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Let's say there are two groups of participants. Each group is randomly split into control subgroup A and task subgroup B. For each of the 4 cases some random variable $x$ is measured, whose mean is denoted by $\mu$. I would like to perform 3 tests:

1. $H_0 : \mu_{A, Group1} \neq \mu_{B, Group1}$
2. $H_0 : \mu_{A, Group2} \neq \mu_{B, Group2}$
3. $H_0 : \mu_{Group1} \neq \mu_{Group2}$ regardless of subgroups

I sketch the tests below

Question: What is the correct way to perform these tests? If I perform 3 independent t-tests, is it fair to apply Bonferroni correction to their p-values, or must I do a more sophisticated multiple comparisons correction. If making independent tests is not a robust procedure, what is? I want to do all 3 tests, so as far as I understand I don't want two-way ANOVA.

Let's say there are two groups of participants. Each group is randomly split into control subgroup A and task subgroup B. For each of the 4 cases some random variable $x$ is measured, whose mean is denoted by $\mu$. I would like to perform 3 tests:

1. $H_0 : \mu_{A, Group1} = \mu_{B, Group1}$
2. $H_0 : \mu_{A, Group2} = \mu_{B, Group2}$
3. $H_0 : \mu_{Group1} = \mu_{Group2}$ regardless of subgroups

I sketch the tests below

Question: What is the correct way to perform these tests? If I perform 3 independent t-tests, is it fair to apply Bonferroni correction to their p-values, or must I do a more sophisticated multiple comparisons correction. If making independent tests is not a robust procedure, what is? I want to do all 3 tests, so as far as I understand I don't want two-way ANOVA.

Let's say there are two groups of participants. Each group is randomly split into control subgroup A and task subgroup B. For each of the 4 cases some random variable $x$ is measured, whose mean is denoted by $\mu$. I would like to perform 3 tests:

1. $H_0 : \mu_{A, Group1} \neq \mu_{B, Group1}$
2. $H_0 : \mu_{A, Group2} \neq \mu_{B, Group2}$
3. $H_0 : \mu_{Group2} \neq \mu_{Group2}$ regardless of subgroups

I sketch the tests below

Question: What is the correct way to perform these tests? If I perform 3 independent t-tests, is it fair to apply Bonferroni correction to their p-values, or must I do a more sophisticated multiple comparisons correction. If making independent tests is not a robust procedure, what is? I want to do all 3 tests, so as far as I understand I don't want two-way ANOVA.

Let's say there are two groups of participants. Each group is randomly split into control subgroup A and task subgroup B. For each of the 4 cases some random variable $x$ is measured, whose mean is denoted by $\mu$. I would like to perform 3 tests:

1. $H_0 : \mu_{A, Group1} \neq \mu_{B, Group1}$
2. $H_0 : \mu_{A, Group2} \neq \mu_{B, Group2}$
3. $H_0 : \mu_{Group1} \neq \mu_{Group2}$ regardless of subgroups

I sketch the tests below

Question: What is the correct way to perform these tests? If I perform 3 independent t-tests, is it fair to apply Bonferroni correction to their p-values, or must I do a more sophisticated multiple comparisons correction. If making independent tests is not a robust procedure, what is? I want to do all 3 tests, so as far as I understand I don't want two-way ANOVA.