# Tukey test in factorial experiment

Use Tukey's test to determine which levels of the pressure factor are significantly different for the data. I already did the anova table My question is when making comparisons in Tukey test, as shown in the table above the interaction between temperature and pressure is not significant. When I read the text the impression I had is that when the interaction is significant, we choose only one level of the factor to make comparisons, ie in this case we chose only one temperature to compare the pressures.

I misunderstood or even when there is no interaction between the factors just choose one of the levels to make comparisons?

One more thing, when using the Tukey test the parameters for $qtukey(1-\alpha,a,ab(n-1))$ right?

Could someone explain me the parameters of $qtukey(1-\alpha,x,y)$? What is $x$ and $y$?

X and Y used only to illustrate

## 1 Answer

I think Tukey originally developed it for 1-way ANOVA, meaning it will work also work for $a*b$ ANOVA with interaction, since the latter is equivalent to 1-way ANOVA with $a*b$ treatments. I tried searching for Tukey formula for $a*b$ ANOVA w/o interaction, but found nothing. However, it is implemented in PROC GLM where you can apply Tukey to an additive model (link).

If you want to do it by hand, then the correct formula is:

$qtukey(1-\alpha,ab,ab(n-1))$

because, when interaction is in, the number of treatements is $a*b$, not $a$.

• But in this case there is no interaction because $p.value=0.47$, I still need to consider a * b treatments? – user72621 Oct 15 '15 at 1:46