Reference: MAT 2375 Introduction to statistics and MAT3378 Analysis of experience plans

Project: Necessary packages.

library (PMCMRplus) # For Nemenyi test

library (PMCMR)

library (tidyverse)

library (ggpubr)

library (rstatix)

Partie I : Non-parametric tests

sample_data <- data. frame(

Resistance = c (14.87, 16.81, 15.83, 15.47, 13.6, 14.76,

17.4, 14.62, 18.43, 18.76, 20.12, 19.11, 19.81, 18.43,

17.16, 16.4, 16.95, 12.28, 12, 13.18,

14.99, 15.76, 19.35, 15.52,8.59, 10.9, 8.6, 10.13,

10.28, 9.98, 9.41, 10.04, 11.55, 13.36,

13.64, 12.16, 11.62, 12.39, 12.05, 11.95),

Type = as. factor (c(rep(1, 8), rep(2, 8),

rep (3, 8), rep(4, 8), (5, 8)))

)

set.seed123 # For the reproducibility

data - sample_data[sample(1:nrow(sample_data), size = 100, replace = TRUE), ]

Questions

Let's consider the dataset: data.

1. Overall comparison of the resistance of different types of materials: Is there a significant variation in resistance between different types of materials?

2. Specific contact between two types: Is there a significant difference of resistance between type one and type two ?

3. Post hoc analysis after Kruskal-Wallisl: Which significant pairs of types have significant differences in strength after finding a significant overall difference?

4. Analysis of trends between the selected types: How does resistance vary from type 1 to type 4?