Repeated-Measures ANOVA with SPSS

Repeated-Measures ANOVA with SPSS

Statistical Package for the Social Sciences (SPSS) is a program for analyzing data collected by researchers in the social sciences. An ANCOVA (Analysis of Covariance) is used to analyze data in which there is one or more independent variables and a dependent variable when the researcher wants to remove the influence of one or more predictor variables on the dependent variable.

Data requirements. In all GLM models, the dependent(s) is/are continuous. The independents may be categorical factors (including both numeric and string types) or quantitative covariates. Data are assumed to come from a random sample for purposes of significance testing. The variance(s) of the dependent variable(s) is/are assumed to be the same for each cell formed by categories of the factor(s) (this is the homogeneity of variances assumption).

Regression in GLM is simply a matter of entering the independent variables as covariates and, if there are sets of dummy variables (ex., Region, which would be translated into dummy variables in OLS regression, for ex., South = 1 or 0), the set variable (ex., Region) is entered as a fixed factor with no need for the researcher to create dummy variables manually. The b coefficients will be identical whether the regression model is run under ordinary regression (in SPSS, under Analyze, Regression, Linear) or under GLM (in SPSS, under Analyze, General Linear Model, Univariate). Where b coefficients are default output for regression in SPSS, in GLM the researcher must ask for "Parameter estimates" under the Options button. The R-square from the Regression procedure will equal the partial Eta squared from the GLM regression model.

The advantages of doing regression via the GLM procedure are that dummy variables are coded automatically, it is easy to add interaction terms, and it computes eta-squared (identical to R-squared when relationships are linear, but greater if nonlinear relationships are present). However, the SPSS regression procedure would still be preferred if the reseacher wishes output of standardized regression (beta) coefficients, wishes to do multicollinearity diagnostics, or wishes to do stepwise regression or to enter independent variables hierarchically, in blocks. PROC GLM in SAS has a greater range of options and outputs (SAS also has PROC ANOVA, but it handles only balanced designs/equal group sizes).

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Testing for Homogeneity of Regression spss

First run the ANCOVA model with a Treatment X Covariate interaction term included1

If the interaction is significant, assumption violated

Depending on the level of treatment, the relationship b/t covariate and DV changes

If not, rerun without interaction term

Or simply run the Covariate-DV regression for each group and assess in that way.2

Regression in GLM is simply a matter of entering the independent variables as covariates and, if there are sets of dummy variables (ex., Region, which would be translated into dummy variables in OLS regression, for ex., South = 1 or 0), the set variable (ex., Region) is entered as a fixed factor with no need for the researcher to create dummy variables manually. The b coefficients will be identical whether the regression model is run under ordinary regression (in SPSS, under Analyze, Regression, Linear) or under GLM (in SPSS, under Analyze, General Linear Model, Univariate). Where b coefficients are default output for regression in SPSS, in GLM the researcher must ask for "Parameter estimates" under the Options button. The R-square from the Regression procedure will equal the partial Eta squared from the GLM regression model.

The advantages of doing regression via the GLM procedure are that dummy variables are coded automatically, it is easy to add interaction terms, and it computes eta-squared (identical to R-squared when relationships are linear, but greater if nonlinear relationships are present). However, the SPSS regression procedure would still be preferred if the reseacher wishes output of standardized regression (beta) coefficients, wishes to do multicollinearity diagnostics, or wishes to do stepwise regression or to enter independent variables hierarchically, in blocks. PROC GLM in SAS has a greater range of options and outputs (SAS also has PROC ANOVA, but it handles only balanced designs/equal group sizes).

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Correct data formatting for a repeated-measures ANOVA in SPSS

Correct data formatting for a repeated-measures ANOVA in SPSS

Overview: The instructions on this sheet cover two procedures: 
1. A one-way within-subjects ANOVA, used when you have one independent variable and one group of subjects measured repeatedly under 3 or more conditions. For example, subjects are measured in a baseline condition, are given a treatment, and are followed up at 3 later points in time. 
2. A 2-way mixed ANOVA, used when you have two independent variables with one within-subjects factor, and one between-subjects factor. The within-subjects factor is the repeated measures factor. On the between-subjects factor, subjects are divided into discrete subgroups, and each subject falls into only one of those subgroups.
To run: From the Data Editor Window 
Click on "Analyze" 
Click on "General Linear Model" 
Click on "Repeated Measures"

The following dialog box will appear:

Begin with the repeated measures factor. The first thing you need to do is to instruct SPSS to treat your repeated measurements not as different variables, but as different levels of the same variable. To do this click the box "Within-Subject Factor Name" and type in a name for your repeated measures variable.

Type in the number of observations you have on each subject in the box labeled, "Number of Levels" 
Click on "Add". The name of your new variable will appear in the box with the number of levels of that variable in parentheses.

Click on "Define" 
The following GLM - Repeated Measures dialog box will appear:

You must now tell SPSS what the different levels of your repeated measures factor are, that is, which variables from the column on the left represent your different levels. Click on each of the variables, i.e. baseline, time2, time3, time4 and click the right arrow key to move those variables to the box labeled, "Within-subjects Variables"

If you are running a one-way repeated measures ANOVA, you are done. 
Click "OK"

If you are running a two-way mixed ANOVA you need to indicate which variable is your between subjects variable. Click on that variable from the column on the left and click the right arrow to move it to the box on the right labeled, "Between-Subjects Factor(s):"

Click on "OK"

Output:

One-way repeated measures ANOVA 
The first table you see lists "Descriptive Statistics" for each of your groups, i.e., mean, standard deviation, and sample size. Note the sample size will be identical for all groups because the same subjects appear in each group.

Look at the table, "Tests of within-subjects effects." 
The first line of this table gives you your F, its degrees of freedom, and the probability of your F.

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