Sample Size for KruskalWallis Test
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 This topic has 3 replies, 2 voices, and was last updated 8 months, 2 weeks ago by Robert Butler.

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January 13, 2020 at 4:08 pm #245008
WojtekParticipant@pacocapo Include @pacocapo in your post and this person will
be notified via email.Hi,
How could I check sample size recommended for KruslaWallis test?
I got 13 subgroups (weight group) with 8 variables each (104 results in total). Data is non normal distributes and box plot shows no outliners.
I run KruskalWallis in Minitab to find out if medians of subgroups are the same. P = 0,000, which is less than 0,05 so Ho is rejected.
Test shows that there is at least one difference among the medians in weight group.
Is there anything alse i should take into concideration?
Regards
0January 13, 2020 at 4:35 pm #245009
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.your post is confusing. What I think you are saying is the following:
You have 13 groups and each group has 8 samples.
The data is nonnormal
You checked the data using boxplots and didn’t see any outliers
You chose the KruskalWallis test because you had more than 2 groups to compare.
You ran this test and found a significant pvalue.
If the above is correct then there are a few things to consider:
1. You don’t detect outliers using a boxplot. The term outlier with respect to a boxplot is not the same thing as a data point whose location relative to the main distribution is suspect.
2. ANOVA is robust to nonnormality – run ANOVA and see if you get the same thing – namely a significant pvalue. If you do get a significant pvalue then the two tests are telling you the same thing.
The issue you are left with – regardless of the chosen test is this – which group or perhaps groups are significantly different from the rest. In ANOVA you can run a comparison of everything against everything and use the TukeyKramer adjustment to correct for multiple comparisons. In the case of the KW you would use Dunn’s test for the multiple comparisons to determine the specific group differences.
If you don’t have access to Dunn’s test you will have to run a sequence of WilcoxonMannWhitney tests and use a Bonferroni correction for the multiple comparisons.
0January 14, 2020 at 4:49 am #245466
WojtekParticipant@pacocapo Include @pacocapo in your post and this person will
be notified via email.Thank you Robert for reply:
1. IMR chart doesn’t show any suspected points.
2. ANOVA provides pvalue=0,000 same as KW. Despite the fact that:
a) each 13 groups is nonnormal distributed;
b) Equal Variances test provides pvalue=0,000.
Turkey Pairwise, provides info, which means are different from each other.
The last question – how could I check if samle size of 8 pcs for each 13 groups have power of 90%?
0January 14, 2020 at 8:55 am #245469
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.To answer your question:
There are two equations one for alpha and one for beta.
What you need to define is what constitutes a critical difference between any two populations (max value, min value)
What you have is the sample size per population (8) and for the conditions you have specified you have 1.645 (for the alpha = .05) and +1.282 ( for beta = .1).
the alpha equation is (Yc – Max value)/(2/sqrt(n)) = 1.645
the beta equation is (Yc – Min value)/(2/sqrt(n)) = 1.282
subtract the two equations and solve for n.
Obviously you can turn these equations around – plug in n = 8 and solve for the beta value and look it up on a cumulative standardized normal distribution function table and see what you have.
A point of order: As I mentioned earlier ANOVA is robust with respect to nonnormality. Question: with 8 samples how did you determine the samples were really nonnormal? If you used one of the many mathematical tests for nonnormality – don’t. Those tests are so sensitive to nonnormality that you can get significant nonnormality declarations from them when using data that has been generated by a random number generator with an underlying normal distribution. What you want to do is plot the values on probability paper and look at the plot – use the “fat pencil test” – a visual check to see how well the data points form a straight line.
If you are interested in seeing just how odd various sized random samples from a normal distribution look I would recommend you get a copy of Daniel and Wood’s book Fitting Equations to Data through interlibrary loan and look at the plots they provide on pages 3443 (in second edition – page numbers may differ for later editions)
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