Statistician's Hospital has decided that variances that are within two standard errors of the budgeted or expected value need not be investigated because they are quite likely to occur simply as a matter of chance. However, if the variance is more than two standard errors, either plus or minus, there is a significant chance that a control problem exists. Investigation is required.

Statistician's has applied this concept quite widely. They examine patient days by DRG. They also examine all line-item cost variances from budget in this manner. Statistician's receives most of its revenues under prospective payment systems. Therefore, control of ancillary usage has become particularly important. They are just beginning to use this approach for control of ancillary usage.

Assume that last year is considered to be a period during which particular effort was made to control ancillary usage. As a result, we are willing to accept last year's results as a reasonable standard of performance.

Assume further that last year, there were eight patients in DRG XXX (this unrealistically low number of patients is used to ease your calculations), and that the number of laboratory tests for each of the eight patients in this DRG was as follows:

Calculate the standard error based on this test group from last year. Suppose that in the first month of this year, the average number of laboratory tests per patient was 35. Is the resulting deviation from the standard great enough to warrant investigation?

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Patient # Number of Tests 1 15 2 28 2456 21 40 33 29 7 22 00 8 36