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when doing a two sample t test, is the sample dofference different from the difference of...

when doing a two sample t test, is the sample dofference different from the difference of the means? example, if the mean age of death is 73 and the mean age of survival is 62...what would be the didference of the means (11?) and would this be the same for the sample difference? there are 51 subjects in the death category and 49 in the survival category (2? for sampel difference?)
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Answer #1

Case 1:

If the 2 samples are of same size:

i.e.,

If Size of Sample 1 = n1 = Size of Sample 2:=n2:

the sample difference is same as the difference of the means,

because of the formula: E(X - Y) = E(X)- E(Y).

Case 2:

If the 2 samples are not of same size:

i.e.,

If Size of Sample 1 = n1 Size of Sample 2:= n2:

For example: there are 51 subjects in the death category and 49 in the survival category :

the sample difference different from the difference of the means, In fact E(X - Y) cannot be calculated because X and Y are of different dimensions.

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