About the influence of rounding errors on distributions of statistics of the goodness-of-fit tests
Most of the existing tests are designed to checking statistical hypotheses regarding continuous random variables. This is a standard assumption, which determines the correct application of the relevant tests. In real situations, this assumption is often violated, since any measurements are accompanied by some rounding error. Therefore, repeated observations appear in the samples, which should not be in the case of continuity of a random variable. The presence of rounding errors can affect the results of applying statistical hypothesis testing criteria, and in some situations lead to incorrect conclusions. Changing the properties of tests due to the influence of rounding errors does not exclude the possibility of their correct application. This work has two goals. First, to show how, depending on the magnitude of the rounding error A and on the volume n of samples, the distributions of statistics of various criteria for testing statistical hypotheses can change. Secondly, to give recommendations on how to proceed in order to ensure the correctness of the conclusion according to the applicable tests, if such changes cannot be ignored. To ensure the ongoing research in the developed software system, the possibility of simulating the distributions of statistics of the corresponding tests under the conditions of violation of the standard assumption of continuity (for given A and n) is implemented. The number of simulation experiments in the study of the corresponding distributions of statistics and the calculation of estimates of the achieved significance level pvalue by statistical simulating methods, as a rule, was not less than N = 106. Using statistical simulating methods, an example of a set of 30 tests (goodness-of-fit tests, special tests for checking normality and checking exponentiality) demonstrates how significantly the distribution of the statistics of the tests can change depending on the rounding error and for limited sample sizes n. To ensure the correctness of the conclusions on the applicable tests for non-standard conditions is proposed applications (and implemented) interactive study of the real distribution of the test statistic (for given A and n) statistical simulating methods. Two samples of volume n = 50 containing the measurement results with a rounding error of ∆ = 0,2 σ show the results of applying the considered set of tests to checking hypotheses about the belonging of the samples to the normal and exponential laws, respectively. A significant difference is shown between the estimates of pvalue obtained from the asymptotic and real distributions of statistics.
Keywords
goodness-of-fit tests,
normality tests,
exponential tests,
statistics,
distribution of statistics,
rounding errorsAuthors
| Lemeshko Boris Yu. | Novosibirsk State Technical University | lemeshko@ami.nstu.ru |
| Lemeshko Stanislav B. | Novosibirsk State Technical University | skyer@mail.ru |
Всего: 2
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