Interpreting Mixed Model ANOVA

Question

In a 3 (condition) X 2 (time) mixed model ANOVA. If I hypothesised that anxiety in group A will increase from time 1 to time 2 and my results found no significant interaction but a significant main condition and time effect can I accept the hypothesis or not?

In addition, if main effect of time showed paranoia increased from time 1 to time 2 and main effect of condition A was higher than condition B but not C, can we infer causation? As in can we infer that condition A caused an increase in anxiety or can we only base this on the interaction between time and condition?

I think I'm just confused about whether to accept the hypothesis based on main effects or reject based on non-significant interaction.

Answer 1

There's some confusion here about null hypothesis statistical testing (NHST) and about causation.

In the first question, you would reject the null hypothesis of no effect. That does not automatically mean that you accept a specific other hypothesis, but it may be consistent with it. Note that the relationship between a statistical hypothesis and a research/scientific hypothesis is complicated - they are not the same thing. Depending on which philosophy you buy into, the goal of a study is arguably to try to falsify your research hypothesis - though this practice is rare in many fields.

In the second question, we can say very little about causation based on the limited information you have provided. Causal inference is complicated and requires a number of conditions to be met for a statistical model to provide strong evidence for it. Take a look at the causality tag for relevant threads. This is a good place to start: Statistics and causal inference?