The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wo...The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wolfowitz one-sample runs test for randomness, to present a novel approach for computing this probability, and to compare the four procedures by generating samples of 10 and 11 data points, varying the parameters n<sub>0</sub> (number of zeros) and n<sub>1</sub> (number of ones), as well as the number of runs. Fifty-nine samples are created to replicate the behavior of the distribution of the number of runs with 10 and 11 data points. The exact two-tailed probabilities for the four procedures were compared using Friedman’s test. Given the significant difference in central tendency, post-hoc comparisons were conducted using Conover’s test with Benjamini-Yekutielli correction. It is concluded that the procedures of Real Statistics using Excel and R exhibit some inadequacies in the calculation of the exact two-tailed probability, whereas the new proposal and the SPSS procedure are deemed more suitable. The proposed robust algorithm has a more transparent rationale than the SPSS one, albeit being somewhat more conservative. We recommend its implementation for this test and its application to others, such as the binomial and sign test.展开更多
The main purpose in many randomized trials is to make an inference about the average causal effect of a treatment. Therefore, on a binary outcome, the null hypothesis for the hypothesis test should be that the causal ...The main purpose in many randomized trials is to make an inference about the average causal effect of a treatment. Therefore, on a binary outcome, the null hypothesis for the hypothesis test should be that the causal risks are equal in the two groups. This null hypothesis is referred to as the weak causal null hypothesis. Nevertheless, at present, hypothesis tests applied in actual randomized trials are not for this null hypothesis;Fisher’s exact test is a test for the sharp causal null hypothesis that the causal effect of treatment is the same for all subjects. In general, the rejection of the sharp causal null hypothesis does not mean that the weak causal null hypothesis is rejected. Recently, Chiba developed new exact tests for the weak causal null hypothesis: a conditional exact test, which requires that a marginal total is fixed, and an unconditional exact test, which does not require that a marginal total is fixed and depends rather on the ratio of random assignment. To apply these exact tests in actual randomized trials, it is inevitable that the sample size calculation must be performed during the study design. In this paper, we present a sample size calculation procedure for these exact tests. Given the sample size, the procedure can derive the exact test power, because it examines all the patterns that can be obtained as observed data under the alternative hypothesis without large sample theories and any assumptions.展开更多
This paper is concerned with the generalized variable-coefficient nonlinear evolution equation（vc-NLEE）.The complete integrability classification is presented,and the integrable conditions for the generalized variab...This paper is concerned with the generalized variable-coefficient nonlinear evolution equation（vc-NLEE）.The complete integrability classification is presented,and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlevé analysis.Then,the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method,and the Lax pairs（LP） of the vc-NLEEs are constructed in terms of the integrable conditions.展开更多
文摘The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wolfowitz one-sample runs test for randomness, to present a novel approach for computing this probability, and to compare the four procedures by generating samples of 10 and 11 data points, varying the parameters n<sub>0</sub> (number of zeros) and n<sub>1</sub> (number of ones), as well as the number of runs. Fifty-nine samples are created to replicate the behavior of the distribution of the number of runs with 10 and 11 data points. The exact two-tailed probabilities for the four procedures were compared using Friedman’s test. Given the significant difference in central tendency, post-hoc comparisons were conducted using Conover’s test with Benjamini-Yekutielli correction. It is concluded that the procedures of Real Statistics using Excel and R exhibit some inadequacies in the calculation of the exact two-tailed probability, whereas the new proposal and the SPSS procedure are deemed more suitable. The proposed robust algorithm has a more transparent rationale than the SPSS one, albeit being somewhat more conservative. We recommend its implementation for this test and its application to others, such as the binomial and sign test.
文摘The main purpose in many randomized trials is to make an inference about the average causal effect of a treatment. Therefore, on a binary outcome, the null hypothesis for the hypothesis test should be that the causal risks are equal in the two groups. This null hypothesis is referred to as the weak causal null hypothesis. Nevertheless, at present, hypothesis tests applied in actual randomized trials are not for this null hypothesis;Fisher’s exact test is a test for the sharp causal null hypothesis that the causal effect of treatment is the same for all subjects. In general, the rejection of the sharp causal null hypothesis does not mean that the weak causal null hypothesis is rejected. Recently, Chiba developed new exact tests for the weak causal null hypothesis: a conditional exact test, which requires that a marginal total is fixed, and an unconditional exact test, which does not require that a marginal total is fixed and depends rather on the ratio of random assignment. To apply these exact tests in actual randomized trials, it is inevitable that the sample size calculation must be performed during the study design. In this paper, we present a sample size calculation procedure for these exact tests. Given the sample size, the procedure can derive the exact test power, because it examines all the patterns that can be obtained as observed data under the alternative hypothesis without large sample theories and any assumptions.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171041)the High-Level Personnel Foundation of Liaocheng University(Grant No.31805)
文摘This paper is concerned with the generalized variable-coefficient nonlinear evolution equation（vc-NLEE）.The complete integrability classification is presented,and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlevé analysis.Then,the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method,and the Lax pairs（LP） of the vc-NLEEs are constructed in terms of the integrable conditions.
