A certain HMO is attempting to show the benefits of managed care to an insurance

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 Uncertifiec board ineligible (0)- 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. c-1-61, n-c= 2 O c1-2, n-c-60 c-1-3, n-c 60

Explanation / Answer

The F-test that is done in ANOVA to check if there is difference in the mean levels of teatments(certification levels) uses the ratio of Mean-Square of treatment to mean square of error.

The treatment considered here is the certification level of the physicians. There are 3 levels which are studied. So the degrees of freedom is (number of treatment levels) - 1 = 3 - 1 = 2.

The total number of observations considered here is 63. So the total degrees of freedom = 63 - 1 = 62.

To obtain the error degrees of freedom, we subtract the treatment derees of freedom from total degrees of freedom = 62 - 2 = 60

Hence the F-test uses the treatment degrees of freedom of c-1 = 2 and n-c = 60.

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