How to control for randomization of within-subjects factor in mixed ANOVA in SPSS?

It depends. I'd note first that randomising order doesn't prevent order effects, it attempts to control them by distributing them evenly across the conditions. You can potentially control for them by including between-participant covariate if you used a small number of random orders. Otherwise no, you probably can't with RM ANOVA, but may be able to with a multilevel model (aka linear mixed model) that allows you to add time-varying covariates.

Ma'Mon Abu Hammad

To control for the randomization of a within-subjects factor in a mixed ANOVA (Analysis of Variance) in SPSS, you need to specify the appropriate covariance structure for the repeated measures factor. This allows you to account for the correlation between repeated measures within the same subject.

Here are the steps to control for randomization in a mixed ANOVA in SPSS:

Open your dataset in SPSS.

Go to "Analyze" in the menu bar and select "General Linear Model" followed by "Repeated Measures."

In the "Repeated Measures" dialog box, move the within-subjects factor(s) from the list of available variables to the list of "Within-Subject Variables."

Specify the between-subjects factor(s) if applicable by moving the variables to the "Between-Subjects Factors" box.

Click on the "Model" button to specify the type of ANOVA model you want to use (e.g., full factorial, custom, etc.).

Next, click on the "Options" button to open the options dialog box.

In the "Options" dialog box, select the "Estimates of Covariance" tab.

Choose the appropriate covariance structure from the list, depending on the design of your study and the assumptions you wish to make about the within-subjects factor.

Select any other desired options (e.g., descriptive statistics, effect size measures) and click "Continue" to return to the "Repeated Measures" dialog box.

Review the settings in the "Repeated Measures" dialog box, and make any necessary adjustments.

Click "OK" to run the mixed ANOVA analysis.

By specifying the appropriate covariance structure, you are accounting for the randomization of the within-subjects factor and controlling for the correlation between repeated measures within the same subject. The choice of covariance structure will depend on your study design and the assumptions you are making about the data. SPSS provides various options, including compound symmetry, unstructured, and autoregressive covariance structures, among others.

Note that the specific steps and options may vary slightly depending on the version of SPSS you are using. Make sure to consult the SPSS documentation or help resources for your specific version for further guidance.

Ma'Mon Abu Hammad

Controlling for the randomization of a within-subjects factor in a mixed ANOVA in SPSS involves specifying the appropriate error term in the analysis. By doing so, you account for the random variation associated with the within-subjects factor. Here's how you can achieve this in SPSS:

Open your dataset in SPSS and navigate to "Analyze" in the top menu.

Select "General Linear Model" and then choose "Repeated Measures" from the drop-down menu.

In the "Repeated Measures" dialog box, move the within-subjects factor(s) from the list of available variables to the "Within-Subject Variables" box.

Specify the between-subjects factor(s) in the "Between-Subject Factors" box, if applicable.

Click on the "Model" button. In the "Model" dialog box, select the appropriate model for your analysis, such as "Univariate" or "Multivariate."

Under the "Method" option, select "Type III (hierarchical)" or "Type III (sequential)" sum of squares, depending on your research design and specific hypotheses. This selection affects the partitioning of variance and can influence the interpretation of results.

Click "Continue" to return to the "Repeated Measures" dialog box.

In the "Repeated Measures" dialog box, click on the "Options" button. This will open the "Repeated Measures: Options" dialog box.

In the "Repeated Measures: Options" dialog box, check the "Display of Estimated Marginal Means" box if you want to obtain post hoc pairwise comparisons of the means.

In the "Repeated Measures: Options" dialog box, click on the "EMMeans Options" button. Here, you can specify additional options for the estimation of marginal means if needed.

Once you have selected your desired options, click "Continue" to return to the "Repeated Measures" dialog box.

Click "OK" to run the mixed ANOVA analysis.

By specifying the within-subjects factor(s) and appropriately selecting the error term (sum of squares) in SPSS, you can control for the randomization of the within-subjects factor in your mixed ANOVA analysis.

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