what test to use on z-scores

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Joanne Hall
Joanne Hall 2023-3-25
评论： Star Strider 2023-3-26
Dear matlab,
I have z-scores of 2 groups. I want to compare them.
What test in matlab should I use for relative comparison using just the z scores?
Thanks in advance for any guidance!
Joanne
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Star Strider
Star Strider 2023-3-26
@Joanne Hall — As I illustrated in my Answer, unless you can reconstitute the original data from the respective means and standard deviations, there is nothing you can do to compare the two groups. Standardizing them erases any differences the two groups may once have had. However if you have the original means and standard deviations from each group, and if they are normally distributed, those are all you need to use to compare them.
Again, if you no longer have the means and standard deviations, you have my sympaties.
Joanne Hall
Joanne Hall 2023-3-26
Thanks Star, see answr below

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Star Strider
Star Strider 2023-3-25
Ran in:
Since the zscore is simply a standardised method of expressing data, and if the mean values and standard deviation (std) values of each group are known, it is possible to map back to the original data and then do a valid comparison. However, if that information is not available and so it is not possible to cannot back-calculate to the original data, then your ability to discriminate the two gropus is likely lost, and no test will produce a valid comparison.
An example using random original and standardised data and the Wilcoxon ranksum test (assuming that the two groups are not paired) illustrates the issue —
x = randn(25,1);
y = randn(25,1)*3+5;
zx = zscore(x);
zy = zscore(y);
[p1,h1,stats1] = ranksum(x,y) % Original Data Are Significantly Different
p1 = 1.3090e-07
h1 = logical
1
stats1 = struct with fields:
zval: -5.2776 ranksum: 365
[p2,h2,stats2] = ranksum(zx,zy) % Standardised Scores OF The Original Data Are Not Significantly Different
p2 = 0.8009
h2 = logical
0
stats2 = struct with fields:
zval: -0.2522 ranksum: 624
So while the original data in this example are significantly different (the ranksum test assumes that both groups have the same underlying distribution, although the distribution itself is irrelevant), the standardised scores of the same data are not.
It is not worth the effort to compare the standardised scores, since any differences between the two groups that might have originally existed are lost in the standardisation process.
You have my sympathies.
.
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