Introduction to SPSS for the PC: Within Subject Analyses
Part 2: Within Subject Analyses
Within SPSS, analyses are generated using either menu
selections or command syntax. Below is a description of how to run
some common within subject analyses using menu selections. Following
each description is the command syntax used to generate the same analyses
along with a brief explanation of the commands (For more help on using
syntax see: Tips
for SPSS Syntax). To generate the results utilized in these examples
you will need to enter the Raw Data
set below.
I. Two-sample Correlated t-test
II. Repeated Measures ANOVA
III. Mixed Factorial ANOVA
VI. Two-sample Correlated t-test
Sample question: Do rates of smoking decrease
from pre-intervention to post-intervention? To answer this question,
you can run a two-sample correlated t-test comparing the preintervention
smoking rates to post-intervention rates.
- Select Analyze > Compare Means > Paired-Samples T test on the menu bar. This will open a window called Paired-Samples T Test.
- The pre- and post-intervention smoking rates represent the within subject variable. Highlight pre. You will see that pre now appears as Variable 1 in the Current Selection box. Now highlight post. You will see that post now appears as Variable 2 in the Current Selection box. Use the arrow button to move the selection to the Paired Variable(s) box.
- Click on OK to run the analysis.
- The first table of the printout contains descriptive statistics while the second table contains inferential statistics. Study the printout below and make sure you can identify n, M, and SD for each group, as well as t, df, and p (p is in the column labeled "Sig. (2-tailed)"). In this case, the mean number of cigarettes smoked prior to the intervention programs was significantly higher than the number of cigarettes smoked after the intervention programs, t(29) = 18.57, p = .001.
Command Syntax for Two-sample Correlated t-test:
T-TESTT-TEST
PAIRS= pre WITH post (PAIRED).
PAIRS= pre WITH post (PAIRED). - The "pairs=" subcommand identifies which pair of variables you want to correlate for your t-test. In this case we type pre WITH post (PAIRED).
Back to Within Subject
Analyses list
II. Repeated Measures Analysis of Variance (ANOVA)
Sample question: Do rates of smoking decrease
across the four data collection periods. That is, does smoking not
only decrease from pre-intervention to post-intervention but also does
the rate continue to decrease during a 6-month and 12-month follow up?
To answer this question you can run a repeated measures ANOVA, comparing
all four time periods for all smokers.
- Select Analyze > General Linear Model > Repeated Measures from the menu bar to open the Repeated Measures Define Factors window.
- In the Within Subject Factor Name box designate a name for the repeated measure factor. In this case, let's call it rate. In the Number of Levels window type in the number of time periods measured. In this case it is 4. Click on Add and then Define. A Repeated Measures box will appear.
- Highlight your first time variable, pre, from the list of variables on the left, and click on the upper arrow button to move it into the Within Subject Variables window. Add the remaining three time variables, post, follow6, and follow12, in the same fashion.
- Click on the Options button. An Options window will appear. Click on the square next to the word Descriptive (a check will now appear in the box). This will cause descriptive statistics to print out along with your ANOVA results. (If you don't do this, the printout will only tell you if the overall ANOVA is significant, but it will not tell you the means of each group.)
- While still in the Options window, highlight rate in the Factor(s) and Factor Interaction box. Click on the arrow button and click on the square next to the word Compare main effects. This will produce multiple pairwise comparisons that can be interpreted if the omnibus test is significant.
- Click on Continue to return to the Repeated Measures window.
- Click on OK to run the analysis. Selected results are printed below.
- The printout from SPSS shows the Within Subject Factor, Descriptive Statistics, A Multivariate Test, A Mauchly's test for Sphericity, Test of Within-Subject Effects, Test of Within-Subject Contrasts, Test of Within-Subject Effects Averaged, Marginal Means, and Pairwise Comparisons. Only those outputs, relevant to the basic repeated measures analysis are presented above. First, be sure you can identify n, M, and SD for each of the four time periods in the descriptive statistics output. Second, examine Mauchly's test of Sphericity to determine if the homogeniety of variance assumption is met. If the p-value is significant (look under Sig.) then the the assumption has been violated. This will determine which values you interpret on the ANOVA table (Tests of Within-Subject Effects). Third, examine the Tests of Within-Subject Effects table (ANOVA table) to determine the significance of your omnibus test. When the Sphericity assumption is not violated, you can interpret the top set of values (i.e., Sum of Squares, df, Mean Sum of Squares, F, and p (Sig.)). When the Sphericity assumption is violated, you can interpret the values associated with Huynh-Feldt test. In this case, there is a significant difference in smoking rates across the time periods, F(1.31, 38.09) = 256.85, p = .001. Since the results of the repeated measures ANOVA are significant, you will want to examine the post-hoc tests to determine between which time periods significant differences are occurring by using the Multiple Comparison table.
- The Multiple Comparisons table provides detailed information concerning the post-hoc results. This table shows all possible comparisons between the four time periods. In the first row, the pre-intervention smoking rates is compared to the post-intervention smoking rates. The mean difference for this comparison is 25.1000 (i.e., the average smoking rate for pre-intervention, 30.5333, is subtracted from the average post-intervention smoking rate, 5.4333). To determine whether this mean difference is statistically significant examine the "Sig. Column" which represents the p-value. The p-value is .000 suggesting that the groups are significantly different from one another. This is also supported by the 95% confidence interval which indicates that zero is within the lower and upper bounds. Following this comparison, a comparison is made between the pre-intervention smoking rates and smoking rates at a six month follow-up which shows a significant difference between the two groups, p = .000. You will notice that SPSS places a star next to mean difference scores that differ significantly. The remaining rows provide the results for the other comparisons. One deficit of SPSS is that it only tells you between which groups you have significant differences and the p-levels, but it does not give you the exact values of the post-hoc tests. In this case, all time periods are significantly different from one another with the exception of the follow up at six months and 12 months.
Command Syntax for Repeated Measures ANOVA:
Back to Within Subject Analyses listGLMGLM
pre post follow6 follow12
/WSFACTOR = rate 4
/EMMEANS = TABLES(rate) COMPARE ADJ(LSD)
/PRINT = DESCRIPTIVE
/WSDESIGN = rate .
pre post follow6 follow12 - This statement indicates all the time variables to be examined.
/WSFACTOR = rate 4 - This statement indicates that the above variables should be treated as a within subject factor. The title of the factor is "rate" which has "4" time variables.
/EMMEANS = TABLES(rate) COMPARE ADJ(LSD) - This command will generate estimated marginal means and conduct a post hoc test (in this case the least significance difference test).
/PRINT = DESCRIPTIVE - The "/print=" subcommand allows the user to print several descriptive and inferential statistical tests that may be important to examine when running a repeated measures ANOVA. To get a complete list of the statistics offered for the Repeated Measures ANOVA refer to the help menu in SPSS (i.e., Select Help > Topics on the menu bar which will open the Help Topics window. Click on the Index tab. Type "GLM" in the box. GLM Repeated Measures will appear in the second box. Highlight Options under GLM Repeated Measures. Click on the Display button.).
/WSDESIGN = rate. - The "/wsdesign=" subcommand identifies the main and interaction effects to be analyzed using a within subject design.
III. Mixed Factorial ANOVA
Sample question: Do the smoking rates differ across
the three types of smoking cessation program over time? That is,
does one program lead to greater reductions in smoking rates among smokers?
To answer this question you can run a Mixed Factorial ANOVA, with pre-
and post intervention smoking rates as the within subject variable and
smoking cessation program as the independent variable.
- Select Analyze > General Linear Model > Repeated Measures from the menu bar to open the Repeated Measures Define Factors window.
- In the Within Subject Factor Name box designate a name for the repeated measure factor. In this case, let's call it time. In the Number of Levels window type in the number of time periods measured. In this case it is 2. Click on Add and then Define. A Repeated Measures box will appear.
- Highlight your first time variable, pre, from the list of variables on the left, and click on the upper arrow button to move it into the Within Subject Variables window. Add the remaining time variable, post, in the same fashion.
- Highlight program and click on the arrow button in front of the Between-Subjects Factor(s) box.
- Click on the Options button. An Options window will appear. Click on the square next to the word Descriptive (a check will now appear in the box). This will cause descriptive statistics to print out along with your ANOVA results. (If you don't do this, the printout will only tell you if the overall ANOVA is significant, but it will not tell you the means of each group.)
- While still in the Options window, highlight time in the Factor(s) and Factor Interaction box. Click on the arrow button and click on the square next to the word Compare main effects. This will produce multiple pairwise comparisons that can be interpreted if the main effect is significant and the interaction effect is found to not be significant. Note: This command does not need to be executed if there are only two time periods. Click on Continue to return to the Repeated Measures window.
- Click on the Post Hoc... button at the bottom of the screen. This opens a window in which you can select which post hoc test(s) you want to run for your between subjects factor. Highlight program in the Factor(s) box. Click on the arrow button to move program to the Post Hoc tests for: box. Select a test, i.e., click on the box in front of one of the tests, in this case Tukey.
- Click on Continue to return to the Repeated Measures window.
- Click on OK to run the analysis. Selected results are printed below.
- The printout from SPSS shows the Within Subject Factor, Between Subject Factor, Descriptive Statistics, A Multivariate Test, A Mauchly's test for Sphericity, Test of Within-Subject Effects, Test of Within-Subject Contrasts, Test of Within-Subject Effects Averaged, Marginal Means, and Pairwise Comparisons. Only those outputs relevant to the basic analysis will be presented here. First, be sure you can identify n, M, and SD for each of the two time periods across the three interventions using the descriptive statistics output. Second, examine the Tests of Within-Subject Effects table (ANOVA table) to determine the significance of your omnibus test. The interaction effect should be examined first to determine if it is significant. In this case, the interaction effect is significant, F(1, 27) = 3.398, p = .05 (used the top set of values - refer to Repeated Measures ANOVA to determine when the top set of values should be used.). This suggests that there is a significant difference in the interventions programs across time. To determine where the significant differences lie, separate hand calculated t-tests must be conducted for each set of values. For example, a comparison between the mean number of cigarettes smoked in the standard intervention program and the behavioral counseling intervention program at post intervention should be compared. All possible comparisons are calculated. Since the interaction is significant, the main effect for time should not be interpreted. If the interaction was not significant, the main effect for time and program could be examined. The main effect for time is found in the Tests of Within-Subjects Effects. The main effect for program is found in the Tests of Within-Subject Effects Averaged (see third table above). This is interpreted similar to a one-way ANOVA. That is, you interpret the main effect for program while ignoring the effect for time. If this result is significant (in this case it is not), you can interpret the Post Hoc tests (see the Multiple Comparison table). Refer to the Repeated Measures ANOVA for a directions on how to interpret a significant post hoc test.
Command Syntax for Mixed Factorial ANOVA:
Back to Within Subject Analyses listGLMGLM
pre post BY program
/WSFACTOR = time 2
/POSTHOC = program ( TUKEY )
/EMMEANS = TABLES(time) COMPARE ADJ(LSD)
/PRINT = DESCRIPTIVE
/WSDESIGN = time
/DESIGN = program .
pre post BY program - This statement indicates the between subject and with subject factors to be utilized when conducting the Mixed ANOVA. The within subject variable is listed first followed by the between subject variable with "By" separating the two.
/WSFACTOR = time 2 - This statement indicates that the above variables should be treated as a within subject factor. The title of the factor is "time" and there "2" time variables.
/POSTHOC = TUKEY - The "/posthoc=" subcommand will generate the post hoc test listed after the equal sign (in this case Tukey's) for the between subject variable(s). For a complete list of post hoc tests refer to the GLM Repeated Measures Options in the SPSS help files.
/EMMEANS = TABLES(time) COMPARE ADJ(LSD) - This command will generate estimated marginal means and conduct a post hoc test (in this case the least significance difference test) for the within subject variable(s).
/PRINT = DESCRIPTIVE - The "/print=" subcommand allows the user to print several descriptive and inferential statistical tests that may be important to examine when running a Mixed ANOVA. To get a complete list of the statistics offered refer to the help menu in SPSS (i.e., Select Help > Topics on the menu bar which will open the Help Topics window. Click on the Index tab. Type "GLM" in the box. GLM Repeated Measures will appear in the second box. Highlight Options under GLM Repeated Measures. Click on the Display button.).
/WSDESIGN = time. - The "/wsdesign=" subcommand identifies the main and interaction effects to be analyzed related to within subject factor(s).
/DESIGN = program. - The "/design=" subcommand identifies the main and interaction effects to be analyzed related to between subject factor(s).
To illustrate how to conduct within subject analyses we will use
the following hypothetical data set based on examining the effectiveness
of smoking cessation programs among heavy smokers who are also recovering
alcoholics. The description of the variables are given below the
data set. Please refer to Setting
Up Data Files to define variables and enter data into SPSS.
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| Variable Name | Description and Coding |
| id | participant identification number |
| gender | 1 = female, 2 = male |
| program | 1 = Standard ALA program pus nicotine anonymous program, 2 = Behavioral counseling plus exercise program, 3 = Behavioral counseling plus nicotine gum |
| pre | Mean # of cigarettes smoked per day Pre-intervention |
| post | Mean # of cigarettes smoked following intervention |
| follow6 | Mean # of cigarettes smoked at six month follow up |
| follow12 | Mean # of cigarettes smoked at 12 month follow up |
