# Two-way ANOVA significant, Oneway ANOVA & T-test not signficant?

Testing for the interaction of Gender on Type (grouping variable, group A & B) for a 'Test' score -

model.lm <- lm(formula= Test~ Type + Gender + Type*Gender,
data=describeDF3,na.action=na.omit)
Anova(model.lm,type='II',white.adjust='hc3')


White adjust as unequal variance.

Results came up as Type significant and Gender significant but no interaction. I used both a oneway.test ANOVA and t-test to check the Gender effect but in these tests it is coming up as not significant. Why is this?

Is it because the two way test shows whether the variable creates a reduction in the deviance of the lm and the oneway tests look at differences in means?

Any help understanding this would be great!

Rachel

## 2 Answers

It's impossible to be sure which of (at least) two possible explanations might apply without seeing actual data (or possibly both), but the first thing I'd suggest is that it's probably because if you leave out an important effect the estimated error variance will be inflated, potentially reducing the test-statistic below significance.

(The second obvious possibility relates to potential negative dependence between factors, but I'd start with the inflated error-variance issue)

There's some discussion of both of these in an answer to this related question: If I'm not interested in the interaction, is there any reason to run a Two-Way ANOVA instead of two One-Way ANOVAs?

(the question is rather different, but one of the answers is similar)

When you do two way ANOVA test, you find both type and gender are significant. It means type factor is significant under the control gender. Gender is the same. But when you do one way type or gender ANOVA test, you doesn't control gender or type, which is why one way ANOVA test shows both type and gender are not significant. Although two way test shows type and gender has no interaction effect, you still need to control one factor to test another factor unless you are sure another factor is not significant.