Application of the T-Test in Health Insurance Cost Analysis: Large Data Sets

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Abstract

In this paper will be analyzed the application of the t-test against the nonparametric Mann - Whitney test in the analysis of health insurance benefit costs in the Republic of Srpska on large samples. This research aims to examine which method produces better results when testing statistical hypotheses. The adequacy of the statistical tests will be tested on primary health insurance cost data for 1,044,690 insureds in 2017. For two samples of size 4,000, the sampling distribution of the difference in two means has a skewness coefficient of 0.05 and a kurtosis coefficient of 3.09. Jarque - Bera test does not reject the hypothesis of normality of distribution with a p-value of 0.135. On the other hand, in the Mann - Whitney test, the real risk of the first species, when there is a difference in skewness between the samples, may be less than 0.001 compared to the nominal risk level of 0.05. Based on the results obtained, it is suggested to use the t-test instead of the Mann - Whitney test if the sample is large enough, which should be verified by the bootstrap method.

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