How to rigorously justify using a T-test rather than just bar(X)-bar(Y)?

balafiavatv

balafiavatv

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2022-08-19

How to rigorously justify using a T-test rather than just X ¯ Y ¯ ?

Answer & Explanation

Kelton Glover

Kelton Glover

Beginner2022-08-20Added 17 answers

When you have to estimate σ based on the sample data, there is some error in the estimate.
When you make predictions on the distubtion of X if you assume normality with an accurate measurement of σ you will predict results in too narrow of a band.
The t-distribution accounts for this mis-estimation in σ and predicts a fatter tailed distribution.

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