Currently I'm thinking about using confidence intervals to compare the difference in means between a few groups. However, if I understand correctly I need to use the Bonferroni correction if I test multiple hypothesis with the same data set. Obviously, this means that my confidence interval becomes more strict. I wonder if the Bonferroni correction is really neccessary. I read papers that discourage using the Bonferroni correction and one should rather take a look on effect sizes to interpret the results.
Are they correct? Is the Bonferroni correction really overrated and one should rather use effect sizes to interpret the results?