I've recently started to brush up my statistics, and have begun doing so with two of the most often used statistical tools in my field: the t-test and ANOVA.
Reading up on popular information sources such as wikipedia (none of which provided citable references for the following statements - sadly) I have concluded that the null hypotheses tested by these tools are:
t-test: The t-test is a method used to test the null hypothesis that means of two compared groups are equal.
(one-way) ANOVA: Formally, ANOVA tests the null hypothesis that the means of multiple defined groups are equal.
My adviser told me both these statements are very wrong, and that “inference-statistical methods do not test the equality of means”; but offered no further clarification. I'm wondering whether I'm misrepresenting the information I have read.
So, could you tell me what the null hypotheses of these tests are then? also, do you know what sources I could cite for this (since it's obvious I'm not stating my own independent conclusions)?