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For paired test statistic, the t-test does not agree with the result of the randomization test. why? For two sample test statistic, the t-test agree

For paired test statistic, the t-test does not agree with the result of the randomization test. why?

For two sample test statistic, the t-test agree with the result of the randomization test. why?

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R Console Paired t-test data: 5 and T t = -2.5868, df = 7, pvalue = 0.03611 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -4.1710914 -0.1871586 sample estimates: mean of the differences 2.179125 Welch Two Sample t-test data: 5 and T t = -2.0746, df = 13.906, p-value = 0.05708 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -4.43345254 0.07520254 sample estimates: mean of x mean of y 4.321000 6.500125 #paired randomization trc =abs(meandiff-tbar))/N round(p_val , 4) [1] 0.0625 #two sample randomization fert =abs(observed-tbar))/N round(p_val , 4) [1] 0. 0693

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