Lab 10: t-tests

Learning Objectives

Getting started

Before you begin the lab activities, review the steps for setting up a project for a lab activity:

Then, complete the following steps to make sure you are fully set up.

  1. Get the Lab Worksheet.

    Pick up a physical copy of the lab worksheet, or print one if you are working outside of class.
    Download Lab Worksheet (PDF, if needed)

  2. Open Posit Cloud and create Lab 10 in Your Workspace.

  3. Create a new R script and save it as lab-10-script.R.

  4. Add the following code to your R script and save the script. Upon save, you should see a message in the source prompting you to install the package. Click “Install”. Then run the line of code.

    # load packages --------------------------------------------------------------

library(tidyverse)
library(haven)
NoteCheckpoint

At this point, you should have:

  • These instructions open in a web browser.
  • Your Lab 10 project open in Posit Cloud in another browser window.
  • The required packages installed and loaded without errors
  • The Lab 10 worksheet in front of you.

Do not continue until all of the above steps are working correctly.

Overview

In this lab, you will analyze the relationship between two categorical variables using contingency analysis. A contingency table summarizes the joint distribution of two categorical variables and allows us to estimate measures of association such as relative risk (RR) and odds ratio (OR). These measures describe the magnitude and direction of an association between two binary variables. We will also conduct a chi-square test of independence to determine whether the observed association is statistically significant.

You will use data from the National Health and Nutrition Examination Survey (NHANES), a large, nationally representative health survey conducted in the United States. For this lab, you will examine the relationship between sleep duration and depressive symptoms among adults.

Prerequisites

In your R script, load the following packages:

Sleep duration: one-sample test

In this activity, you will:

  • read in NHANES sleep data and keep the first 100 observations
  • visualize the data using a histogram
  • assess the distribution to decide between a t-test and a Wilcoxon test
  • test whether mean (or median) sleep duration differs from 8 hours
  • interpret the result in plain language

Code

slq_data <-
  read_xpt("https://wwwn.cdc.gov/Nchs/Data/Nhanes/Public/2021/DataFiles/SLQ_L.xpt") |> 
  drop_na(SLD012) |>
  slice_head(n = 100)

slq_data |>
  ggplot(aes(x = SLD012)) +
  geom_histogram(binwidth = 1, boundary = 0) +
  labs(
    x = "Hours of sleep",
    y = "Frequency",
    title = "Distribution of sleep duration"
  ) +
  theme_minimal()

Bison body mass: two-sample comparison

In this activity, you will:

  • read in the bison dataset and keep 100 observations for each sex
  • visualize body mass distributions for males and females using histograms
  • assess the distributions to decide between a t-test and a Mann–Whitney test
  • compare body mass between sexes using either t.test() or wilcox.test()
  • interpret the results in terms of differences between groups

Use the following code:

bison_data <-
  knz_bison |> 
  drop_na(animal_sex, animal_weight) |>
  slice_head(n = 100, by = animal_sex)

bison_data |>
  ggplot(aes(x = animal_weight)) +
  geom_histogram(binwidth = 50) +
  facet_wrap(~animal_sex, ncol = 1)

In this activity, you will work with a dataset of shoulder strength measurements.

  • each row represents an individual
  • variables include Left and Right shoulder strength measurements
  • individuals are classified as Swimmer or Control (non-swimmer)
  • the goal is to compare strength within individuals, not between individuals

You will:

  • calculate strong arm and weak arm for each individual
  • note that comparing left vs right directly is misleading because people are left- or right-handed
  • instead, compute strong arm − weak arm to create a meaningful paired comparison
  • perform paired t-tests comparing strong vs weak arm strength
  • run separate tests for: - swimmers - non-swimmers
  • optionally, test left vs right in non-swimmers to confirm the difference is near zero
  • interpret results in terms of within-individual differences

Code

library(PairedData)
data("Shoulder")

shoulder_data <- 
  Shoulder |> 
  as_tibble() |> 
  rowwise() |>
  mutate(
    strongarm = max(Left, Right),
    weakarm = min(Left, Right)
  ) |>
  ungroup()

shoulder_data |>
  ggplot(aes(x = strongarm)) +
  geom_histogram(bins = 10)

shoulder_data |>
  ggplot(aes(x = weakarm)) +
  geom_histogram(bins = 10)

swimmers <- 
  shoulder_data |> 
  filter(Group == "Swimmer") |>
  print()
# A tibble: 15 × 6
   Subject Group    Left Right strongarm weakarm
   <chr>   <fct>   <dbl> <dbl>     <dbl>   <dbl>
 1 S1      Swimmer   193   192       193     192
 2 S2      Swimmer   208   207       208     207
 3 S3      Swimmer   198   198       198     198
 4 S4      Swimmer   201   203       203     201
 5 S5      Swimmer   196   194       196     194
 6 S6      Swimmer   196   193       196     193
 7 S7      Swimmer   211   214       214     211
 8 S8      Swimmer   206   207       207     206
 9 S9      Swimmer   197   195       197     195
10 S10     Swimmer   204   198       204     198
11 S11     Swimmer   197   198       198     197
12 S12     Swimmer   205   206       206     205
13 S13     Swimmer   207   200       207     200
14 S14     Swimmer   204   204       204     204
15 S15     Swimmer   204   205       205     204
nonswimmers <-
  shoulder_data |> 
  filter(Group == "Control") |>
  print()
# A tibble: 15 × 6
   Subject Group    Left Right strongarm weakarm
   <chr>   <fct>   <dbl> <dbl>     <dbl>   <dbl>
 1 S16     Control   184   197       197     184
 2 S17     Control   172   187       187     172
 3 S18     Control   178   180       180     178
 4 S19     Control   186   175       186     175
 5 S20     Control   194   192       194     192
 6 S21     Control   188   189       189     188
 7 S22     Control   164   185       185     164
 8 S23     Control   202   168       202     168
 9 S24     Control   182   204       204     182
10 S25     Control   186   181       186     181
11 S26     Control   188   182       188     182
12 S27     Control   186   172       186     172
13 S28     Control   192   183       192     183
14 S29     Control   204   189       204     189
15 S30     Control   178   198       198     178

Wrap-up and Submission

  1. Make sure your script is saved in your project on Posit Cloud.
  2. Ask the instructor to explain anything you aren’t sure about.
  3. Show your handout to a Learning Assistant for a completion grade before you leave lab. You may do this as soon as you finish. Keep the handout for yourself.