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Emma0627 · 2023年08月05日

为什么不能当做independent populations判断?

NO.PZ2022071202000084

问题如下:

Question
Using the following sample results drawn as 25 paired observations from their underlying distributions, test whether the mean returns of the two portfolios differ from each other at the 1% level of statistical significance. Assume the underlying distributions of returns for each portfolio are normal and that their population variances are not known.

t-statistic for 24 degrees of freedom and at the 1% level of statistical significance = 2.807

Null hypothesis (H0): Mean difference of returns = 0

Based on the paired comparisons test of the two portfolios, the most appropriate conclusion is that H0 should be:

选项:

A.rejected because the computed test statistic exceeds 2.807. B.accepted because the computed test statistic exceeds 2.807. C.accepted because the computed test statistic is less than 2.807.

解释:

Solution

A is correct.

In this case, the test statistic equals: (4.25-0)/(6.25/25)= 3.40. Because 3.40 > 2.807, the null hypothesis that the mean difference is zero is rejected.

B is incorrect because a too large (or too small) test statistic leads to the rejection of the null hypothesis.

C is incorrect because the correctly computed test statistic exceeds the critical value of 2.807. A reasonable way to reach response C is to fail to divide the standard error by the square root of the sample size, erroneously using 4.25/6.25 = 0.68 as the test statistic.

我通过给出的两个标准差算t检验,表格第四行two independent populations和paired comparison有什么区别?

1 个答案

星星_品职助教 · 2023年08月06日

同学你好,

paired comparison test的前提就是样本的抽取不独立(dependent samples),故该test的t统计量计算公式和independent samples的公式是截然不同的。

本题已经明确要求要“Based on the paired comparisons test”,所以只能用paired的公式,不能用其他公式。