Discussion
An experimenter conducts an experiment using a control group containing 8 subject and an experimental group containing 8 subjects. How many degrees of freedom are there in this experimental design if the groups were matched ?
Answer: A
The degrees of freedom are 7, the first option. When the groups are matched, the 8 subjects of the control group are paired with the 8 of the experimental group, and the test is made on the differences between the pairs, so the degrees of freedom are the number of pairs minus one:
\[ df = N - 1 \]
\[ df = 8 - 1 = 7 \]
The value 14 would be the degrees of freedom for two independent groups of 8, \(8 + 8 - 2\), and 15 and 8 do not arise in either design, so only 7 fits the matched design.
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