Whithin-subjects design - Mauchly's sphericity test on interaction effect - Statistica General Discussion - Statistica - Dell Community

# Whithin-subjects design - Mauchly's sphericity test on interaction effect

#### Whithin-subjects design - Mauchly's sphericity test on interaction effect

Hello,

When running a Mauchly's sphericity test on the data from a repeated measures ANOVA with two factors of 5 levels each, I do receive results for the two main effects but not the interaction. Could anyone please tell me why that is? Thank you.

Katja

All Replies
• Hello, Katja. The Mauchly's sphericity test is to test if the sphericy assumption holds. The sphericity assumption is a necessary and sufficient condition for the F-test to be valid; it states that the within-subject "model" consists of independent (orthogonal) components. As such, you will only get the sphericity test result for the within group effect in a repeated ANOVA, such as time, location and ect. It is not designed to test any between group effects. More information about sphericity test can be found in Statistica e-manual or here.

• Hello Wendy, Thank you for your reply. The design that I refer to does not have any between-group manipulations. It has one factor A with five levels and one factor B with 5 levels. Both factors are manipulated within group. Therefore, the interaction A x B does contain different within-group combinations as well. Why do I not receive an output of the Mauchly Test for the interaction with this type of design? Thank you. Katja

• Hi Katjia, Which module are you using in Statistica? If you are using repeated ANOVA, only one within group effect is allowed in this module. As such, there is no interaction term for the within group effect.The within group effect refers to the repeated measurement effect. A factor often refers to a categorical variable that indicates between-group effect. See an repeated ANOVA example here. In this example, R1 (repeated measures) is the single within group effect, Gender and ADVERT are the between group factors. So you will only get the Sphericity test result for the R1.

• Hello Wendy, Thank you for your reply. Sorry for the confusion which is probably due to using the term "factor" differently than it is used in the software. I don't have between group effects in my design, only within group effects. It is a 5 x 5 repeated measures ANOVA and I do get a within group interaction term in the ANOVA output. The one thing which I don't receive is a Mauchly result for the interaction. Could you please tell me why? Thank you. Katja

• Hello, Katja. which module in Statistica are you using?

• Higher (non)-linear models -->  General Linear Model --> Repeated Measures ANOVA

Note that I translated this from my German interface so it might be slightly different.

Thank you.

Katja

• Hi Katja. When you click "All effects" under GLM Results dialog, do you see the interaction term listed under the first column "effect"? If possible, can you share the screenshots of your ANOVA table and Sphericity table results from Statistica? And also, here is an example of running repeated ANOVA in GLM. Could you please check if you set up the analysis properly?

• Hello Wendy, Yes, I do see it listed. Please find the screenshots attached. And, yes, I set up the ANOVA correctly. Kind regards. Katja

• Hi Katja, thanks for your clarification! I would suggest you to open a support service request to get assistance from our support engineers for further investigation, since this seems to be related to the data you are using. And we will need to replicate this at our side by your data and find the cause. Here is a KB article of how to open a service request.

• Hello Wendy, Thank you for your suggestion. I think that there is a mathematical reason behind this as I also do not receive a value for the Mauchly test of the interaction with SPSS, so it is not something specific to Statistica. I was wondering whether you could help me regarding this matter or whether you think opening a service request would be more appropriate in this situation? Thank you. Katja

• Hi Katja. Either through this tech forum or our support service, we would be happy to help Statistica users with questions related to our software. If it is a mathematical/ data setup issue resulted from your particular analytic question rather than our software, I would recommend you to study the proper design/data requirement for analyzing data via repeated ANOVA through statistics references, online statistical general forum or consult a Statistician. But if you would like to open a service request with us, we still want to try to replicate this issue at our end and make sure this is not software issue. Thanks!