK" in the original window.

The results now pop out in the "Output" window. We can now interpret the result.

From A in the third table, since the p-value is 0, we can reject the null hypothesis and conclude that there is a relationship between gender and career preference at 5% significant level. From the second table, it appears that males tend to work in the area of clinical psychology and females tend to work in the field of

The second option. You create a nominal variable as usual, but also create a frequency or count variable which will contain the number of cases belonging to each category. This means that each row will not represent a different participant, but instead a different category If you use this method, you must tell SPSS that the numbers in the frequency variable are not scores for individual participants, but overall counts. To do this, go to the Data menuWeight Cases, and transfer across the variable that contains the frequencies or counts to the Frequency Variable box. Click on OK.

The Wilcoxon Sign Test in SPSS In SPSS we need to have two variables representing the before and after The Wilcoxon sign test can be found in Analyze/Nonparametric Tests/2 Related Samples

In the next dialogue box for the nonparametric two dependent samples tests we need to define the paired observations. Enter X as variable 1 of the first pair and Y as Variable 2 of the first pair

We also need to select the Test Type. The Wilcoxon Signed Rank Test is marked by default

The Wilcox sign test output contains only two tables. The first table contains all statistics that are required to calculate the Wilcoxon signed ranks tests W. These are the sample size and the sum of ranks. It also includes the mean rank, which is not necessary to calculate the W-value but helps with the interpretation of the data.

n our example we see that 20*2 observations were made for X and Y. The Wilcox Sign Test answers the question if the difference is significantly different from zero, and thus if the observed difference in mean ranks (4.5 vs. 10.65) can also be found in the general population The answer to this question is in the second table, which contains the test of significance statistics The SPSS output contains the z-value of -3.472. The test value z is approximately normally distributed for large samples that are n>10, so that p = 0.001. Thus we can reject the null hypothesis that both samples are from the same population, and we might assume that the novel teaching method caused a significant increase in literacy scores.

Mann Whitney U Test compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.

Select Analyze | Nonparametric Tests | 2 Independent Samples:

The Two-Independent-Samples Tests dialog box appears:

Select the dependent variable of interest from the list at the left by clicking on it, and then move it into the Test Variable List by clicking on the upper arrow button. Select the independent variable of interest from the list at the left by clicking on it, and then move it into the Grouping Variable box by clicking on the lower arrow button.

Next, we must define the groups of the independent variable. Click on the Define Groups button that is just below the Grouping Variable box. The Two Independent Samples: Define Groups dialog box appears: Enter the value that corresponds to one level of the independent variable in the Group 1 box and the value that corresponds to the other level of the independent variable in the Group 2 box.

Click on the Continue button in the Two Independent Samples: Define Groups dialog box. The Two-Independent Samples Test dialog box should be on top now. Make sure that the Mann-Whitney U option is selected in the Test Type frame. That is, there should be a check mark next in the box to the left of Mann-Whitney U:

Click on the Options button. The Two-Independent- Samples: Options dialog box appears: Select the Descriptive statistics option by clicking in the box to the left of Descriptives if it does not already have a check mark in it:

Click on the Continue button in the Two-Independent-Samples: Options dialog box. Click on OK in the Two-Independent-Samples Tests box to perform the Mann-Whitney U test. The SPSS output viewer will appear. It should contain three sections: The first section gives the descriptive statistics for the dependent variable and (less usefully) for the independent variable. In this example, there were 31 people (N) who responded to the PLANNER question. They gave a mean response of 2.42 (between AGREE and UNDECIDED) with a standard deviation of 1.43 (although this number may not be meaningful in this example

The second section of the output shows the number (N) of people in each condition (8 people do not intend to get a Ph.D. or Psy.D in psychology and 23 people do) and the mean rank and sum of ranks for each group (useful if you were calculating the U statistic by hand.)

In this example, the Mann-Whitney U value is 92.0. There are two p values given -- one on the row labeled Asymp. Sig (2- Tailed) and the other on the row labeled Exact Sig. [2*(1- tailed Sig.)]. Typically, we will use the Exact significance, although if the sample size is large, the asymptotic signifance value can be used to gain a little statistical power. Decide whether to reject H0. We will use the exact p value. It is a two-tailed p value, but we have a one-tailed test. So we need to divide the two-tailed p value by 2 to get the one- tailed p value: 1.000 / 2 = .500. Since the exact p value is greater than the specified level (.05), we fail to reject H0. Thus, we have insufficient evidence to conclude that people who intend to get a Ph.D. or Psy.D. in psychology are more likely to use a day planner or calendar than the people who do not intend to get a Ph.D. or Psy.D. in psychology.

"Kruskal-Wallis Test" The Kruskal-Wallis test is the nonparametric test equivalent to the one-way ANOVA, and an extension of the Mann-Whitney U test to allow the comparison of more than two independent groups.

Click Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples

There are two ways transfer your variables. You can either highlight drag-and-drop each variable into the respective boxes or you highlight the variable by using the cursor and clicking thebutton. Make sure that the Kruskal-Wallis H checkbox is ticked in the Test Type box.

Press the button and type "1" into the Minimum box and "3" into the Maximum box. This is defining the range of the values for the categories of the independent variables. In this case, there are 3 groups/categories, called Drug A, Drug B and Drug C. If there had been 4 groups, but you did not want to include the first group in the analysis, you would have entered "2" and "4" into the Minimum and Maximum boxes, respectively (assuming you ordered the groups numerically).

Click the button Click the button. Tick the Descriptive checkbox if you want descriptives and/or Quartiles if you want quartiles. You will be presented with the following if you select Descriptives .

Click the button Click thebutton we can report that there was a statistically significant difference between the different drug treatments

Friedman Test The Friedman test is the non-parametric alternative to the one- way ANOVA with repeated measures. One group that is measured on three or more different occasions Group is a random sample from the population. Your dependent variable should be measured at the ordinal or continuous level. Examples of ordinal variables include Likert scales (e.g., a 7-point scale from strongly agree through to strongly disagree),

Click Analyze > Nonparametric Tests > Legacy Dialogs > K Related Samples... on the top menu, as shown below:

You will be presented with the Tests for Several Related Samples dialogue box

Transfer the dependent variables none, classical and dance to the Test Variables: box by using the button or by dragging-and- dropping the variables into the box. You will end up with the following screen:

Make sure that Friedman is selected in the Test Type area. Click the button. You will be presented with the following Several Related Samples: Statisticsnwohs sa ,xob eugolaid woleb: Click thebutton. This will return you back to the Tests for Several Related Samplesxob eugolaid

Click the button to run the Friedman test The Descriptives Statisticsdetceles uoy fi decudorp eb lliw elbat noitpo selitrauQ eht

The Ranks table shows the mean rank for each of the related groups The Friedman test compares the mean ranks between the related groups and indicates how the groups differed, and it is included for this reason. However, you are not very likely to actually report these values in your results section, but most likely will report the median value for each related group.

The table above provides the test statistic (2) value ("Chi- square"), degrees of freedom ("df") and the significance level ("Asymp. Sig."), which is all we need to report the result of the Friedman test. From our example, we can see that there is an overall statistically significant difference between the mean ranks of the related groups.

chart builder We can also use graphs to visualize the statistical relationships between variables. For example, we want to discover if there is any relationship between miles per gallon and car weight Enter variables into the X-and Y-axis boxes by selecting the variable and clicking the arrow to the left ofthe box.

The Gallery includes many different predefined charts, which are organized by chart type Example bar chart .

Icons representing the available bar charts in the Gallery appear in the dialog box. The pictures should provide enough information to identify the specific chart type. If you need more information, you can also display a ToolTip description of the chart by pausing your cursor over an icon. Click Bar if it is not selected

Drag the icon for the simple bar chart onto the "canvas," which is the large area above the Gallery. The Chart Builder displays a preview of the chart on the canvas. Note that the data used to draw the chart are not your actual data. They are example data.

The drop zone for the x axis is required. The variable in this drop zone controls where the bars appear on the x axis Depending on the type of chart you are creating, you may also need a variable in the y axis drop zone. For example, when you want to display a summary statistic of another variable (such as mean of salary), you need a variable in the y axis drop zone. Scatterplots also require a variable in the y axis. In that case, the drop zone identifies the dependent variable.

Now drag Job satisfaction from the Variables list to the x axis drop zone.

The Element Properties window allows you to change the properties of the various chart elements.

Return to the Chart Builder dialog box and drag Household income in thousands from the Variables list to the y axis drop zone.

ou can also add titles and footnotes to the chart. Click the Titles/Footnotes tab.

The title appears on the canvas with the label T1. The bar chart reveals that respondents who are more satisfied with their jobs tend to have higher household incomes.

interpretation According to significance we remain or reject null hypothesis If the Sig. is greater than 0.05, the data is normal. If it is below 0.05, the data significantly deviate from a normal distribution.