Background:
In a mixed ANOVA (2 timepoints, 3 interventiongroups, so 2x3 factorial ANOVA), the homogeneity of the residual variance was violated as indicated by significant Levene test, for the post-intervention measurement timepoint (T2)
As far as I understand it, this prohibits any further analysis for the output of the ANOVA. Thus, we did perform a box-cox-transformation on the data from measurement timepoint T2 (following this stackoverflow post).
Question / Problem:
As our original variable has a range from -10 to + 10 we added a Constant (minimum value in T2 + 0.0001) to Perform the Box-Cox transformation. This results in a strongly distorted plot of the effect. The line plot showing the differential effect with different lines for each group and measurement time on x-axis are now distorted. We are thus wondering, would it be possible / statistically allowed/valid, to just standardize (z-transformation) all values, e.g., pre-intervention time points (T1) as well as the already box-cox transformed post-intervention (T2) values in order to make the scaling for both measurement time points comparable? Or can / shold we just transform values at T1 in a similar fashion (adding constant, minimum + 0.0001, followed by Box-Cox transformation)?
In a mixed ANOVA (2 timepoints, 3 interventiongroups, so 2x3 factorial ANOVA), the homogeneity of the residual variance was violated as indicated by significant Levene test, for the post-intervention measurement timepoint (T2)

As far as I understand it, this prohibits any further analysis for the output of the ANOVA. Thus, we did perform a box-cox-transformation on the data from measurement timepoint T2 (following this stackoverflow post).
Question / Problem:
As our original variable has a range from -10 to + 10 we added a Constant (minimum value in T2 + 0.0001) to Perform the Box-Cox transformation. This results in a strongly distorted plot of the effect. The line plot showing the differential effect with different lines for each group and measurement time on x-axis are now distorted. We are thus wondering, would it be possible / statistically allowed/valid, to just standardize (z-transformation) all values, e.g., pre-intervention time points (T1) as well as the already box-cox transformed post-intervention (T2) values in order to make the scaling for both measurement time points comparable? Or can / shold we just transform values at T1 in a similar fashion (adding constant, minimum + 0.0001, followed by Box-Cox transformation)?
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