Chapter 11 Linear mixed models
In the previous chapter we learned how to test hypotheses based on the comparions of means between sets of data when we were able to meet our two base assumptions. These parametric tests are preferred over non-parametric tests because they are more robust. However, when we simply aren’t able to meet these assumptions we must not despair. Non-parametric tests are still useful. In this chapter we will learn how to run non-parametirc tests for two sample and multiple sample datasets. To start, let’s load our libraries and chicks data if we have not already.
# First activate libraries
library(tidyverse)
library(ggpubr)
# Then load data
chicks <- as_tibble(ChickWeight)With our libraries and data loaded, let’s find a day in which at least one of our assumptions are violated.
# Then check for failing assumptions
chicks %>%
filter(Time == 0) %>%
group_by(Diet) %>%
summarise(norm_wt = as.numeric(shapiro.test(weight)[2]),
var_wt = var(weight))R> # A tibble: 4 x 3
R> Diet norm_wt var_wt
R> <fct> <dbl> <dbl>
R> 1 1 0.0138 0.989
R> 2 2 0.138 2.23
R> 3 3 0.00527 1.07
R> 4 4 0.0739 1.1111.1 Wilcox rank sum test
The non-parametric version of a t-test is a Wilcox rank sum test. To perform this test in R we may again use compare_means() and specify the test we want:
compare_means(weight ~ Diet, data = filter(chicks, Time == 0, Diet %in% c(1, 2)), method = "wilcox.test")R> # A tibble: 1 x 8
R> .y. group1 group2 p p.adj p.format p.signif method
R> <chr> <chr> <chr> <dbl> <dbl> <chr> <chr> <chr>
R> 1 weight 1 2 0.235 0.23 0.23 ns WilcoxonWhat do our results show?
11.2 Kruskall-Wallis rank sum test
11.2.1 Single factor
The non-parametric version of an ANOVA is a Kruskall-Wallis rank sum test. As you may have by now surmised, this may be done with compare_means() as seen below:
compare_means(weight ~ Diet, data = filter(chicks, Time == 0), method = "kruskal.test")R> # A tibble: 1 x 6
R> .y. p p.adj p.format p.signif method
R> <chr> <dbl> <dbl> <chr> <chr> <chr>
R> 1 weight 0.475 0.48 0.48 ns Kruskal-WallisAs with the ANOVA, this first step with the Kruskall-Wallis test is not the last. We must again run a post-hoc test on our results. This time we will need to use pgirmess::kruskalmc(), which means we will need to load a new library.
library(pgirmess)
kruskalmc(weight ~ Diet, data = filter(chicks, Time == 0))R> Multiple comparison test after Kruskal-Wallis
R> p.value: 0.05
R> Comparisons
R> obs.dif critical.dif difference
R> 1-2 6.95 14.89506 FALSE
R> 1-3 6.90 14.89506 FALSE
R> 1-4 4.15 14.89506 FALSE
R> 2-3 0.05 17.19933 FALSE
R> 2-4 2.80 17.19933 FALSE
R> 3-4 2.75 17.19933 FALSELet’s consult the help file for kruskalmc() to understand what this print-out means.
11.2.2 Multiple factors
The water becomes murky quickly when one wants to perform mutliple factor non-parametric comparison of means tests. TO that end, we will not cover the few existing methods here. Rather, one should avoid the necessity for these types of tests when designing an experiment.
11.3 Generalised linear models
11.3.1 Sign Test
11.3.2 Wilcoxon Signed-Rank Test
11.3.3 Mann-Whitney-Wilcoxon Test
11.3.4 Kruskal-Wallis Test
11.3.5 Generalised linear models (GLM)
11.4 Exercises
11.5 Exercise 1
Write out the hypotheses that we tested for in this chapter and answer them based on the results we produced in class.