R 中 wilcox_test() 和 wilcox.test() 之间的不同 P 值

Question

While I was trying to perform a paired Wilcoxon test for the variable:"Metabolite", I noticed different P-values between wilcox_test() & wilcox.test(), when I tested the following variable:

structure(list(Visit = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L), .Label = c("BSL", "LV"), class = "factor"), Metabolite = c(NA, 
9.602, 9.0102, 4.524, 3.75, NA, 6.596, 7.065, 6.877, NA, NA, 
10.1846, 13.521, 7.8219, NA, 4.9149, 4.0754, 4.7635, 8.8554, 
4.3442, NA, 16.659, NA, 3.698, 6.623, 5.158, 11.719, 3.206, NA, 
2.225, 7.417, 1.42, NA, NA, 2.752, 6.504, 7.594, 6.652, NA, NA, 
3.784, 2.7311, 4.1749, 2.6659, 0.5592, NA, 4.2326, 4.3808, 3.624, 
4.29, 7.098, 6.532, 3.699, 9.297, 8.275, NA)), class = "data.frame", row.names = c(NA, 
-56L))



# The P-value derived from result 1 (p=0.0079) is different from that from result 2 (p=0.003279):


        result1 <- wilcox_test(data=Data_pairs,  Metabolite~Visit, paired = TRUE)
        
        # A tibble: 1 x 7
        #.y.     group1 group2    n1    n2 statistic      p
        #* <chr>   <chr>  <chr>  <int> <int>     <dbl>  <dbl>
        #        1 Metabolite BSL    LV        28    28       131 0.0079
        
        
        result2 <- wilcox.test(data=Data_pairs,  Metabolite~Visit, paired = TRUE)
        #   Wilcoxon signed rank exact test
        
        #data:  Metabolite by Visit
        #V = 197, p-value = 0.003279
        #alternative hypothesis: true location shift is not equal to 0
 

Using different statistical software, it seems that the wrong P-value is that derived from result2.

Is there any suggestion/advice on how to correct my code, and what is the reason for this difference?

Thank you in advance for your help.

Answer 1

You should point out you are using rstatix to avoid the confusion:

rstatix::wilcox_test(data=Data_pairs,  Metabolite~Visit, paired = TRUE)
# A tibble: 1 x 7
  .y.        group1 group2    n1    n2 statistic      p
* <chr>      <chr>  <chr>  <int> <int>     <dbl>  <dbl>
1 Metabolite BSL    LV        28    28       131 0.0079

If it is indeed paired data, then you need to ensure you provide the complete pairs, taking your data, we can place them side by side, assuming the your observations 1 to 28 and from the same sample as 29 to 56:

da = do.call(cbind,split(Data_pairs$Metabolite,Data_pairs$Visit))
da

          BSL     LV
 [1,]      NA     NA
 [2,]  9.6020 2.2250
 [3,]  9.0102 7.4170
 [4,]  4.5240 1.4200
 [5,]  3.7500     NA
 [6,]      NA     NA
 [7,]  6.5960 2.7520
 [8,]  7.0650 6.5040
 [9,]  6.8770 7.5940
[10,]      NA 6.6520
[11,]      NA     NA
[12,] 10.1846     NA
[13,] 13.5210 3.7840
[14,]  7.8219 2.7311
[15,]      NA 4.1749
[16,]  4.9149 2.6659
[17,]  4.0754 0.5592
[18,]  4.7635     NA
[19,]  8.8554 4.2326
[20,]  4.3442 4.3808
[21,]      NA 3.6240
[22,] 16.6590 4.2900
[23,]      NA 7.0980
[24,]  3.6980 6.5320
[25,]  6.6230 3.6990
[26,]  5.1580 9.2970
[27,] 11.7190 8.2750
[28,]  3.2060     NA

We test only the complete:

wilcox.test(da[complete.cases(da),1],da[complete.cases(da),2],paired=TRUE)

data:  da[complete.cases(da), 1] and da[complete.cases(da), 2]
V = 131, p-value = 0.007904
alternative hypothesis: true location shift is not equal to 0

Answer 2

There's a few things going on here. The most important is you're not doing a paired test with coin::wilcox_test (assuming you're using the coin package - we can't be sure from your question). There is no paired argument for the function. If we compare coin::wilcox_test with the exact distribution and the unpaired wilcox.test , we'll get the same result. There will also be the same result with the argument paired = TRUE supplied to coin::wilcox_test .

coin::wilcox_test(data = Data_pairs,  Metabolite ~ Visit, distribution = "exact")
#> 
#>  Exact Wilcoxon-Mann-Whitney Test
#> 
#> data:  Metabolite by Visit (BSL, LV)
#> Z = 2.503, p-value = 0.01167
#> alternative hypothesis: true mu is not equal to 0

wilcox.test(data = Data_pairs, Metabolite ~ Visit)
#> 
#>  Wilcoxon rank sum exact test
#> 
#> data:  Metabolite by Visit
#> W = 320, p-value = 0.01167
#> alternative hypothesis: true location shift is not equal to 0

coin::wilcox_test(data = Data_pairs,  Metabolite ~ Visit, paired = TRUE, distribution = "exact")
#> 
#>  Exact Wilcoxon-Mann-Whitney Test
#> 
#> data:  Metabolite by Visit (BSL, LV)
#> Z = 2.503, p-value = 0.01167
#> alternative hypothesis: true mu is not equal to 0

However, the p-values with default options will not be the same between the functions regardless. The p-values derived from coin::wilcox_test are asymptotic and computed from permutation tests. The p-values from wilcox.test are exact p-values. You can get exact p-values from coin::wilcox_test by specifying the distribution = "exact" as I did above. Comparing the default options, you'll see they differ.

coin::wilcox_test(data = Data_pairs,  Metabolite ~ Visit)
#> 
#>  Asymptotic Wilcoxon-Mann-Whitney Test
#> 
#> data:  Metabolite by Visit (BSL, LV)
#> Z = 2.503, p-value = 0.01231
#> alternative hypothesis: true mu is not equal to 0

wilcox.test(data = Data_pairs,  Metabolite ~ Visit)
#> 
#>  Wilcoxon rank sum exact test
#> 
#> data:  Metabolite by Visit
#> W = 320, p-value = 0.01167
#> alternative hypothesis: true location shift is not equal to 0

I would spend some time looking through the functions with ?coin::wilcox_test or ?wilcox.test and making sure you understand what test you want to apply and what results they supply.

Answer 3

To maintain reproducibility you should always use set.seed(1) in your R code. Maybe this is the case?