# HOW TO RUN GLM REPEATED MEASURES TEST IN SPSS

## What is a GLM Repeated Measures Test?

### Using GLM Repeated Measures Test in Research

This easy tutorial will show you how to run the GLM Repeated Measures test in SPSS, and how to interpret the result.

The GLM Repeated Measures procedure provides an analysis of variance when the same measurement is made several times on each subject or case. If between-subjects factors are specified, they divide the population into groups. Using this general linear model procedure, you can test null hypotheses about the effects of both the between-subjects factors and the within-subjects factors. You can investigate interactions between factors as well as the effects of individual factors. In addition, the effects of constant covariates and covariate interactions with the between-subjects factors can be included. (Source)

GLM Repeated Measures is an ANOVA with repeated measures. We use ANOVA with repeated measures when we want to determine whether there is a difference between continuous variables measured multiple times in the same group of participants. For example, we want to determine whether exercise has an effect on weight loss in a group of 20 participants. Therefore, we will measure the weight of those participants before exercise, after 3 months of exercise, and after 6 months of exercise and we will compare the mean values of each group using an ANOVA with repeated measures.

### Assumptions of the GLM Repeated Measures :

• continuous dependent variable
• categorical independent variable with two or more related groups
• normal data distribution
• no significant outliers
• equal variances of the differences between all combinations of related groups (sphericity).

### An Example in SPSS: The GLM Repeated Measures

Null hypothesis:

There is no effect of the intervention on the dependent variable.

Alternative hypothesis:

There is an effect of the intervention on the dependent variable.

We collected data about the Math test score from 51 students before training, after one-month training, and after 2 months of training. We wanted to examine whether there is an effect of training on Math test scores. Therefore, we will use ANOVA with repeated measures. We have a continuous dependent variable (Math test score) and categorical independent variable with three groups (before, after 1 month, after 2 months).

Methods. Type I, Type II, Type III, and Type IV sums of squares can be used to evaluate different hypotheses. Type III is the default.

Statistics. Post hoc range tests and multiple comparisons (for between-subjects factors): least significant difference, Bonferroni, Sidak, Scheffé, Ryan-Einot-Gabriel-Welsch multiple F, Ryan-Einot-Gabriel-Welsch multiple ranges, Student-Newman-Keuls, Tukey’s honestly significant difference, Tukey’s b, Duncan, Hochberg’s GT2, Gabriel, Waller Duncan t-test, Dunnett (one-sided and two-sided), Tamhane’s T2, Dunnett’s T3, Games-Howell, and Dunnett’s C. Descriptive statistics: observed means, standard deviations, and counts for all of the dependent variables in all cells; the Levene test for homogeneity of variance; Box’s M; and Mauchly’s test of sphericity.

This easy tutorial will show you how to run the GLM Repeated Measures test in SPSS, and how to interpret the result.

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

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

#### STEP 2

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 the 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.

#### STEP 4

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).

#### STEP 5

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.

#### STEP 6

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 to 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.

#### STEP 7

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 at 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 the three groups.

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

A repeated-measures ANOVA 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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