music

references:
- ISI, example 7.1, p.383

random assignment to two independent groups

paired design using repeated measures

Imagine an experiment attempting to measure the efficacy of two different diets. Participants are randomly assigned to \(dietA\) and \(dietB\). Each participant is weighed before the diet begins, \(W.before\), and then again after the diet ends, \(W.after\), but it is the difference, \[W.diff = W.before - W.after\] of those two numbers that is of primary interest.

A data set for this experiment might look like this.

participant diet W.before W.after W.diff
1 dietA 172 168 4
2 dietA 127 122 5
3 dietB 161 163 -2

Each participant submits two numbers to the researchers (repeated measures), but those two numbers are then summarized by a single difference measurement, and the analysis of the experiment becomes an analysis of a single column of numbers, the differences.

paired design using matching

A company would like to test a new tool for riveting airplane wings. The repeated measures experimental design would call for each participant in the experiment to rivet two aiplane wings, once using the standard tool and then again using the new tool. The matching experimental design might rank all the participants on how quickly they could rivet an aircraft wing, and then pair the two fastest workers, and then the next two fastest workers, etc. In the experiment, one member of each pair would use the new tool, and the other would use the standard tool. Each pair submits two numbers to the researchers, \(time.new\) and \(time.standard\) to complete the task, but then those two numbers would be summarized by taking a difference, \[time.diff = time.standard - time.new\] and the analysis of the experiment becomes an analysis of a single column of numbers, the differences.