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I have used a non parametric ANCOVA to analyze scores of a questionnaire (BSCS) with factors: Type of intervention(A and B) and timepoint (pre- and post) as well as baseline (same distribution as pre-) as a covariate. I have done this on SPSS and I'll write down my steps below: Steps:

1. Rank the Dependent Variable and Covariates: Rank the dependent variable (e.g., scores at the BSCS) ignoring the between-subject factor (Type of Intervention) and within-subject factor (Time: Pre and Post). Also rank the covariate (pre or baseline scores at the BSCS) across all cases ignoring the between-subject factor (Type of Intervention)

2. Save these as new variables (e.g., RBSCS, meaning Rank of BSCS scores and RBSCS_Co meaning rank for BSCS_Baseline scores which is the baseline). Manually separe between RBSCS-pre and RBSCS-post by simply creating a new column.

3/4. Linear Regression on Ranks for Each Time Point: 4. For each time point (pre and post), run separate linear regressions of the ranks of the dependent variable on the ranks of the covariates. The rank of the variable: questionnaire scores is split into two categories (Pre and Post) while the group factor is still ignored for the moment.

5. Save the unstandardized residuals for each time point (e.g., RES_BSCS_Pre and RES_BSCS_Post).

6. Two-way Mixed Model ANOVA:Perform a two-way mixed-model ANOVA using the residuals as the dependent variable. The between-subject factor will be the Type of Intervention, and the within-subject factor will be Time (pre and post).

7. The F-statistic Quade will come from this ANOVA.

8. Post-Hoc Comparisons: If significant effects or interactions are found, you can proceed with post-hoc tests to examine pairwise differences, while adjusting for multiple comparisons.

Is this method valid? I have read Quades' non-parametric ancova paper but this is a bit different cause it is a mixed-methods non-parametric ancova. To be honest, i did not find any other source in the literature so i was wondering:

  1. is there a theoretical article or an experimental article describing something similar?
  2. despite this analysis pipeline makes total sense to me, i wanted to know if you see some mistake or loopholes that i am missing?
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    $\begingroup$ Have you looked into ordinal regression? That's a semi-parametric method that doesn't make assumptions about the distributions of error terms, allows for the same types of multiple regression models as in fully parametric models, and is reasonably insensitive to violations of its assumptions. See this page for information and links. This UCLA web page illustrates in SPSS. $\endgroup$
    – EdM
    Commented Jan 17 at 17:22

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