A Study Randomly Assigned Adult Subjects to One of Three

Short Answer

A study randomly assigned adult subjects to one of three exercise treatments: (1) a single long exercise period five days per week; (2) several ten-minute exercise periods five days per week; and (3) several ten-minute periods five days per week using a home treadmill. The study report contains the following summary statistics about weight loss (in kilograms) after six months of treatment:
$$\begin{array} { | l | c | c | c | } \hline \text { Treatment } & \text { Mean } & \text { Std. Dev. } & \boldsymbol { n } \\\hline \text { Long periods } & 10.2 & 4.2 & 37 \\\hline \text { Multiple short periods } & 9.3 & 4.5 & 36 \\\hline \text { Multiple short periods with treadmill } & 10.2 & 5.2 & 42 \\\hline\end{array}$$ Here is a partial ANOVA table based on these data:
$$\begin{array}{l}\begin{array} { l | l r } &\text {Source }&\text {df }&\text {Sums of Squares }&\text {Mean Square}&\text { F-Ratio}&\\\hline\text {group }&&&20.032\\\text { Error} && & &21.8967\\\hline\text {Total }&\end{array}\end{array}$$ The numerator degrees of freedom for the ANOVA is _______.