Abstract
In health-screening tests the normality of measured values are usually judged according to what is said to be the range of normal values. However, the accuracy of the judgment would be greater if the decision were based upon accumulated data of each subject. The justification for this test has been presented for actual data by comparing the variance of individual data and those of the whole group.
The main part of this paper deals with the problem of detecting any change of the population to which the measurement values of a subject are assumed to belong. The well-known t-test provides the answer to this problem under certain conditions.
In the present work the population mean is assumed to change with time. When the change is gradual instead of a jump, then the test may be deteriorated because of the violation of the conditions for the test. To examine the performance of the t-test in such a case, a model of a changing population mean is presented and the test is applied to it, yielding what can be considered as the average performance of the test.
Two methods (methods A and B) are examined. In method A, the n+1-th measurement value is compared with the mean of the past n values. Method B compares the mean of the recent two values with that of the past n-1 values. The results show how the number of independent “healthy” values and the rate of the change affect the performance.
The performance has been calculated using approximated formulas and the results of simulations using normal random variables show that the approximation is sufficient for roughly estimating the performance.
