# t-test or f-test

#### craighopper

##### New Member
Hi all,

Apologies for the nature of my post but I'm a relative beginner to statistical tests. What I would like to know, is if I have two sets of data (as I'm a microbiologist, the data sets are likely to be bacterial colony size measurements on two different agar plate types), why would I choose to do the t-test over the f-test and vice versa?

From my understanding, the t-test is used when the standard deviations of the two sets of data are not significantly different from one another, and the f-test is used when the SDs are significantly different from one another. But my question would be: how do we define "signficantly different from one another" without performing some kind of analysis? Any help would be appreciated. Go easy!

Thanks,

Craig

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Are you interested in comparing central tendency? If so, the distribution of the residuals and sample size usually dictate if you run a parametric or nonparametric test. T-test is a parametric test used to compare two means. The f-test is not used for this specific purpose, it can be used for an overall test if you have 3 or more groups you are comparing and then the t-test is used for pairwise comparisons.

So if you have two sets you would examine the residuals and see if the t-test or Wilcoxon rank sum would be appropriate. If you had more groups you may use the f-test within ANOVA to initially compare all of the groups if the residuals were normally distributed or the same size large enough (sometimes a cutoff of n=30 is used). Then you may follow-up with pairwise ttests. Another test is typically used to examine the equality of the variance to help understand which ttest results to use.