A researcher has taken tissue cultures from 25 subjects. Each culture is divided

Question

A researcher has taken tissue cultures from 25 subjects. Each culture is divided in half, and a treatment is applied to one of the halves chosen at random. The other half is used as a control. After determining the percent change in the sizes of all culture sections, the researcher calculates the independent sample $t$-analysis. Finding that the paired $t$-analysis gives a slightly larger standard error (and gives only half the degrees of freedom), the researcher decides to use the results from the unpaired analysis. Is this legitimate? Discuss whether the $p$-value from the independent sample $t$-analysis will be too big, too small, or about right

Explanation / Answer

P-value from the unpaired test will be smaller in size than the p-value from the paired t-test because intra-subject vriability is reduced.

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