Suppose that I sample 4 independent datasets from different, 1D normal distributions: data1, data2, data3 and data4.

I want to test if data1 and data2 have closer means compared to data3 and data4, e.g if

I define the following variable

Then,

At the end I can compare

Do you think that to be correct if then I correct the final alpha for multiple testing ?

Thank you in advance

I want to test if data1 and data2 have closer means compared to data3 and data4, e.g if

**|m_1 - m_2| < |m_3 - m_4|**I define the following variable

**Zij**:**if m_i - m_j > 0 (do a ttest): Z_ij = x_i - x_j**

elseif m_i - m_j < 0: Z_ij = x_j - x_i

where x_i ~ N(m_i, s_i), x_j ~ N(m_j, s_j)elseif m_i - m_j < 0: Z_ij = x_j - x_i

where x_i ~ N(m_i, s_i), x_j ~ N(m_j, s_j)

Then,

**Z_ij ~ N(|m_i - m_j|, sqrt(sigma_i^2+sigma_j^2))`.**At the end I can compare

**Z_12**and**Z_34**with another**ttest**.Do you think that to be correct if then I correct the final alpha for multiple testing ?

Thank you in advance

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