One-sample t-test | R for Psychological Research

Set up

R code

library(tidyverse)
library(rstatix)
students <- read_csv("data/students.csv", show_col_types = FALSE)

The question

Wellbeing is rated from 1 to 7, so 4 is the midpoint: neither good nor bad. At the start of semester, is students' wellbeing different from 4?

Dot plot of wellbeing at the start of semester with a dashed line at 4 and a solid line at the group mean, a little above 4

Describe first

R code

students %>% get_summary_stats(Wellbeing_T1, type = "mean_sd")

Output

# A tibble: 1 × 4
  variable         n  mean    sd
  <fct>        <dbl> <dbl> <dbl>
1 Wellbeing_T1   300  4.43  1.05

Run the test

Wellbeing_T1 ~ 1 means "test this one variable"; mu is the value to compare with.

R code

students %>% t_test(Wellbeing_T1 ~ 1, mu = 4)

Output

# A tibble: 1 × 7
  .y.          group1 group2         n statistic    df        p
* <chr>        <chr>  <chr>      <int>     <dbl> <dbl>    <dbl>
1 Wellbeing_T1 1      null model   300      7.10   299 8.87e-12

statistic = t = 7.10. Bigger t = bigger difference relative to the spread.
df = 299 (n − 1).
p = 8.87e-12, far below .05: significant. Report as p < .001.

How big is the difference?

Significant doesn't mean big. Cohen's d gives the size, in SDs:

R code

students %>% cohens_d(Wellbeing_T1 ~ 1, mu = 4)

Output

# A tibble: 1 × 6
  .y.          group1 group2     effsize     n magnitude
* <chr>        <chr>  <chr>        <dbl> <int> <ord>    
1 Wellbeing_T1 1      null model   0.410   300 small

d = 0.41: a small-to-medium effect (0.2 small, 0.5 medium, 0.8 large).

Exercises

Exercise 14.1 Dataset: students.csv

Do students sleep enough?

Adults are advised to sleep at least 7 hours. Do students sleep a different amount from 7 hours?

Get the mean and SD of Sleep.
Run the t-test against 7, and get Cohen's d.
Report it.

Show answerHide answer

R code

students %>% get_summary_stats(Sleep, type = "mean_sd")
students %>% t_test(Sleep ~ 1, mu = 7)
students %>% cohens_d(Sleep ~ 1, mu = 7)

Output

# A tibble: 1 × 4
  variable     n  mean    sd
  <fct>    <dbl> <dbl> <dbl>
1 Sleep      290  6.41 0.819
# A tibble: 1 × 7
  .y.   group1 group2         n statistic    df        p
* <chr> <chr>  <chr>      <int>     <dbl> <dbl>    <dbl>
1 Sleep 1      null model   290     -12.2   289 5.87e-28
# A tibble: 1 × 6
  .y.   group1 group2     effsize     n magnitude
* <chr> <chr>  <chr>        <dbl> <int> <ord>    
1 Sleep 1      null model  -0.717   290 moderate

Students slept significantly less (M = 6.41, SD = 0.82) than the recommended 7 hours, t(289) = −12.22, p < .001, d = −0.72. The 10 students with no sleep answer are left out automatically, so df = 289.

Exercise 14.2 Dataset: students.csv

Stress

Stress is rated 1 to 10, so the midpoint is 5.5. Is students' average stress different from 5.5? Report it.

Show answerHide answer

R code

students %>% get_summary_stats(Stress, type = "mean_sd")
students %>% t_test(Stress ~ 1, mu = 5.5)
students %>% cohens_d(Stress ~ 1, mu = 5.5)

Output

# A tibble: 1 × 4
  variable     n  mean    sd
  <fct>    <dbl> <dbl> <dbl>
1 Stress     300  5.94  1.84
# A tibble: 1 × 7
  .y.    group1 group2         n statistic    df         p
* <chr>  <chr>  <chr>      <int>     <dbl> <dbl>     <dbl>
1 Stress 1      null model   300      4.16   299 0.0000414
# A tibble: 1 × 6
  .y.    group1 group2     effsize     n magnitude
* <chr>  <chr>  <chr>        <dbl> <int> <ord>    
1 Stress 1      null model   0.240   300 small

Students' stress (M = 5.94, SD = 1.84) was a little above the midpoint, t(299) = 4.16, p < .001, d = 0.24: significant, but a small effect.

Key points

t_test(variable ~ 1, mu = value) compares a mean with a value.
cohens_d() gives the effect size.
Report M, SD, t(df), p and d.