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 

Stats: Independent ANOVA

 

Last time we looked at how to do a correlational analysis, today we look at the independent ANOVA. This examines whether the means of 2 or more separate samples are significantly different. An example might be a control group vs. a group with intervention A vs. a group with intervention B. Our research question is – are the means for the 3 groups significantly different from each other? The independent variable is condition (control, group A or group B), the dependent variable is the scores on a test. Our null hypothesis is that there will be no difference between the groups. 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
Condition	numeric	8	0	Condition	*(see below)	Ignore the rest
score	numeric	8	0	Score	None	Ignore the rest

 *For condition, labels: 1= control; 2 = group A, 3 = group B 

Go back to Data View and enter the following: 

Condition	Score
1	5
1	3
1	7
1	2
1	6
2	6
2	7
2	9
2	10
2	8
3	4
3	8
3	7
3	9
3	5

Go to Analyze/ General Linear Model/ Univariate. Move your score variable into Dependent Variable. Move condition into Fixed Factors. Go to Post Hoc (button on right side of variable screen), move condition into right box for post hoc tests. For now, choose Tukey's test (note, there are many different post hoc tests, check a stats book or the SPSS book listed below to choose the correct one for your data). Press continue to return to the variable screen. Go to Options, move Overall and condition to right to display means. Also, check descriptive statistics. Press continue to return to the variable screen. Press ok. 

Your results should look like the following:

 

Descriptive Statistics
Dependent Variable: Score
Condition	Mean	Std. Deviation	N
control	4.60	2.074	5
group A	8.00	1.581	5
group B	6.60	2.074	5
Total	6.40	2.293	15

 

Tests of Between-Subjects Effects
Dependent Variable: Score
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	29.200a	2	14.600	3.946	.048
	614.400	1	614.400	166.054	.000
condition	29.200	2	14.600	3.946	.048
Error	44.400	12	3.700
Total	688.000	15
Corrected Total	73.600	14
a. R Squared = .397 (Adjusted R Squared = .296)

 

Multiple Comparisons
Dependent Variable: Score  Tukey HSD
(I) Condition	(J) Condition	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
control	group A	-3.40*	1.217	.040	-6.65	-.15
	group B	-2.00	1.217	.266	-5.25	1.25
group A	control	3.40*	1.217	.040	.15	6.65
	group B	1.40	1.217	.503	-1.85	4.65
group B	control	2.00	1.217	.266	-1.25	5.25
	group A	-1.40	1.217	.503	-4.65	1.85
Based on observed means.  The error term is Mean Square(Error) = 3.700.
* The mean difference is significant at the .05 level.

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

An independent ANOVA was conducted comparing the control group (M = 4.6; SE = .86) to group A (M = 8.0; SE = .86) and group B (M = 6.6; SE = .86). The result (F(2, 12) =3.95, p= .048) indicates that there is a significant difference between the groups and the null hypothesis is rejected. Tukey's post hoc tests examined which groups differed. It was found that only the control group and group A differed (p< .05).

A great resource for SPSS is

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

Next time, we will look at repeated measures ANOVA. 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