"In statistics, family-wise error rate (FWER) is the probability of making one or more false discoveries, or type I errors, among all the hypotheses when performing multiple hypotheses tests."
"The false discovery rate (FDR) is one way of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons."
I don't understand the difference between these two concepts. How do they not mean the same?
Perhaps you can help me by further elaborating the following example:
Say the probability for an unbiased coin to substantially deviate from a 50/50 head/tail-distribution in a sequence of 1,000 tosses is 0.001.
If I want to find out if one coin is biased I throw it 1,000 times and if it shows heads ~500 times I can be quite sure it is not biased.
However if I throw a million coins 1,000 times and deem those biased who don't show a 50/50-distribution of heads and tails, I will categorize unbiased coins as biased, because the probability of an unbiased coin showing deviating from the 50/50-distribution is multiplied by the number of coins (1 million).
Thus from a set of one million unbiased coins, I have to expect about 1,000,000*0.001=1,000 coins to deviate substantially from the 50% tails, 50% heads-distribution.
As far as I understood this is multiple hypotheses testing (synonymous: multiple comparisons?) as I am testing the hypothesis "coin is unbiased" a million times, and the false discovery rate FDR is 1,000 in this example.
But what, then, is the FWER (family wise error rate)?