Verification: Which Jonckeere Terpstra Test to Use • drcHelper

library(drcHelper)


library(tidyverse)

Summary

Jonckheere’s test and Kendall’s tau) are closely related. In some software implementations, the two test produce identical p-values.

JtTest from npordtests are doing the same as in cor.test with method being “kendall”. Both function actually performs a kendall test and treat the dose column as numeric. On the other hand PMCMRplus::jonckheereTest and DescTools::JonckheereTerpstraTest do similar things.

Data from Jonckheere (1954)

data(jdata)

prelimPlot3(jdata,dose_col = "X",response_col = "Y")

plot of chunk unnamed-chunk-3


dunnett_test(jdata,"Y","X",include_random_effect = FALSE)
#> Dunnett Test Results
#> -------------------
#> Model type: Fixed model with homoscedastic errors 
#> Control level: 1 
#> Alpha level: 0.05 
#> 
#> Results Table:
#>  comparison estimate std.error statistic   p.value  conf.low conf.high significant
#>       2 - 1    15.50  34.05051 0.4552061 0.9401315 -75.78264  106.7826       FALSE
#>       3 - 1    39.75  34.05051 1.1673833 0.5307511 -51.53264  131.0326       FALSE
#>       4 - 1    60.25  34.05051 1.7694300 0.2322884 -31.03264  151.5326       FALSE
#> 
#> NOEC Determination:
#> No significant effects detected at any dose. NOEC is at or above the highest tested dose.

library(npordtests)
res1 <- JtTest(Y~X,jdata)
#> --------------------------------------------------------- 
#>   Test : Jonckheere-Terpstra Test 
#>   data : Y and X 
#> 
#>   Statistic = 71 
#>   Mean = 48 
#>   Variance = 114.6667 
#>   Z = 2.147876 
#>   Asymp. p-value = 0.0158618 
#> 
#>   Result : Null hypothesis is rejected. 
#> ---------------------------------------------------------
res1$p.value *2
#> [1] 0.03172359

res2 <- DescTools::JonckheereTerpstraTest(Y~X,jdata)
res2
#> 
#>  Jonckheere-Terpstra test
#> 
#> data:  Y by X
#> JT = 71, p-value = 0.03368
#> alternative hypothesis: two.sided
res2$statistic == res1$statistic
#>   JT 
#> TRUE

res3 <- PMCMRplus::jonckheereTest(Y~X,jdata)
res3$statistic=res2$statistic
res3$p.value -  res2$p.value
#> [1] -0.001960184

res4 <- cor.test(as.numeric(jdata$X),as.numeric(jdata$Y),method="kendall")
res4$statistic
#>        z 
#> 2.147876
res4$p.value
#> [1] 0.03172359

data(lehmann)
res <- JtTest(Values~Group,lehmann)
#> --------------------------------------------------------- 
#>   Test : Jonckheere-Terpstra Test 
#>   data : Values and Group 
#> 
#>   Statistic = 1159 
#>   Mean = 857.5 
#>   Variance = 9305.917 
#>   Z = 3.125415 
#>   Asymp. p-value = 0.0008877709 
#> 
#>   Result : Null hypothesis is rejected. 
#> ---------------------------------------------------------
res4$p.value - 2*res1$p.value
#> [1] 1.387779e-17

Data from Lehmann (1975)

data("lehmann")
DescTools::JonckheereTerpstraTest(Values~Group,lehmann)
#> 
#>  Jonckheere-Terpstra test
#> 
#> data:  Values by Group
#> JT = 1159, p-value = 0.001776
#> alternative hypothesis: two.sided
PMCMRplus::jonckheereTest(Values~Group,lehmann)
#> 
#>  Jonckheere-Terpstra test
#> 
#> data:  Values by Group
#> z = 3.1337, p-value = 0.001726
#> alternative hypothesis: two.sided
#> sample estimates:
#>   JT 
#> 1159