Thanks for coming back to me on this Karabiner.

I have three groups of males (n1 = 89, n2 = 295 and n3 = 66). The dependent variable (DV) is body mass (kg) and the covariate (CV) is age (yrs). I wanted to use ANCOVA to test the *H*0: *M*1 = *M*2 = *M*3 on the group masses holding the covariate stable.

Only three of the five assumptions underpinning parametric ANCOVA were met in my data.

**Linearity between the DV and the CV **- *r*448 = 0.061, *P* = 0.097 - based on this the assumption is confirmed. However, there is also an issue related to significant differences in the mean ages between the three groups (G1 = 19.1 ± 6.0 yrs, G2 = 24.8 ± 8.4 yrs, G3 = 27.1 ± 5.7 yrs; *F*2,447 = 25.4, *P* < 0.001). I concluded therefore that parametric ANCOVA would be inappropriate.

**Homogeneity of error variances** Levene’s test: *L*2,447 = 7.76, *P* < 0.001. This assumption is **violated**.

**Independence of residuals** – the scatterplot is orthogonal: *r*448 = -0.063, *P* = 0.093, *R*2 = 0.004, *R*2adj = 0.002. The assumption is **confirmed**.

**Normality of residuals** – Kolmogorov-Smirnov and Shapiro-Wilk tests: K-S450 = 0.061, *P* < 0.001; S-W450 = 0.957, *P* < 0.001; *S*kewness = 0.02 and *K*urtosis = -1.19. The residuals are not badly skewed (i.e. *S* is within ±1.96). I am less concerned about the *K* index, which is still within acceptable limits. Indeed, it is not at all unusual to see issues with the peaks of normal curves in biological data. I was inclined to assume that a parametric ANCOVA is robust enough to apply to these scores, based on these outcomes, i.e. the assumption is **confirmed**.

**Homogeneity of regression slopes** – the slopes of the DV *vs* CV OLS regression lines for the three groups are not equivalent – this assumption is **violated**.

Consequently I ran Quade's rank ANCOVA:

1. I rank ordered the DV (mass) and the CV (age).

2. I ran an OLS regression as: Rank Mass = a + (b x Rank Age), and I saved the unstandardised residuals in the process.

3. I ran a one-way ANOVA with the unstandardized residuals saved in 2 as the DV and the grouping variable as the Factor

Results: *F*2,447 = 24.28 (*P *< 0.001) which allowed me to reject the *H*0 in favour of the *H*1: *M*1 ≠ *M*2 ≠ *M*3.

My issue is how can I run a *post-hoc* test to identify which of the group means differ, but report the results related to the original units of measurement of the DV (kg)?

Any advice would be most welcome.

Steve