Hello Pruthviraj,

Be sure to ask for estimated marginal means by each factor level (and combinations, if there's any hint of interaction). The EMMs and standard errors give you all you need to conduct any further post hoc comparisons (with adjustments for any covariates in the model).

Good luck with your work.

Hi David,

Thanks for your response. I am getting the EMMs & SEs for each of the 6 levels of the fixed factor (picture attached). The fixed factor is significant at p

Hello again Pruthviraj,

For any pair of levels you wish to compare, construct a t-test as follows:

t = (M1 - M2) / SE(diff) (with df = n1 + n2 - 2)

where M1 & M2 are the means for the two respective levels, and

SE(diff) is the standard error of the difference for two independent groups.

Find SE(diff) by:

1. SS1 = n1*(SE1^2)*(n1 - 1)

2. SS2 = n2*(SE2^2)*(n2 - 1)

3. SSpooled = SS1 + SS2

4. Variance(pooled) = SSpooled / (n1 + n2 -2)

5. SE(diff) = Sqrt(Variance(pooled)/n1 + Variance(pooled)/n2)

where: n1, n2 are group sample sizes; SE1 and SE2 are group SEs.

If you want to build in protection against too-high an aggregate alpha level (sometimes called family-wise alpha), test each comparison at a lower alpha level. There are many variants on this theme, but a simple one is the Bonferroni adjustment, in which the per-comparison alpha level = FWalpha / c, where FWalpha is the acceptable aggregate risk of one or more type I errors for the set of comparisons; and c is the total number of comparisons to be run.

Good luck with your work.

Thanks for the solution David Morse