Hello Xiaoming Yang. Carving quantitative variables into categories prior to analysis is rarely if ever justified. You can find a long list of problems here:

• https://discourse.datamethods.org/t/categorizing-continuous-variables/3402

If you say more about your research question and the software you use, someone may be able to advise you on how to include language proficiency as a quantitative variable.

Thank you so much, Bruce Weaver. The predictor is reading medium (i.e., paper vs. mobile), the outcome variable is reading performance, and the moderator is language proficiency. The research design is repeated measures. I would like to perform data analysis using SPSS.@Bruce Weaver

Hello Xiaoming Yang. If I follow, each participant reads under two conditions, paper vs. mobile. Right? If so, have you counterbalanced the order too? That would be another between-Ss factor in your model if you have.

Assuming you have counterbalanced the order, a wide file layout would have these variables:

• ID (a unique ID code for each participant)
• LangProf (language proficiency score)
• Order (between-Ss factor)
• Y1 (reading performance for paper)
• Y2 (reading performance for mobile)

One option would be to use GLM > Repeated Measures to estimate a repeated measures ANCOVA model, with language proficiency as the covariate. If you do want to use that approach, you would be wise to mean-center language proficiency. See this letter to the editor for details:

Article Use of covariates in randomized controlled trials

But if I was you, I would restructure the data from WIDE to LONG, and then use the MIXED command. When you use GLM Repeated Measures, your hands are tied about which interaction terms involving the covariate are included in the model. When you use MIXED, on the other hand, you have complete control over which terms are included in the model. The following UCLA web pages have examples you should find helpful.

• https://stats.oarc.ucla.edu/spss/seminars/spss-mixed-command/
• https://stats.oarc.ucla.edu/spss/seminars/repeated-measures/

HTH.

Thank you so much for you answers, @Bruce Weaver. They are really helpful.