I have a very simple model where I measure the effect of tone of voice on purchase intention, moderated by brand alignment. I have a 2x2 between subjects model, with tone of voice levels being informal vs formal, and brand alignment levels being warm vs competent.

When I run a two-way anova, I see that the main effect for tone of voice is not significant. However when I run it in a one way ANOVA, this effect is significant. Can someone explain why this is, and if i were to report the one way anova would this be incorrect?

for bachelors thesis