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I have a dataset containing the selling price of mineral stones that were sold in five different countries (namely Germany, France, Italy, Belgium and Spain). I am running multiple t-tests check if average selling prices in the selected countries significantly different from each other (i.e. Null hypotheses are: average price Germany= average price of France; average price Italy = average price Belgium; average price France= average price Spain etc.).

I know that running multiple t-tests increases the chances of committing a Type I error and I have found that the Bonferroni correction can be used to protect from Type I error. The question is, should I use it in this case?

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    $\begingroup$ The Bonferroni correction is certainly one way to protect against a Type I error. But do you need to protect yourself against that? I'm not saying you don't. But one needs to think of the consequences of doing so or not doing so. And, do you really need to perform hypothesis tests? In other words, is "estimation" more appropriate than hypothesis testing? $\endgroup$
    – JimB
    Apr 17 '20 at 17:32
  • $\begingroup$ Thank you for answering! Unfortunately, my supervisor wants me to run hypothesis testing with t-tests. $\endgroup$
    – Matrix2020
    Apr 17 '20 at 17:42
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If you want to control type I error probability you may use Bonferroni, but this is an all-around method which is not best in all situations. From what you say of your problem, I think using the studentized range distribution or Scheffé's test might be more adequate.

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If you want to compare the average price across 5 countries this should be a one-way ANOVA with post-hoc tests to identify significant differences between pairs. Any standard software will allow a range of multiple comparison corrections. Bonferroni is one option but I would go for Tukey's HSD and/or Fisher's LSD. Tukey's HSD is more conservative and better when looking at confidence intervals, Fisher's LSD is better when you are interested in a specific comparison as it controls comparison-wise Type 1 error.

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