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The asymptotic distribution of these tests has only been studied under the restrictive assumption of errors with known scale or symmetric distribution.
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As with the test of reading and vocabulary, there is considerable sample variation; similar to the distribution of verbal skills, the distribution of these test scores also appears to be symmetric and approximately normal, with a mean of 17.7 points (SD 6.1).
The distribution of these test values are used to estimate the null distribution.
The analysis shows that such above simplistic strategies to combine p-values are unsound, i. e. the tests are overly conservative or liberal, and in order to avoid this issue, one can instead use our proposed joint two-dimensional distribution of these test statistics.
The asymptotic distributions of these tests are available under both stationary and non-stationary assumptions, thereby enable us to conservatively control type-I errors and meanwhile ensure the proposed tests enjoy the asymptotically optimal statistical power.
The distributions of these test results were similar across most sites (Table 2).
This demonstrates the adequacy of proposed distribution of the test statistic constructed in these methods under the null hypothesis and, in turn, the appropriate control of the type I error of the statistical tests.
The GST plot displays the ranked test statistics (red line) and empirical cumulative distribution function of these test statistics for expressed genes in a gene set (solid line).
How will the distribution of the test go forward?
The asymptotic distribution of the test statistic is the chi-square distribution.
The reference distribution is the distribution of the test statistic when the null hypothesis is true.
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CEO of Professional Science Editing for Scientists @ prosciediting.com