A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 21 physicians from each of the three certification levels-Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-and recorded the total per-member, per-month charges for each (a total of 63 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Give the degrees of freedom appropriate for conducting the ANOVA F-test.
A) numerator $\mathrm { df } = 3$, denominator $\mathrm { df } = 60$
B) numerator $\mathrm { df } = 61$, denominator $\mathrm { df } = 2$
C) numerator $\mathrm { df } = 2$, denominator $\mathrm { df } = 60$
D) numerator $\mathrm { df } = 61$, denominator $\mathrm { df } = 3$

Question

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 21 physicians from each of the three certification levels-Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-and recorded the total per-member, per-month charges for each (a total of 63 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Give the degrees of freedom appropriate for conducting the ANOVA F-test. 
A) numerator $\mathrm { df } = 3$, denominator $\mathrm { df } = 60$
B) numerator $\mathrm { df } = 61$, denominator $\mathrm { df } = 2$
C) numerator $\mathrm { df } = 2$, denominator $\mathrm { df } = 60$
D) numerator $\mathrm { df } = 61$, denominator $\mathrm { df } = 3$

Quizplus · Accepted Answer

The numerator degrees of freedom for ANOVA is the number of groups minus one (3 - 1 = 2), and the denominator degrees of freedom is the total number of observations minus the number of groups (63 - 3 = 60).

A Certain HMO Is Attempting to Show the Benefits of Managed