BOXCOX values

[Antonia.98]

Hi,

I´m currently working with a Mixed ANOVA model, unfortunately the levene test came out significant for my dependent variables. So I was looking into using a robust measure or transforming, stumbled upon BoxCox. I simply used the integrated jamovi formula BOXCOX(VariableY).

1) It gave out values that were very far from the original ones, is that supposed to happen? (e.g. sum score of 26 in the original variable is now a 113.430).
2) the levene test still comes out as significant - does anybody have any experiences with that? The two groups that are being compared are pretty unbalanced (n = 53 & n = 16)....

Thanks a lot in advance!
Anni

[MAgojam]

Hey Anni,

just to give you some background: the BOXCOX() function you used in jamovi is actually implemented under the hood in Python (you can see the code here: https://github.com/jamovi/jamovi/blob/current-dev/server/jamovi/server/compute/functions.py#L305-L322).
Knowing this can help to understand why the values look so different.

1. Why are the values so different?
BOXCOX() doesn’t just rescale your data – it estimates a λ (lambda) value that maximizes the normality of the distribution. Once λ is chosen, the whole variable is mathematically transformed.
That’s why the transformed values may look very far from the originals (e.g., 26 becoming 113).
The transformation is not intended to preserve the original scale but to improve distributional properties.

2. Why is Levene’s test still significant?
Box–Cox mainly helps with normality of residuals, but it doesn’t guarantee equal variances. With unbalanced groups (like n=53 vs n=16), Levene’s test is especially sensitive and often stays significant even after transformations.

3. What you can consider

• Use analyses that are robust to unequal variances. In jamovi, you can find robust ANOVA in the Walrus module, which may be a good alternative for your data.
• Try other transformations (log, sqrt, etc.) if they are theoretically justified, although Box–Cox already searches for the “best” λ.

In summary:

• It’s normal for Box–Cox to produce values that look very different.
• It won’t necessarily “fix” Levene’s test, especially with unbalanced samples.
• For robustness, the Walrus module in jamovi is worth trying.

Cheers,
Maurizio
https://www.jamovi.org/about.html

[Antonia.98]

Hello dear Maurizio,

thank you so much for this very good explanation! Also for the link, it's really better to grasp what is happening in the background of my analysis.

I thought about the robust ANOVA, I´m just not sure whether it is possible to include the repeated measurements factor in this module of jamovi. or is there any trick to it that I`m not aware of?

Thanks again, I really appreciate your input!

Cheers,
Anni

[MAgojam]

I thought about the robust ANOVA, I´m just not sure whether it is possible to include the repeated measurements factor in this module of jamovi.

I have to apologize for stumbling over my own code, anticipating an upcoming Walrus update with robust ANCOVA and RMANOVA, but it's not yet available in the jamovi library.
If you're familiar with R, you might find and try the robust RMANOVA in the WRS2 package.
Author: Patrick Mair [cre, aut], Rand Wilcox [aut], Indrajeet Patil [ctb]

Cheers,
Maurizio

[Antonia.98]

Don´t worry about it, that's also good to know! And thank you for all the info, its really helped me move forward

Cheers
Anni