ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.

🎬 Example File

This analysis is demonstrated on the following example dataset for Education Sciences:

Egitim_Bilimleri/109_crossed_lmm_A_B.xlsx

Suppose we ran a study where every level of one factor is observed in
combination with every level of another, for example each teaching condition
delivered with each set of materials. Here factor_a has four levels A1 to A4
and factor_b has four levels B1 to B4, fully crossed across 128
observations, with the continuous outcome value. A Crossed Mixed Model is
appropriate because both factors can be treated as random effects that cross
each other, letting us separate the variability due to factor_a, the
variability due to factor_b, and the residual, rather than forcing a nested
structure. This is the standard model for fully crossed educational designs.

Unlike nesting, here two factors are crossed: each A level is combined with each B level (fully factorial). A
striking result: both main effects are non-significant (A: p = 0.77, B: p = 0.48), but the interaction is highly
significant (F = 14.67, p < .001). This is a classic case of a “pure interaction”: A and B alone say nothing, but
TOGETHER — specific A-B combinations — they create a strong effect. Looking only at the main effects and saying
“nothing is significant” would be a major error; the interaction changes everything. The crossed mixed model is
the right way to capture interactions that emerge when factors are tested jointly — a critical inference in
educational experiments (such as method x content).