12.25 Pain tolerance among sports teams. Many have argued that sports such as football require the ability to withstand pain from injury for extended periods of time. To see if there is greater pain tolerance among certain sports teams, a group of researchers assessed 183 male Division II athletes from five sports.6 Each athlete was asked to put his dominant hand and forearm in a 3°C water bath and keep it in there until the pain became intolerable. The total amount of time (in seconds) that each athlete maintained his hand and forearm in the bath was recorded. Following this procedure, each athlete completed a series of surveys on aggression and competitiveness. In their report, the researchers state:
A univariate between subjects (sports team) ANOVA was performed on the total amount of time athletes were able to keep their hand and forearm in the water bath, and found it to be statistically significant, F(4,146) = 4.96, p < .001.
Further analysis revealed that the lacrosse and soccer players tolerated the pain for a significantly longer period of time and swimmers tolerated the pain for a significantly shorter period of time than athletes from the other teams.
(a) Based on the description of the experiment, what should the degrees of freedom be for this analysis?
(b) Assuming that the degrees of freedom reported are correct, data from how many athletes were used in this analysis?
(c) The researchers do not comment on the missing data in their report. List two reasons these data may not have been used, and for each, explain how the omission could impact or bias the results.