Paired samples t-test

Runs a paired-samples t-test and prints the results in a readable format.

Usage

pairedSamplesTTest(
  formula,
  data = NULL,
  id = NULL,
  one.sided = FALSE,
  conf.level = 0.95
)

Arguments

formula: A formula describing the data. For wide-format data use a one-sided formula such as ~ time1 + time2. For long-format data use outcome ~ group + (id), or outcome ~ group together with the id argument.
data: An optional data frame containing the variables named in formula. Tibbles are accepted and converted automatically. If data is omitted the variables are looked up in the workspace.
id: The name of the participant ID variable as a character string (e.g., id = "subject"). Required when using long-format data with a plain outcome ~ group formula instead of outcome ~ group + (id).
one.sided: Set to FALSE (default) for a two-sided test. Set to the name of the group or variable expected to have the larger mean for a one-sided test (e.g., one.sided = "time2").
conf.level: The confidence level for the confidence interval. The default is 0.95 for a 95% interval.

Value

Prints a summary showing the variable names, descriptive statistics (including the mean and standard deviation of the differences), null and alternative hypotheses, test results (t-statistic, degrees of freedom, p-value), a confidence interval, and Cohen's d as a measure of effect size. The underlying results are also returned as a list, so the output can be assigned to a variable and inspected if needed.

Details

Runs a paired-samples t-test and prints the results in a beginner-friendly format. The calculations are done by t.test and cohensD.

There are two ways to supply data. If the data are in wide format (one row per participant, with the two measurements in separate columns), use a one-sided formula such as ~ time1 + time2. The first row of time1 is paired with the first row of time2, and so on.

If the data are in long format (two rows per participant), use a two-sided formula. The recommended style is outcome ~ group + (id), where the participant ID variable is enclosed in parentheses. Alternatively, use the plain formula outcome ~ group and supply the ID variable name via the id argument. The lme4-style notation outcome ~ group + (1|id) is also accepted as equivalent to outcome ~ group + (id).

Participants with missing measurements are removed with a warning.

Examples

# long-format data: one row per participant per time point
df <- data.frame(
  id = factor(
    x = c(1, 1, 2, 2, 3, 3, 4, 4),
    labels = c("alice", "bob", "chris", "diana")
  ),
  time = factor(
    x = c(1, 2, 1, 2, 1, 2, 1, 2),
    labels = c("time1", "time2")
  ),
  wm = c(3, 4, 6, 6, 9, 12, 7, 9)
)

# wide-format data: one row per participant
df2 <- longToWide(df, wm ~ time)

# three equivalent ways to run the same test
pairedSamplesTTest(formula = wm ~ time, data = df, id = "id")
#> 
#>    Paired samples t-test 
#> 
#> Outcome variable:   wm 
#> Grouping variable:  time 
#> ID variable:        id 
#> 
#> Descriptive statistics: 
#>             time1 time2 difference
#>    mean     6.250 7.750     -1.500
#>    std dev. 2.500 3.500      1.291
#> 
#> Hypotheses: 
#>    null:        population means equal for both measurements
#>    alternative: different population means for each measurement
#> 
#> Test results: 
#>    t-statistic:  -2.324 
#>    degrees of freedom:  3 
#>    p-value:  0.103 
#> 
#> Other information: 
#>    two-sided 95% confidence interval:  [-3.554, 0.554] 
#>    estimated effect size (Cohen's d):  1.162 
#> 
pairedSamplesTTest(formula = wm ~ time + (id), data = df)
#> 
#>    Paired samples t-test 
#> 
#> Outcome variable:   wm 
#> Grouping variable:  time 
#> ID variable:        id 
#> 
#> Descriptive statistics: 
#>             time1 time2 difference
#>    mean     6.250 7.750     -1.500
#>    std dev. 2.500 3.500      1.291
#> 
#> Hypotheses: 
#>    null:        population means equal for both measurements
#>    alternative: different population means for each measurement
#> 
#> Test results: 
#>    t-statistic:  -2.324 
#>    degrees of freedom:  3 
#>    p-value:  0.103 
#> 
#> Other information: 
#>    two-sided 95% confidence interval:  [-3.554, 0.554] 
#>    estimated effect size (Cohen's d):  1.162 
#> 
pairedSamplesTTest(formula = ~ wm_time1 + wm_time2, data = df2)
#> 
#>    Paired samples t-test 
#> 
#> Variables:  wm_time1 , wm_time2 
#> 
#> Descriptive statistics: 
#>             wm_time1 wm_time2 difference
#>    mean        6.250    7.750     -1.500
#>    std dev.    2.500    3.500      1.291
#> 
#> Hypotheses: 
#>    null:        population means equal for both measurements
#>    alternative: different population means for each measurement
#> 
#> Test results: 
#>    t-statistic:  -2.324 
#>    degrees of freedom:  3 
#>    p-value:  0.103 
#> 
#> Other information: 
#>    two-sided 95% confidence interval:  [-3.554, 0.554] 
#>    estimated effect size (Cohen's d):  1.162 
#> 

# one-sided test: is time2 larger than time1?
pairedSamplesTTest(formula = wm ~ time, data = df, id = "id", one.sided = "time2")
#> 
#>    Paired samples t-test 
#> 
#> Outcome variable:   wm 
#> Grouping variable:  time 
#> ID variable:        id 
#> 
#> Descriptive statistics: 
#>             time1 time2 difference
#>    mean     6.250 7.750     -1.500
#>    std dev. 2.500 3.500      1.291
#> 
#> Hypotheses: 
#>    null:        population means are equal, or smaller for measurement 'time2' 
#>    alternative: population mean is larger for measurement 'time2' 
#> 
#> Test results: 
#>    t-statistic:  -2.324 
#>    degrees of freedom:  3 
#>    p-value:  0.051 
#> 
#> Other information: 
#>    one-sided 95% confidence interval:  [-Inf, 0.019] 
#>    estimated effect size (Cohen's d):  1.162 
#> 

# missing value: that participant is removed with a warning
df$wm[1] <- NA
pairedSamplesTTest(formula = wm ~ time, data = df, id = "id")
#> Warning: 1 case(s) removed due to missingness
#> 
#>    Paired samples t-test 
#> 
#> Outcome variable:   wm 
#> Grouping variable:  time 
#> ID variable:        id 
#> 
#> Descriptive statistics: 
#>             time1 time2 difference
#>    mean     7.333 9.000     -1.667
#>    std dev. 1.528 3.000      1.528
#> 
#> Hypotheses: 
#>    null:        population means equal for both measurements
#>    alternative: different population means for each measurement
#> 
#> Test results: 
#>    t-statistic:  -1.89 
#>    degrees of freedom:  2 
#>    p-value:  0.199 
#> 
#> Other information: 
#>    two-sided 95% confidence interval:  [-5.461, 2.128] 
#>    estimated effect size (Cohen's d):  1.091 
#> 

# missing row: that participant is also removed with a warning
df <- df[-1, ]
pairedSamplesTTest(formula = wm ~ time, data = df, id = "id")
#> Warning: 1 case(s) removed due to missingness
#> 
#>    Paired samples t-test 
#> 
#> Outcome variable:   wm 
#> Grouping variable:  time 
#> ID variable:        id 
#> 
#> Descriptive statistics: 
#>             time1 time2 difference
#>    mean     7.333 9.000     -1.667
#>    std dev. 1.528 3.000      1.528
#> 
#> Hypotheses: 
#>    null:        population means equal for both measurements
#>    alternative: different population means for each measurement
#> 
#> Test results: 
#>    t-statistic:  -1.89 
#>    degrees of freedom:  2 
#>    p-value:  0.199 
#> 
#> Other information: 
#>    two-sided 95% confidence interval:  [-5.461, 2.128] 
#>    estimated effect size (Cohen's d):  1.091 
#>

Usage

Arguments

Value

Details

See also

Examples