1. ## Questions about Tukey's HSD/Scheffe Test

I heard Tukey Test can be used for unequal sample sizes. My assumption is that you must use some kind of weighted average of n for all groups. Correct me if I am wrong.

Anyone know the general formula to compute Scheffe Test? I've found a few resources on it, but they kind of had conflicting information.

Also, is there a calculator of some sort to compute the q statistic for Tukey's HSD? The data I am trying to analyze has a k = 13 and the q tables on the web only have values up to k = 10.

2. Correct me if I am wrong.

Well, the computation of q is based on the harmonic mean of the samples (taken pairwise) i.e.

q=(YBari-YBarj)/Sqrt[MSw/n*] where n*=2/(1/ni + 1/nj) and MSw is the Mean Square Within (or Error) from the overall ANOVA analysis. Note that YBari and YBarj are the means of group i and group j.

This is as the Tukey-Kramer post hoc test.

As to Scheffe test it is:

Fcv=(k-1)F_alpa-rate(k-1,dfw), where the alpha-rate is, say .05, and dfw is the degrees of freedom within (error) from the overall ANOVA summary.

Note that the Scheffe test is a conservative test and I would not use this.

Last Part: If you give me your degrees of freedom within (dfw), I can provide you with the critical value.

Note: If you use SPSS for k=13 groups then you should have any trouble doing this.

3. Originally Posted by Dragan
As to Scheffe test it is:

Fcv=(k-1)F_alpa-rate(k-1,dfw), where the alpha-rate is, say .05, and dfw is the degrees of freedom within (error) from the overall ANOVA summary.

Note that the Scheffe test is a conservative test and I would not use this.

Last Part: If you give me your degrees of freedom within (dfw), I can provide you with the critical value.

Note: If you use SPSS for k=13 groups then you should have any trouble doing this.
So, it is best to use Tukey's method for post-hoc pairwise comparisons? Do I have any other options? And, df(w) = 582.

4. Originally Posted by this_barb
So, it is best to use Tukey's method for post-hoc pairwise comparisons? Do I have any other options? And, df(w) = 582.
The critical value of q = 4.68 for alpha=0.05.

As to the first part, Tukey's test is often complained about as being too conservative as well (but Scheffe's test is even worse). There's also the Student-Newman-Kuels (S-N-K) but this is also complained about in the literature and texts as being too liberal.

It appears your doing these calculations by hand calculator. Is that right?

I would suggest that you get access to SPSS and enter your data and use the Ryan procedure (so-called REGWQ test). I think that would be your best way to go. This test is sort of a compramise between Tukey's conservative test and the S-N-K liberal test.

If your stuck, and don't have access, I'd suggest you use Tukey's test.

5. Originally Posted by Dragan
The critical value of q = 4.68 for alpha=0.05.

As to the first part, Tukey's test is often complained about as being too conservative as well (but Scheffe's test is even worse). There's also the Student-Newman-Kuels (S-N-K) but this is also complained about in the literature and texts as being too liberal.

It appears your doing these calculations by hand calculator. Is that right?

I would suggest that you get access to SPSS and enter your data and use the Ryan procedure (so-called REGWQ test). I think that would be your best way to go. This test is sort of a compramise between Tukey's conservative test and the S-N-K liberal test.

If your stuck, and don't have access, I'd suggest you use Tukey's test.
Yes, since I don't have access to any of the statistical programs, I am using Excel and a calculator. Thank you for your timely response.

6. I am able to use SPSS in the psych lab at my college. I tried using the REGWQ post hoc test, but I'm not sure how to interpret the results. More specifically, it states that it shows homogeneous subsets of means, but I'm not even sure what a subset is. For reference, here is the results table.

How should I go about interpreting this?

7. How should I go about interpreting this?[I]

Reject the following hypotheses:

Mu1=Muj for j=3,4,5,...,14
Mu2=Muj for j=3,4,5,...,14
Mu3=Muj for j=8,10,11,...,14
Mu4=Muj for j=8,10,11,...,14
Mu5=Muj for j=8,10,11,...,14
Mu6=Muj for j=8,10,11,...,14
Mu7=Muj for j=10,11,12
Mu8=Mu12
Mu9=Muj for j=10,11,12

and that should do it.

8. Originally Posted by Dragan
How should I go about interpreting this?[I]

Reject the following hypotheses:

Mu1=Muj for j=3,4,5,...,14
Mu2=Muj for j=3,4,5,...,14
Mu3=Muj for j=8,10,11,...,14
Mu4=Muj for j=8,10,11,...,14
Mu5=Muj for j=8,10,11,...,14
Mu6=Muj for j=8,10,11,...,14
Mu7=Muj for j=10,11,12
Mu8=Mu12
Mu9=Muj for j=10,11,12

and that should do it.
Ah, thank you very much. Now it makes sense.

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