T-test on real data using tidyverse

t.test()
tidyverse
Learn t-test on real data using tidyverse with this comprehensive R tutorial. Includes practical examples and code snippets.
Published

August 28, 2024

Introduction

A t-test is a statistical test used to compare means between groups or against a known value. This tutorial demonstrates how to perform t-tests using tidyverse tools for data manipulation and analysis, making the process more intuitive and reproducible.

Getting Started

library(tidyverse)
library(palmerpenguins)

Example 1: One-Sample T-test

The Problem

We want to test whether the average body mass of penguins differs significantly from a hypothesized population mean of 4000 grams.

Step 1: Explore the Data

Let’s examine the penguin body mass data to understand its distribution.

penguins |>
  select(body_mass_g) |>
  drop_na() |>
  summary()

This shows us the basic statistics for penguin body mass, including the mean and quartiles.

Step 2: Visualize the Distribution

Creating a histogram helps us assess normality before running the t-test.

penguins |>
  drop_na(body_mass_g) |>
  ggplot(aes(x = body_mass_g)) +
  geom_histogram(bins = 20, alpha = 0.8, fill = "steelblue", color = "white") +
  geom_vline(xintercept = 4000, color = "red", linetype = "dashed",
             linewidth = 1.2) +
  labs(title = "Distribution of Penguin Body Mass",
       subtitle = "Red dashed line: hypothesized population mean (4000g) for one-sample t-test",
       x = "Body Mass (g)", y = "Count") +
  theme_minimal()

Histogram in R with ggplot2 showing penguin body mass distribution with a hypothesized mean reference line for a one-sample t-test

The histogram shows the distribution of body mass with our hypothesized mean marked in red.

Step 3: Perform One-Sample T-test

Now we test if the mean body mass significantly differs from 4000 grams.

penguin_mass <- penguins |>
  drop_na(body_mass_g) |>
  pull(body_mass_g)

t.test(penguin_mass, mu = 4000)

The t-test results show a significant difference (p < 0.05), indicating penguin body mass differs from 4000 grams.

Example 2: Two-Sample T-test

The Problem

We want to compare body mass between male and female penguins to determine if there’s a significant difference between sexes. This is a common research question in biological studies.

Step 1: Prepare the Data

First, we’ll clean the data and examine the sample sizes for each group.

penguin_sex_data <- penguins |>
  filter(!is.na(body_mass_g), !is.na(sex)) |>
  select(sex, body_mass_g)

penguin_sex_data |>
  count(sex)

This gives us clean data with body mass and sex information, showing balanced sample sizes.

Step 2: Compare Group Means

Let’s calculate summary statistics for each group to preview potential differences.

penguin_sex_data |>
  group_by(sex) |>
  summarise(
    mean_mass = mean(body_mass_g),
    sd_mass = sd(body_mass_g),
    n = n()
  )

The summary shows clear differences in average body mass between male and female penguins.

Step 3: Visualize Group Differences

A boxplot effectively shows the distribution differences between groups.

penguin_sex_data |>
  ggplot(aes(x = sex, y = body_mass_g, fill = sex)) +
  geom_boxplot(alpha = 0.7, outlier.shape = NA) +
  geom_jitter(width = 0.15, alpha = 0.5) +
  labs(title = "Penguin Body Mass by Sex",
       subtitle = "Two-sample t-test comparison of body mass between sexes",
       x = "Sex", y = "Body Mass (g)") +
  theme_minimal() +
  theme(legend.position = "none")

Boxplot with jitter in R with ggplot2 comparing penguin body mass between male and female penguins for a two-sample t-test

The boxplot reveals that male penguins appear to have higher body mass than females.

Step 4: Perform Two-Sample T-test

Now we’ll test if the observed difference is statistically significant.

male_mass <- penguin_sex_data |>
  filter(sex == "male") |>
  pull(body_mass_g)

female_mass <- penguin_sex_data |>
  filter(sex == "female") |>
  pull(body_mass_g)

t.test(male_mass, female_mass)

The t-test confirms a highly significant difference (p < 0.001) in body mass between male and female penguins.

Step 5: Alternative Approach Using Formula

We can also perform the same test using R’s formula interface for cleaner code.

t.test(body_mass_g ~ sex, data = penguin_sex_data)

This produces identical results but with more concise syntax using the formula notation.

Summary

  • One-sample t-tests compare a sample mean against a hypothesized population value
  • Two-sample t-tests compare means between two independent groups
  • Always visualize your data before testing to check assumptions and understand distributions
  • Clean your data by removing missing values before analysis using drop_na()

  • The tidyverse approach makes data preparation and exploration more intuitive and reproducible