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Sorry for the dumb question. Perhaps this is too obvious but i don't see it. Will appreciate any help. We're analyzing a gene expression dataset of 64 autistic individuals vs 82 normally developed individuals. This dataset is used in this paper here: paper We find that the mean and standard deviation of the (log normalized) data from each group is almost exactly the same. A previous question using this data was asked here: how to interpret normal plot shaped like sigmoid

The plots comparing mean (x-axis) and std. deviation(y-axis) for two groups above look as below: normal plot

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    $\begingroup$ Why shouldn't it? Mean number of legs in human (or any other specie) males and females is exactly the same, you can find a number of other properties like this. $\endgroup$ – Tim Nov 27 '18 at 9:25
  • $\begingroup$ @Tim thanks :) but then,if those are the only features (legs) available, then we have no means to discriminate between the 2,isn't it?Here,we have 54000 genes.If the mean and sd of the genes in each population group is same,then,this means the genes are not useful for differentiating between these 2 groups of people,is it not? $\endgroup$ – Mvkt Nov 27 '18 at 9:46
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    $\begingroup$ I guess the genes are correlated, am I correct? So the "effective" number of them is smaller. Random link from the web told me that I'm 99.5% similar to any other human in terms of genes and ~97% to chimpanzees, and 60% to flies, so I guess it could be hard to spot the difference based on some global summary statistics... $\endgroup$ – Tim Nov 27 '18 at 9:54
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    $\begingroup$ That the mean and sd distribution are similar does not mean that at individual level of the genes there might be a lot of differences (which is the basis of all the differential expression analysis). $\endgroup$ – llrs Nov 27 '18 at 11:02
  • $\begingroup$ @llrs ok,thank you.Can you please provide a good reference textbook for differential gene expression analysis with R/matlab/python ? $\endgroup$ – Mvkt Nov 27 '18 at 11:12
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There is no reason why two different populations can't have very similar mean and standard deviations. As pointed out by Tim in a comment to your question, if you are measuring similar things in two different populations, but the thing you are measuring is not affected by the differences between the groups, then the measurements for those two groups should be similar.

For instance, if you are estimating the effect of some treatment on a disease, and the treatment in question has no effect whatsoever, then the treated and the controls should have similar means and standard deviations of the outcome. Similarly, if you are investigating if the income of an individual depends on the weekday that he or she was born, then it seems very reasonable that the distribution of the income should be very similar in both those groups too!

It is worth noting, however, that even if the two populations have the same mean and standard devation, this does not mean that their distributions are equivalent. A classic illustration of this phenomenon is the famous Anscombe's quartet. (Though I am personally very fond of its humorous extension known as the Datasaurus Dozen.)

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  • $\begingroup$ Thanks Phil.Yes,I just replied back to Tom's answer.Like you point out,using day of week to predict income is not going to be useful.But here,we have gene expressions of control vs differently abled samples.It is fair to expect that the mean and sd of the 50K+ gene features are different,is it not?In this case,it also seems that the distributions are equivalent.Pls see the qqplot in the previous question(link provided in question) $\endgroup$ – Mvkt Nov 27 '18 at 9:49

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