# Comparing two F-test statistics

I have two groups A and B, each of which consists of 5 samples. Each sample is described in a vector of length (>1000) of continuous numeric values (characteristics). I want to test if the sample in the first group varies between each other more than the sample in the second group.

I tried one-way ANOVA for each group independently and calculated the F-test statistic for each group. Now, can I compare the two obtained statistics directly (so if statistic 1 > statistic 2 I say the first group has more variance between its samples than the second group)? or do I need to perform statistical significance to compare the two statistics?

• Have you tried two way ANOVA?
– SAAN
Aug 3, 2013 at 3:23
• +1 to two-way as the way forward. Note: Various problems of terminology here. I have edited fairly strongly and assumed that by "scores" you mean "statistics". Aug 3, 2013 at 7:57
• Thanks @NickCox for the answer and the accurate edit. As far as I know, the purpose of two-way ANOVA is to find out whether data from two groups have a common mean. However, I want to prove that samples in one group are more different between each other than the difference between samples in the other group. So, I think two-way ANOVA may not work. I performed one-way ANOVA on each group independently to prove that samples in each group are different between each other. Then used the F-statstic scores to compare the group1 difference to group2 difference. What do you think? Aug 3, 2013 at 15:50
• What you describe sounds like an interaction. A two-way ANOVA would still be the way to go but you would simply not be primarily interested in the main effects, only in the interaction term.
– Gala
Aug 3, 2013 at 17:05
• The question is unclear. Your data are in two 5 x 1000+ matrices: one for group A, one for group B. In each matrix, rows correspond to samples and columns correspond to characteristics. Are all the characteristics in the same (or comparable) units? What variances are you talking about: down each column, giving you 1000+ variances for each group; or across each row, giving you 5 variances for each group? Aug 4, 2013 at 6:35

• If you have several response variables (Category $A$ have five samples it does not mean five variable) than it is multivariate regression model. And do not think "shall I generate a regression model for each group" because it highly influenced precision of the model. You must have one data file under the columns response variable and classified variables. In response variable distinct columns can come and in classified variables( I think you have two, category and Samples) e.g first response variable belong to category $A=1$ and first sample=1, second value category $A=1$ second sample=2.