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维尔克松t检验

维尔克松T检验(The Wilcoxon T test)

对应于相关样本t检验,用于检验重复方差设计的两种处理条件之间的差异。

Corresponding to the correlation sample t test, and is used to test the difference between the two treatment conditions of the repeated variance design


维尔克松T检验的步骤 (Steps of Wilcoxon T test)

1、确定虚无假设和备择假设 (Determine null hypothesis and alternative hypothesis)

H0:不同处理间没有显著差异。(There is no significant difference among different treatments.)

H1:不同处理间有显著差异。(There are significant differences among different treatments.)

2、计算差异分数并排序 (Calculate the difference scores and rank them)

计算每个样本不同处理下的分数差,此处差异分数的排序是按照差异分数绝对值的大小进行排序。

Calculate the score difference under different treatments for each sample, where the difference scores are sorted according to the magnitude of the absolute value of the difference scores.

3、计算正负差异分数的秩和 (Calculate the rank sum of positive and negative difference scores)

排序后每个差异分数对应一个秩,分别计算正的差异分数的秩之和∑R+和负的差异分数的秩之和∑R-

After sorting, each difference score corresponds to a rank. Then calculate the rank sum of the positive difference score ∑R+ and the rank sum of the negative difference score ∑R- respectively.

4、取T值并与临界T值比较 (Take the T-value and compare it with the critical T-value)

T=min(∑R+,∑R-

查表可以得到临界值Tcrit

The criticle value Tcrit can be obtained by looking up the table.

若T<Tcrit,则拒绝H0

If T<Tcrit, then reject H0.


大样本条件下的维尔克松T检验

当n>25时,T分布近似服从正态分布。

该正态分布的均值为: 方差为: 由此可以将T分数标准化为z分数,查z分数表进行比较。


相同的等级和0分数

在Wilcoxon 检验中,有两类相同的等级:

1、不同被试在不同处理条件下的差异分数相同;

2、同一个被试在不同处理条件下得到相同的分数,因此算出的差异分数为0。

对于0分数,有两种做法:

1、去掉差异分数为0的被试;

2、将0差异分数均匀地分配在正负两组中,即在计算正负差异分数的秩和时将0分数的秩平均分配于两组,这样将增大T值。

维尔克松t检验.txt · 最后更改: 2024/05/10 02:48 由 zzzz