非参数方差分析与非配对 t 检验

R 中的假设检验

Richie Cotton

Data Evangelist at DataCamp

非参数检验

"非参数检验"是不对检验统计量假定分布的假设检验。

非参数检验有两类：

基于模拟。
基于秩。

t_test()

$H_{0}$：$\mu_{child} - \mu_{adult} = 0$ $H_{A}$：$\mu_{child} - \mu_{adult} > 0$

library(infer)
stack_overflow %>% 
  t_test(
    converted_comp ~ age_first_code_cut,
    order = c("child", "adult"),
    alternative = "greater"
  )

# A tibble: 1 x 6
  statistic  t_df p_value alternative lower_ci upper_ci
      <dbl> <dbl>   <dbl> <chr>          <dbl>    <dbl>
1      2.40 2083. 0.00814 greater        8438.      Inf

计算原假设分布

基于模拟的流程

null_distn <- stack_overflow %>% 
  specify(converted_comp ~ age_first_code_cut) %>%

  hypothesize(null = "independence") %>%

  generate(reps = 5000, type = "permute") %>%

  calculate(
    stat = "diff in means", 
    order = c("child", "adult")
  )

t 检验（用于对比）

library(infer)
stack_overflow %>% 
  t_test(
    converted_comp ~ age_first_code_cut,
    order = c("child", "adult"),
    alternative = "greater"
  )

计算观测统计量

基于模拟的流程

obs_stat <- stack_overflow %>% 
  specify(converted_comp ~ age_first_code_cut) %>% 
  calculate(
    stat = "diff in means", 
    order = c("child", "adult")
  )

t 检验（用于对比）

library(infer)
stack_overflow %>% 
  t_test(
    converted_comp ~ age_first_code_cut,
    order = c("child", "adult"),
    alternative = "greater"
  )

获取 p 值

基于模拟的流程

get_p_value(
  null_distn, obs_stat, 
  direction = "greater"
)

# A tibble: 1 x 1
  p_value
    <dbl>
1  0.0066

t 检验（用于对比）

library(infer)
stack_overflow %>% 
  t_test(
    converted_comp ~ age_first_code_cut,
    order = c("child", "adult"),
    alternative = "greater"
  )

# A tibble: 1 x 6
  statistic  t_df p_value alternative lower_ci upper_ci
      <dbl> <dbl>   <dbl> <chr>          <dbl>    <dbl>
1      2.40 2083. 0.00814 greater        8438.      Inf

向量的秩

x <- c(1, 15, 3, 10, 6)

rank(x)

1 5 2 4 3

"Wilcoxon-Mann-Whitney 检验"（又称"Wilcoxon 秩和检验"）大致相当于对数值输入的秩进行 t 检验。

Wilcoxon–Mann–Whitney 检验

wilcox.test(
  converted_comp ~ age_first_code_cut,
  data = stack_overflow,
  alternative = "greater",
  correct = FALSE
)

    Wilcoxon rank sum test

data:  converted_comp by age_first_code_cut
W = 967298, p-value <2e-16
alternative hypothesis: true location shift is greater than 0

¹ 亦称"Wilcoxon 秩和检验"和"Mann-Whitney U 检验"。

Kruskal–Wallis 检验

Kruskal–Wallis 检验之于 Wilcoxon–Mann–Whitney 检验，正如 ANOVA 之于 t 检验。

kruskal.test(
  converted_comp ~ job_sat,
  data = stack_overflow
)

    Kruskal-Wallis rank sum test

data:  converted_comp by job_sat
Kruskal-Wallis chi-square = 81, df = 4, p-value <2e-16

让我们练习吧！

R 中的假设检验