Hello Jakub,

You do not have evidence of a significant interaction in the "post hoc" tests. What you did find is (I presume) a significant t-test for differences by race condition within the no-disclosure condition and non-significant t-test for differences by race within the disclosure condition. That may well seem paradoxical, given the absence of a statistically significant interaction.

However, do note:

1. The error term and sampling distribution for the overall test of interaction are different than the error terms and sampling distribution for each of the two post-hoc tests for the simple effect of race. That alone could account for the discrepancy.

2. The hypotheses evaluated by each are not the same. The test of interaction is evaluating whether the B - W difference for non-disclosure condition is equal to the B - W difference for the disclosure condition. (Alternatively, whether the disclosure - nondisclosure mean difference is equal across the two levels of race in your design.)

The two post hoc tests are evaluating whether B - W difference = 0 within a specific condition.

In general, the absence of interaction should convince you that, given your sample size and chosen Type I error risk, the degree of difference in B - W across disclosure conditions was not sufficiently different from equality to pursue via post hoc tests. That is, that only the main effects are the influences that reach the level of statistical significance.

Good luck with your work.

If a 2x2 ANOVA (two-way ANOVA) results in significant main effects but an insignificant interaction effect, this indicates that the two independent variables (factors) have significant individual effects on the dependent variable, but their combined effect (interaction effect) is not significant.

In other words, the two independent variables significantly affect the dependent variable regardless of their level combination. The absence of a significant interaction effect suggests that the effect of one independent variable on the dependent variable does not depend on the level of the other independent variable.

For example, suppose we conduct a 2x2 ANOVA to examine the effect of two different types of exercise (factor 1: cardio or strength) and gender (factor 2: male or female) on heart rate (dependent variable). Suppose the analysis shows that there is a significant main effect for factor 1 (type of exercise) and a significant main effect for factor 2 (gender), but no significant interaction effect. This means that the type of exercise and gender both significantly affect heart rate, but the effect of one factor does not depend on the level of the other factor. In other words, the effect of exercise on heart rate is consistent across genders, and the effect of gender on heart rate is consistent across types of exercise.

This is a helpful explanation! Thanks, Ma'Mon Abu Hammad Do you need any main effects analyses or because there are only two groups, you can just interpret the means?