If I understand you... you are not correct.

1. To compare the

**means **you need to run the One way ANOVA test and then the "regular" Tukey HSD

http://www.statskingdom.com/180Anova1way.html
It will also give you the R code, so you may run on R if you don't trust an online calculator.

2. To compare the variances you need to run the Levenes test, I believe the Tukey HSD test in the Levene's calculator runs over the differences, say compared only the variances.

You may get there also the R code for the Levenes test, but not for the Tukey HSD over the differences.

But calculating the differences is very easy so you may also try to run on R.

3. When comparing the

**variances **should you use

**median **or

**average**?

I assume using the median is more robust for non-normal data, but probably less powerful, that's probably why the p-values were higher.

If the data is reasonably normal your the sample size is more than 30 you should probably use the mean as the center.

PS did you calculate the sample size before?

OBH and Katxt -- Thanks so much for these extremely informative and helpful responses. I'm replying to OBH's above message because I understand it to be a summary of the approach I should use to test both hypotheses. The process for testing the first hypothesis (comparison of the

**means**) is now clear to me. From what I understand, the tests for H1 should be conducted separately from the Levene's test using the ANOVA/Tukey operations described above. This all seems very straightforward, but please let me know if I'm mistaken.

Regarding the tests for H2 (comparison of the variances), I'll summarize your advice here, and you can let me know if this is correct:

First, I'll address a point that we haven't yet discussed explicitly: I assume the standard deviations calculated as part the Levene's test (or Brown-Forsythe if using the median) can be reported as measures of internal variance for each group. I'm asking this because the Tukey output for the Levene's calculator appears to report differences between group

**means**, not between group

**variances**. When I hover the cursor above the "differences" column in the Tukey table, it tells me that "differences" actually refers to group means. In the event that the differences in variance

**aren't **automatically calculated in Levene's, OBH notes that "calculating the differences is very easy so you may also try to run on R," but I'm not sure how exactly this should be done. Can you clarify?

Second, when

**comparing **the group variances (pairwise), the p-values in the Levene's test Tukey table should indicate whether the differences in variance are statistically significant. If my data are reasonably normal and the sample size is above 30 (as it is), I should select the

**mean** as the center. In this case, the test I'm conducting is Levene's. Otherwise, if the groups have non-normal distributions, I should select the

**median.** If I select the median, the test is called Brown-Forsythe, even though I'll be using the Levene's calculator to get the results. Notably, Katxt orignially wrote: "What Zach is looking for (I think) is which particular groups have variances that are probably different from other particular groups." This is absolutely correct, and it led Katxt to recommended different tests, but from what I understand, Katxt now agrees with the above advice from OBH.

Is all of this correct? Are OBH and Katxt in agreement? Also, if possible, could you clarify how the differences in variance might be calculated? Again,

**THANK YOU** for this extraordinary advice!

Zach