The section "Bonferroni Comparisons" in the book Applied Statistics for Engineers and Scientists, Petruccelli at el. (1999), the authors wrote:
Bonferroni intervals are ideal for making a small number of pre-specified comparisons (i.e., comparisons decided on before looking at the data).
I don't understand how the comparisons can be made without looking into the data (= it means data snooping?)? I mean without data how one can even construct the interval?
Yes, prespecified comparison can easily be misunderstood. What is meant here should be seen in a situation where you can make many tests with the same data. The most common case is: you have two samples, and many variables measured on them, and you want to test if the samples come from the same population. Then you could make a separate test on each of the variables.
For example, you measure 100 variables like height, weight, bmi, age, ... on people from town A and town B and want to check the null hypothesis, that it does not matter if you come from town A or B.
Then it is not correct to make 100 tests and say, if one of them is significant, then I conclude that A and B are different. For example, if you set significance level to 5%, you would on average in such a situation have 5 tests that are significant, even if A and B are in fact the same population.
The Bonferroni correction takes care for that by adjusting the significance level for each of the $m=100$ tests. It requires that you have to have at least one test with a p-value of $\alpha/m$ in order to be allowed to say that A $\neq$ B. In our example, one of the 100 tests would need to reach $p \leq 0.0005$!
To avoid that you need one test with a very low p-value, it is a good idea to work with fewer tests. Selecting these tests in advance is meant by "prespecified comparisons". One should typically look at the scientific question and decide for which of the 100 variables you would expect a difference at all, if the populations of A and B are not the same.
In practice, people often look at the data in advance, but this is not correct methodology. Then the comparison are no longer prespecified.
