Is the null-hypothesis for the t-test always "there is no difference"?
It seems like, with the t-test, you always start with "there is no difference". Then you can have either of two things happen:
- The null hypothesis is rejected. In this case, there is a meaningful difference between the two groups.
- The null hypothesis cannot be rejected. In this case, it is inconclusive. You cannot say whether the groups are meaningfully different or not.
It seems weird to me to always start with "the two groups are the same" as your null hypothesis. But I think you are always supposed to use that null hypothesis, regardless of what you are trying to find. Is this true?