Stats: Repeated Measures ANOVA

Last time we looked at how to do an independent ANOVA, today we look at the (one-way) repeated measures ANOVA. This examines whether the means of 2 or more related samples (i.e., using the same people) are significantly different. An example might be a pretest, immediate posttest, and a posttest 6 mon. later. Our research question is – are the means for the 3 times significantly different from each other? The independent variable is time (pretest, immediate posttest, 6 mon posttest), the dependent variable is the scores on a test. Our null hypothesis is that there will be no difference between the time periods. An important point: our ANOVA will only tell us if there is a significant difference present, it will NOT tell us, which groups are different from each other. To find this out, we will need to post hoc tests (more on this later). Let's do an example together. So open SPSS and enter the following data for your samples: 

Under Variable view (see tab at bottom of page), It should look like: 

Name	Type	Width	Decimals	Label	Values	Ignore the rest
prettest	numeric	8	0	Pretest	None	Ignore the rest
posttest1	numeric	8	0	Immediate Posttest	None
posttest2	numeric	8	0	6mon Posttest	None	Ignore the rest

 Go back to Data View and enter the following: 

Pretest	Immediate Posttest	6mon Posttest
3	6	9
5	8	3
2	5	5
4	9	7
1	6	4

 Go to Analyze/ General Linear Model/ Repeated Measures. For the first screen (Within Subject Factor) write in Time where says Factor 1, give it 3 levels. Press Define. Move all of your variables into Within Subjects Variables box. Press Options and the Descriptive statistics and Estimates of effect size boxes in the area labeled display. Request post hoc tests by selecting Time in the Factor and Factor Interactions sections and moving it in Display Means box. Tick compare main effects. In the Confidence interval adjustment section, click on the down arrow and choose the option Bonferroni. Press continue and ok. 

You will get a lot of tables for this- we are only going to use the following: 

Descriptive Statistics
	Mean	Std. Deviation	N
Pretest	3.00	1.581	5
Immediate Posttest	6.80	1.643	5
6mon Posttest	5.60	2.408	5

 

Multivariate Testsa
Effect		Value	F	Hypothesis df	Error df	Sig.	Partial Eta Squared
time	Pillai's Trace	.939	22.971b	2.000	3.000	.015	.939
	Wilks' Lambda	.061	22.971b	2.000	3.000	.015	.939
	Hotelling's Trace	15.314	22.971b	2.000	3.000	.015	.939
	Roy's Largest Root	15.314	22.971b	2.000	3.000	.015	.939
a. Design:  Within Subjects Design: time
b. Exact statistic

 

Pairwise Comparisons
Measure: MEASURE_1
(I) time	(J) time	Mean Difference (I-J)	Std. Error	Sig.b	95% Confidence Interval for Differenceb
					Lower Bound	Upper Bound
1	2	-3.800*	.490	.004	-5.740	-1.860
	3	-2.600	1.288	.341	-7.703	2.503
2	1	3.800*	.490	.004	1.860	5.740
	3	1.200	1.319	1.000	-4.025	6.425
3	1	2.600	1.288	.341	-2.503	7.703
	2	-1.200	1.319	1.000	-6.425	4.025
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
b. Adjustment for multiple comparisons: Bonferroni.

What does this mean? There is a significant difference between the 3 times (see where I marked in yellow above). This does not tell you which groups are different from each other, to find this out we did Bonferroni post hoc tests and found that the pretest varied significantly from the immediate posttest (see data marked in yellow above), no other groups differed. So let's write it up as you would in your paper: 

A repeated measures ANOVA was conducted to compare scores at the pretest (M = 3.0; SD = 1.58), immediate posttest (M = 6.8; SD = 1.6), and the 6 mon posttest (M = 5.6; SE = 2.4). The results (Wilks' Lambda = .061. F(2, 3) =22.97, p= .015, multivariate eta squared = .939 [large effect]) indicates that there is a significant difference between the time periods and the null hypothesis is rejected. Bonferroni post hoc tests examined which groups differed. It was found that only the pretest and immediate posttest scores differed (p< .05). 

A great resource for SPSS is

Pallant, J. (2013). The SPSS Survival Manual, 5^th edition. Open University Press. 

We have examined the most common (and easy to explain in a blog) statistical tests. Next time, we will take a look at anxiety and the dissertation. Do you have an issue or a question that you would like me to discuss in a future post? Send me an email with your ideas. leann.stadtlander@waldenu.edu