# Non-parametric Tests

## the Wilcoxon rank-sum test(Mann-Whitney test)

comparing two independent conditions

compares two conditions when different participants take part in each condition and the resulting data violate any assumption of the independent t-test

### 原理

（N为每个组的人数，其实这个就是等差数列1...N的和最后除以N）

### calculating effect size

r=z/sqrt(N)

if p-value<0.05, then the two groups are significantly different

## the Wilcoxon signed-rank test

comparing two related conditions

two set of scores, from the same participants, and the resulting data violate an assumption of the dependent t-test

### 原理

mean和standard error的计算方法见p670

if p-value<0.05, then the two groups are significantly different

## Kruskal-Wallis test

comparing several conditions when different participants take part in each condition and the resulting data violate an assumption of one-way independent ANOVA

#### post hoc test

R中的方法见p683

if p-value<0.05, then the two groups are significantly different

R中的方法见p685

## Friedman's test

differences between conditions when there are more than two conditions and the same participants have been used in all conditions(each case contributes several scores to the data)+violated an assumption of one-way repeated-measures ANOVA

Friedman's ANOVA

post hoc test的方法见p691的15.7.6.

if p-value<0.05, then the two groups are significantly different