Hello,
I have two samples of proteins. The data represent the presence (1) or absence (0) of each protein in each sample, such as I obtain a table like in the image below, with a protein either present in one (0 1 or 1 0) or both sample (1 1), with the names representing my proteins and the clubs my samples.
My goal is to have a statistical test that would determine if the samples, containing hundreds of proteins, are homogeneous (that is, there is a lot of proteins present in both samples) or heterogeneous (few or very few proteins in common). Right now the only thing I could do is just a percent share between the samples (for example 30/142 in common, which is 21%) but I am being asked for a statistical test that would show a probability, between 0 and 1, that the sample are homogeneous or heterogeneous.
Thanks !
Hi Alexis,
The test you need is called McNemar's Test and is found in all major statistical packages. Line up the two samples as such:
In Sample 1 In Sample 2
Protein A Y Y
Protein B Y Y
Protein C Y N
The statistic:
(N (Yes in Sample 1 No in sample 2) - N(No in Sample 1 Yes in Sample 2))^2
/
(N(Yes in Sample 1 No in Sample 2) +N(No in Sample 1 Yes in Sample 2))
has a chi-square distribution with one degree of freedom (in case you want to compute the probability by hand.)
Wikipedia has a fuller account along with some examples:
https://en.wikipedia.org/wiki/McNemar%27s_test
Best,
Aran
McNemar won't do what the question is asking.
For McNemar's test, a result is positive (significant ) if the count of cases for 0, 1 are much greater than count of cases for 1, 0 (or vice-versa). In the test, cases for 0, 0 and 1, 1 aren't considered. So, if half of the cases were 0, 1 and half were 1, 0 the p-value would be 1 (no effect), even though the samples were perfectly heterogeneous. But if nearly all the samples were 0, 0 or 1, 1, the p-value would also be 1 (no effect), even though the samples were nearly perfectly homogeneous.
Off the top of my head, I might recommend counting the cases considered to be homogeneous and counting the cases considered to be heterogeneous, and using a binomial test to see if the proportion of heterogeneous cases is different from an "expected" or null proportion.
The difficulty will be determining what makes sense for a null proportion. The usual way is to assume that you are testing against the cases being randomly distributed to the categories, or a proportion of 0.5 for two categories. But some other null proportion may make sense in reality for your data.
Below is code in R for an example.
zero_zero = 12
zero_one = 22
one_zero = 19
one_one = 11
homogeneous = zero_zero + one_one
heterogeneous = zero_one + one_zero
total = homogeneous + heterogeneous
homo_percent = homogeneous / total
homo_percent
hetero_percent = heterogeneous / total
hetero_percent
binom.test(heterogeneous, total, 0.5)
Thanks for the answers !
There are no zero_zero conditions though, only the three others, so homogeneous would be only one_one.
Right now binom.test(heterogeneous,total,0.5) rejects the null hypothesis with 95% confidence (result is > 0.05) so that would mean the samples are homogeneous ? Could I do instead binom.test(homogeneous,total,0.5) which gives me a result
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