This is an implementation of ANCOVA in R, though the variables in question are not statistically significant difference.

In this notebook, I have used two approaches for the non-parametric alternative of the two-way ANOVA and why I used both: Aligned Rank Transform (ART) ANOVA is a non-parametric approach to factorial ANOVA that enables you to analyze the interaction as well as the main effects. The nparLD package in R is used for performing non-parametric analysis of longitudinal data (i.e., repeated measures) or factorial experiments where assumptions like normality and homogeneity of variance are violated.

Friedman test is the non-parametric equivalent to one-way ANOVA wiht repeated measures

Two-way ANOVA with Repeated Measures between Sleep sufficiency and chronotype among 3 repeated assessments

Repeated Measures ANOVA in R using Datanovia's implementation to practice Two-way ANOVA with repeated measures