「個人の健診データの異常への移行の検出方法に関する考察」への補遺

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  • Addendum to “Detection of the Change of Individual Test Data in Health-Screening”
  • コジン ノ ケンシン データ ノ イジョウ エ ノ イコウ ノ ケンシュツ ホ

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The authors previously reported on the detection of change of individual test data in health screening. The expected behavior of t-test was discussed which showed how the statistical test would work when the population mean changed with time, deteriorating the assumption required for the t-test. The present report is a theoretical addition to the previous report and shows the distribution density function of, √V which then is used to obtain the expected value of.117. The latter, in the previous paper, was replaced by the square root of the expected value of V which naturally incurred some error. This paper shows that the distribution density function for, √V can be obtained by the use of noncentral chi-square distribution, and actual derivation of the function is carried out, using the model of the change of the population mean proposed in the previous report. The expected value of Arif is then obtained and compared with the square root of the expectation for V which was used as approximation of the former in the previous work. The difference is shown to be small enough to leave the obtained results in the previous report unaltered.

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