# Tukey's Post-Hoc and pairwise exp error vs experimentwise wise error

#### edieb

##### Senior Member
10+ Year Member
Just a quick question: I know that one advantage of employing a Tukey's HSD vs. an N-K after a significant F ratio is that, unlike N-K, Tukey's does not inflate the experimenterwise error rate. However, isn't it true that Tukey's also keeps the pairwise pairwise error rate at your pre-determined alpha level, too? I guesss I don't see how it can keep both comparisonwise (pairwise) and experimenterwise error rates the same, especially when you look at the experimenterwise equation

experimenterwise error = c(alpha)

c = the # of comparisons

comparisonwise error = alpha

so, from this equation, experimenterwise error will always be greater than comparisonwise. So if the ANOVA alapha is .05 and tukey's keeps this rate the same for comparisonwise error (e.g., .05) then, looking at the experiemeterwise equation, this has to increase if you are doing more than one comparison... can someone explain this?

#### Ollie123

##### Full Member
10+ Year Member
Don't have time to dig through my stats books right now, but I think you are interpreting the equation wrong. I'd read that as c*alpha is the actual error rate, not what you should set your p value at. In other words if you set p = .05 and c = 2, your chances of making a type 1 error are inflated to .1. Thus you need to set a lower p value in order to adjust for this. I know the Bonferroni equation is just .05 divided by number of comparisons. I can't remember Tukey offhand, but I'd look for another equation.

#### edieb

##### Senior Member
10+ Year Member
thanks, that clears it up!