# Reporting Repeated ANOVA Test in SPSS

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## What is a GLM Repeated Measures Test?

## How to Run GLM Repeated Measures Test in SPSS: Explanation Step by Step

**From the SPSS menu, choose Analyze – General Linear Model – Repeated Measures**

**A new window will open. In the box, the Within-Subject Factor Name is already written factor1. You should write the name of your within-subject factor. In our example, it is Time because we measured the Math test score before training, after one month, and after two months. Therefore, we will write Time instead of factor1.**

**In the Number of the Level box;**

**you should write the number of categorical groups. In our example, we measured Math test score 3 times (before, after one month, after two months of training), so we will write 3 in the Number of Levels box. Click on the Add button, and the name of the factor and number of levels will appear in the box. Click Define, and a new window will open.**

**The left box transfer variables PreTraining, AfterOneMonth, AfterTwoMonths into Within-Subject Variables (Time) using the arrow, so that occurred (before, after one month, after two months).**

**Click on the Plots button and a new window will open. **

**From the Factors box transfer variable Time into Horizontal Axis box. **

**Click the Add button and the variable will transfer to the Plots box. Click Continue, and you will return to the previous box.**

**Please click the Options button, and a new window will appear. From the Factor(s) and factor Interactions, box transfer Time variable in Display Means for the box. Choose Compare main effects, and in the Confidence interval adjustment, choose Bonferroni. In the Display box, choose Descriptive statistics, Estimates of effect size. Click Continue, and you will return to the previous window.**

**The GLM repeated measures results would appear in the output window.**

## How to report a GLM Repeated Measures results: Explanation Step by Step

### How to Report the Within-Subject Table in SPSS Output?

Table Within-Subject Factors shows the groups of the independent variable.

### How to Report Descriptive Statistics Table in SPSS Output?

Table Descriptive Statistics shows the number of observations, the mean and standard deviation of dependent variable Math test score across all three categories (before training, after 1-month training, after two months of training).

The average Math test score before training was 61.27 (M=61.27; SD=5.80), after 1-month training was 78.96 (M=78.96; SD=6.52), and after 2 months of training was 94.24 (M=94.24; SD=5.56).

### How to Report Multivariate Tests Table SPSS Output?

Table Multivariate tests show the results of Wilks’ Lambda test.

**If p > 0.05**, there is no statistically significant impact of an independent variable on the dependent variable.

**If p < 0.05**, there is a statistically significant impact of an independent variable on the dependent variable.

In our example, p = 0.00, so we reject the null hypothesis and conclude that there is a statistically significant difference in Math test score before, after one month, and after two months.

### How to Report Mauchly’s Test of sphericity Table in SPSS output?

Table Mauchly’s Test of sphericity shows whether variances of the differences between all combinations of related groups are equal.

If p > 0.05, assumption is not violated.

If p < 0.05, assumption is violated.

In our example, p = 0.645 > 0.05, so the sphericity is assumed.

### How to Show Tests of Within-Subjects effects in SPSS Output?

In the table tests of Within-subjects effects, we should look row sphericity assumed if the assumption is not violated, and the row Greenhouse-Geisser if the assumption is violated.

If p > 0.05, there is not an overall significant difference between the means at different time points.

If p < 0.05, there is an overall significant difference between the means at different time points.

In our example, p = 0.00 < 0.05, so we reject the null hypothesis and conclude that there is an overall significant difference between the means Math test score at the different time points (before, after one month, after two months).

### How to Show Pairwise Comparisons in SPSS Output?

Table Pairwise Comparisons shows whether there is a difference between each group. One is a Math test score before training, 2 is a Math test score after one-month training, and 3 is a Math test score after two months of training.

If p < 0.05, there is a difference between the two groups.

If p > 0.05, there is no difference between the two groups.

In our example, p = 0.000 < 0.05, for each pair of groups, so we may conclude that there is a difference between Math test score before training and Math test score after one-month training; between Math test score before training and Math test score after two months training; between Math test score after one-month training and Math test score after two months training.

### How to Show Plot Chart in SPSS Output?

Finally, there is a plot showing the difference between the means of three groups.

## How to Interpret a GLM Repeated Measures Results in APA Style?

**A repeated ANOVA** test was used to determine whether there is an effect of Time (before, after one-month training, after two-months training) on Math test scores. The result of the GLM Repeated Measures Test is significant, F(2, 100) = 437.144, p = 0.00 < 0.05, so we reject the null hypothesis and conclude that there is an overall significant difference between the means Math test score at the different time points (before, after one month, after two months).

### Post hoc Result

Post hoc tests using the Bonferroni correction revealed that one-month training improved Math test scores significantly (p = 0.000). The average Math test score before training was 61.27 (M=61.27; SD=5.80) and after 1 month training was 78.96 (M=78.96; SD=6.52). The results indicate that two-month training also improved the Math test score (p = 0.00). The average Math test score before training was 61.27 (M=61.27; SD=5.80) and after 2 months training was 94.24 (M=94.24; SD=5.56). Therefore, we may conclude that there is a significant effect of Time (before, after one month, after two months) on the Math test score.

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