Analyses of Total severity scores mink data

Method: A kruskall-wallis test is a non-parametric equivalent to an ANOVA. Instead of using the actual values of the score, it uses the ranking so it is valid for any type of ordinal data. We start this test by loading the data.

setwd("C:\\Users\\Admin\\OneDrive\\Documents\\Bursian")
library(lubridate)
library(tidyverse)
library(readxl)
library(ggplot2)
library(ggpubr)
dts<-read_xlsx("JawL.xlsx")
dts<-rename(dts,TS2=`Total Severity Score2`)

Graphics

Then we apply the Kruskal-wallis test to find significant differences

setwd("C:\\Users\\Admin\\OneDrive\\Documents\\Bursian")

kruskal.test(TS2 ~ Trt1, data = dts)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  TS2 by Trt1
## Kruskal-Wallis chi-squared = 38.466, df = 8, p-value = 6.174e-06

Followed by the wilcoxon test to implement pairwise-group comparison (like pairwise t-test after an ANOVA.). We need to correct for multiple testing, so we use the Benjamini-Hochberg procedure.

pairwise.wilcox.test(x = dts$TS2,g = dts$Trt1,p.adjust.method = "BH")
## 
##  Pairwise comparisons using Wilcoxon rank sum test 
## 
## data:  dts$TS2 and dts$Trt1 
## 
##     0     1.3   2.5   5     7.5   10    15    20
## 1.3 -     -     -     -     -     -     -     - 
## 2.5 -     -     -     -     -     -     -     - 
## 5   0.453 0.453 0.453 -     -     -     -     - 
## 7.5 0.453 0.453 0.453 1.000 -     -     -     - 
## 10  0.246 0.246 0.246 0.453 0.453 -     -     - 
## 15  0.014 0.014 0.014 0.016 0.016 0.048 -     - 
## 20  0.014 0.014 0.014 0.014 0.014 0.014 0.246 - 
## 40  0.014 0.014 0.014 0.014 0.014 0.014 0.246 - 
## 
## P value adjustment method: BH

Interpretation: there are no difference between levels 0-10. There are no difference between levels 15-40. but there are differences between these two groups.

Methods paragraph

Due to the ordinal nature of Total severity scores, the data was analyzed using non-parametric methods. First, a Kruskal-Wallis [1] test was applied to determine if there were differences between treatments (doses). Subsequently, all possible pairwise comparisons between doses were performed using the Wilconxon Test [2]. Due to the large number of comparisons (36 in total), the resulting p-values were corrected for multiple testing using the Benjamini and Hochberg procedure [3].

References

[1] Kruskal-Wallis test: Myles Hollander and Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 115-120.

[2] wilcoxon test: Myles Hollander and Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 68-75.

[3] p-value adjustment: Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B 57, 289-300.