# Effect size with nonparametric data

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• #1117
Alice Ranger
Participant

Dear all,

I have a problem with calculating effect sizes for nonparametric data and would be very grateful for some advice.

In Andy Fields book I found the following formula for calculating effect sizes with data, which is not normally distributed: r = Z/N

Th Z I can find in the SPSS-Ouput of the Wilcoxon-Test and the N is the number of observations.

I measured physiological parameters of 20 twenty newoborns before and after an music intervention, so my N is 40. Is this right?

The interpretation is >.1 small, >.3 medium, >.5 large effect.

Unfortunately I got some strange results using this formula. For example two negative effect sizes, altough the direction of change in physiological parameters was different (one time an increase and one time a decrease).

Has anybody an idea, what or if I’m doing someting wrong?

I hope I described my probelm in an understandable way and haven’t to much errors in my english.

Alice

#1123
Steve Moran
Member

Hi Alice

looks to me like you’re comparing one sample with itself pre & post the stimuli or two different conditions.

According to Chris Chatfield (Problem solving, a statisticians guide p256, ISBN 0-412-60630-5)

“The Wilcoxon signed rank test is a non-parametric substitute for the one sample student-t test and

is particularly suitable for paired differences. He goes on to compare the Wilcoxon rank sum  and the Mann-Whitney U-Test used for two samples.

As for N, it is the number of comparisons.

To test for normality check out the Anderson-darling test then if normal use t-tests etc.

also check out  (Greene & D ‘Oliveira, 0-335-20377-9)  it explains non-parametric techniques using worked examples

(This is all  bringing back memories, believe me lol)

hope this helps

Steve

#1122
Stephen Gorard
Participant

Hi,

As far as I can tell, this is a before and after design with no comparator. Therefore strictly speaking there is no ‘effect’ for any effect size. The design would not permit causal claims. You could simply state the average gain score.

But if you wanted to calibrate the gain scores you could present the mean scores for pre and post, each divided by the mean absolute deviation. As ever with such approaches you have to decide whether use the deviation for all 40 values, or the pre only…. This is distribution free and much simpler than using those fiddly standard deviations.

#1121
Alice Ranger
Participant

Hi,

Maybe I should explain the study design a bit better.

I measured physiologic parameters of 20 newborns before, during and after a music intervention. The same newborns also participated in a control condition where in the “intervention” period no music was played (standard care).

The data is not normally distributed and therefore I chose nonparametric tests.

Alice

#1120
Alice Ranger
Participant

Hi,

Maybe I should explain the study design a bit better.

I measured physiologic parameters of 20 newborns before, during and after a music intervention. The same newborns also participated in a control condition where in the “intervention” period no music was played (standard care).

The data is not normally distributed and therefore I chose nonparametric tests.

Alice

#1119
Stephen Gorard
Participant

This is the first mention of tests. I assume you mean significance tests. These will not help. Ignore them.

You have problems of aging and order in the design you now specify. But ignoring these, you can still summarise the difference between scores for different conditions at the same stage by dividing their mean difference by their mean absolute deviation.

#1118
Alice Ranger
Participant

I don’t think I have problems of aging and order. The two measurements took place at the same day and the order of conditions was randomized.

I will think it through at the weekend!

Alice

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