Date:         Tue, 2 Sep 2003 10:19:04 +0200
Reply-To:     Asesoría Bioestadística
              <bioestadistica@eresmas.net>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Asesoría Bioestadística
              <bioestadistica@eresmas.net>
Subject:      Re: ANOVA or Kruskal-Wallis ANOVA
Content-Type: text/plain; charset=us-ascii

> Marta, in response to your questions about:
>
> - Every sample size (not just the total sample size)
> - Skewness/Kurtosis for every sample
>
> Here it is:
>
> Group A (n=17) Mean= 8.76 (SD=4.42) Min, Max (2,16)
> Skewness= -0.087 (SE=0.550) Kurtosis =-1.256 (SE=1.06)
> Normality:  Shapiro Wilk .937, df=17, p=0.281
>
> Group B (n=22) = 5.50 (SD=2.60) Min, Max (1,12)
> Skewness= 0.611 (SE=0.491) Kurtosis =0.649 (SE=0.95)
> Normality: Shapiro Wilk .957, df=22, p=0.425
>
> Group C (n=8) Mean=6.50 (SD=4.24) Min, Max 0 12
> Skewness= -0.539 (SE=0.752) Kurtosis =-0.863 (SE=1.48)
> Normality: Shapiro Wilk .937, df=8, p=0.580
>
> Group D (n=26) Mean=5.08 (SD=3.10) Min, Max 1,12
> Skewness= 0.613 (SE=0.456) Kurtosis =-0.203 (SE=0.887)
> Normality:  Shapiro Wilk .934, df=26 p=0.099
>
> 1)  By the way, what is the difference between Shapiro Wilk & the Kolmogorov-Smirnov
> Test?

Montecarlo simulations have shown that Shapiro-Wilk test is better than K-S(Lilliefors).

> 2) So within each group, the p-value is not significant for the normality test so the
> hypothesis of normality cannot be rejected
>
> 3) Levene Test 3.17, df1=3, df2=69, p=0.030
> > Homogeneity of variances was rejected
>
> So - do you think a case can be made using ANOVA and then the Tamhane test?

Yes, use Welch or Brown-Forsythe test (if you have SPSS11.x) instead of ordinary ANOVA.
Remember that Tamhane test is highly conservative. If you want something more sensitive
use contrasts and decide which p-value adjustment you are going to use.

This is the coefficient matrix for the contrasts:

-1  1  0  0
-1  0  1  0
-1  0  0  1
 0 -1  1  0
 0 -1  0  1
 0  0 -1  1


> Also - when I ran this, the p-values the output provides are not adjusted for multiple
> comparisons, correct?

Are you talking about Tamhane test. It is already adjusted (and heavily, too). Only
contrasts are not adjusted in any way.
Regards

Marta Garcia-Granero