Hypothesis tests

1 Presentation

You can download the course slides for this section here

2 Roadmap to your test

Getting Started

• Make sure that you are working in your course project
• Create a new quarto document and name it “hypothesis_tests.qmd”
• Insert a code chunk and load 2 important libraries
• Insert a new code chunk- Write source(here("scripts", "01_import.R")) in the chunk
• Write a short headline to each code chunk
• Change the YAML header to style your document output.

TipThe YAML header can look like this

---
title: "TITLE"
subtitle: "SUBTITLE"
author: "ME"
date: today
format: 
  html:
    toc: true
    toc-depth: 2
    embed-resources: true
    number-sections: true
    number-depth: 2
    code-fold: true
    code-summary: "Show the code"
    code-tools: true
execute:
  message: false
  warning: false
---

Add the gtsummary, ggstatsplot, statsExpressions and rstatix packages to the code chunk where you have your library calls.

If you need to install any of the packages:

• use install.packages(c("package_name", "package_name")) to download the packages.
• This is done in the console and NOT in your script.

library(tidyverse)        # import, tidy, transform, visualize
library(here)             # filepath control
library(gtsummary)        # tables (with stats)
library(ggstatsplot)      # statistical plots
library(rstatix)          # statistical tests
library(statsExpressions) # statistical tests

2.1 The bugs_long dataset

bugs_long provides information on the extent to which men and women want to kill arthropods that vary in disgustingness (low, high) and freighteningness (low, high) (four groups in total). Each participant rated their attitude towards all four kinds of anthropods. bugs_long is a subset of the data reported by Ryan et al.(2013) .

bugs_long is included in the ggstatsplot package.

Note that this is a repeated measures design because the same participant gave four different ratings across four different conditions (LDLF, LDHF, HDLF, HDHF).

• desire - The desire to kill an arthropod was indicated on a scale from 0 to 10
• gender Male/Female
• region
• condition
  • LDLF: low disgustingness and low freighteningness
    
  • LDHF: low disgustingness and high freighteningness
    
  • HDLF: high disgustingness and low freighteningness
    
  • HDHF: high disgustingness and high freighteningness

Picture from Ryan et al. (2013) https://doi.org/10.1016/j.chb.2013.01.024

In bugs_long, is there a difference within the participants in their desire to kill bugs from the four different conditions?

• Should you use ggwithinstats() or ggbetweenstats() when comparing
• Is it reasonable to assume normality?

bugs_long |> group_by(condition) |> shapiro_test(desire)

# qqplot
bugs_long |> 
  ggplot(aes(sample = desire, group = condition)) +
  geom_qq_line(color = "red", linewidth = 1)+
  geom_qq()+
  facet_wrap(~condition)


# Density plot
bugs_long |> 
  ggplot(aes(x = desire, fill = condition)) +
  geom_density(alpha = 0.2)

• Make the appropriate test

bugs_long |> 
  ggwithinstats(x = condition,
                y = desire,
                type = "nonparametric")

bugs_long |> 
  
  # Friedman test only works with complete data
  # Some subjects have missing data in desire
  # We need to remove these
  drop_na(desire, condition, subject) |> 
  add_count(subject) |> 
  filter(n == 4) |> 
  
  # Send the complete data
  friedman_test(desire ~ condition | subject)

bugs_long |>
  oneway_anova(
    x = condition,
    y = desire,
    type = "nonparametric",
    paired = TRUE
  )

# This is not straightforward to do in gtsummary 
# because you are looking at a repeated measures test (each subject has 4 rows)
#
# However, it can be done. See this link for how the author of the gtsummary package solves it
#
# https://stackoverflow.com/questions/75003882/how-to-do-repeated-measures-anova-and-friedman-test-in-gtsummary

• What is your interpretation?
• What is the consequence if you change the type of test?

Is there a difference between men and women in the desire to kill bugs that are LDHF (low disgustingness and high freighteningness).

• Create a filtered data frame of bugs_long

bugs_long_LDHF_only <- bugs_long |> filter(condition == "LDHF")

• Should you use ggwithinstats() or ggbetweenstats() for this test?
• Is it reasonable to assume normality?

bugs_long_LDHF_only |> 
  filter(!is.na(gender), !is.na(desire)) |> 
  group_by(gender) |> 
  shapiro_test(desire)

# qqplot
bugs_long_LDHF_only |> 
  ggplot(aes(sample = desire, color = gender)) +
  geom_qq_line(color = "red", linewidth = 1) +
  geom_qq()+
  facet_wrap(~gender)


# Density plot
bugs_long_LDHF_only |> 
  ggplot(aes(x = desire, fill = gender)) +
  geom_density(alpha = 0.2)

• Make the appropriate test

bugs_long_LDHF_only |> 
  ggbetweenstats(x = gender,
                 y = desire,
                 type = "nonparametric")

bugs_long_LDHF_only |> 
  wilcox_test(desire ~ gender)

bugs_long_LDHF_only |> 
  two_sample_test(
    x = gender, 
    y = desire, 
    type = "nonparametric", 
    paired = FALSE
  )

bugs_long_LDHF_only |> 
  select(gender, desire) |> 
  tbl_summary(by = "gender") |> 
  add_p()

• What is your interpretation?
• What is the consequence if you change the type of test?
• Confused by all the different names in this example? Its not you. This test has many synonyms. Quote from wikipedia: “Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test)…”

Is there a difference in the frequency of men and women between North America and the remaining regions?.

• First, lump region togehter to two levels (fct_lump())
• Reduce the data to one row pr subject ID, and discuss why this is a good idea.

bugs_long_region_lump <- bugs_long |>
  mutate(region = fct_lump(region, 1)) |> 
  group_by(subject) |> 
  slice(1) |> 
  ungroup()

• Should you use ggwithinstats() or ggbetweenstats() or perhaps ggbarstats() for this test?
• Should you asses normality?

# Both variables are factors (categorical/nominal). Normality has to do with continuous data

• Make the appropriate test

bugs_long_region_lump |> 
  ggbarstats(x = gender,
             y = region)

# rstatix is somewhat complicated here
# First we need to make table
# table is not pipe friendly

table(bugs_long_region_lump$region , bugs_long_region_lump$gender) |> 
  
  # Then pass the table to the test
  chisq_test()

bugs_long_region_lump |> 
  contingency_table(gender, region)

# Notice that gtsummary is switching to Fishers exact test.
# Fishers exact test is actually the right tests to use if one of the groups has 5 or fewer observations
bugs_long_region_lump |> 
  select(gender, region) |> 
  tbl_summary(by = gender) |> 
  add_p()

# If we absolutely want to run the chisquared test we do it like this
bugs_long_region_lump |> 
  select(gender, region) |> 
  tbl_summary(by = gender) |> 
  add_p(test = list(all_categorical() ~ "chisq.test"))

# If you want to see a contigency table
# With row and column sum counts
bugs_long_region_lump |> 
  drop_na() |> # Remove observations with missing values
  tbl_cross(gender, region) |> 
  add_p()

• What is your interpretation?

2.2 The ToothGrowth dataset

ToothGrowth gives information on tooth length in 60 guinea pigs. Each animal received one of three dose levels of vitamin C (0.5, 1, and 2 mg/day) by one of two delivery methods, orange juice or ascorbic acid (a form of vitamin C and coded as VC).

• len Tooth length
• supp Supplement type
  • VC Vitamin C as ascorbic acid
  • OJ Orange Juice
• dose Dose in milligrams/day (0.5, 1, or 2)

Is there a difference in Tooth length based on the type of supplement?

• Should you use ggwithinstats() or ggbetweenstats() when comparing
• Is it reasonable to assume normality?

ToothGrowth |> group_by(supp) |> shapiro_test(len)

# qqplot
ToothGrowth |> 
  ggplot(aes(sample = len, color = supp)) +
  geom_qq()+
  geom_qq_line()

# Density plot
ToothGrowth |> 
  ggplot(aes(x = len, fill = supp)) +
  geom_density(alpha = 0.2)

• Make the appropriate test

ToothGrowth |> 
  ggbetweenstats(x = supp,
                 y = len,
                 type = "parametric")

# It is likely completely fine to run this as a "parametric" test, but you could consider type = "robust"

ToothGrowth |> 
  t_test(len ~ supp,
         paired = FALSE)

# We run this as a "parametric" test

ToothGrowth |> 
  two_sample_test(x = supp, 
                  y = len, 
                  paired = FALSE, 
                  type = "parametric")

# It is likely completely fine to run this as a "parametric" test, but you could consider type = "robust".

ToothGrowth |> 
  select(supp, len) |> 
  tbl_summary(
    by = supp, 
    statistic = list(all_continuous() ~ "{mean} ({sd})")) |> 
  add_p(test = list(all_continuous() ~ "t.test"))

• What is your interpretation?

Improve your home assignment

• Return to your home assignment and add some statistical tests if and where it makes sense
• Remember to change project (top right corner in Rstudio)
• Using the menu in the top right corner, you can switch between your course project and your home assignment

Roadmap to your test (r4phd.sdu.dk)