A new runner has decided to purchase a new pair of running shoes. He has narrowed his choices to two brands, each of which would
be appropriate for his use. His concern is whether there is a significant difference in the average wear between the two brands of shoes. He enlisted a random sample of 6 veteran runners to test the shoes. Each runner wore each brand of shoe until it wore out. What method of analysis is more appropriate to use for this problem
The paired difference t test is a type of statistical test which is used to examine if difference exists in th population mean of two samples. The paired difference test usually involves samples taken within subjects. That is, the sample mean for each set of measurement is taken from the Same subject, In the scenario described above, the subjects which are the 6 veteran runners each wore each of the two shoe brands, this means that two readings were produced by each runner ; one reading for brand A and the other brand B.
The difference between the two readings are taken for each runner and used to perform a hypothesis test:
t = μd/ (s/√n)
s = sample standard deviation ; n = sample size ; μd = mean difference
