MOTE (version 1.2.2)

d_dep_t_diff: Cohen's d for Paired t Using the SD of Difference Scores

Description

**Note on function and output names:** This effect size is now implemented with the snake_case function name `d_dep_t_diff()` to follow modern R style guidelines. The original dotted version `d.dep.t.diff()` is still available as a wrapper for backward compatibility, and both functions return the same list. The returned object includes both the original element names (e.g., `mdiff`, `Mlow`, `Mhigh`, `sddiff`) and newer snake_case aliases (e.g., `m_diff`, `m_diff_lower_limit`, `m_diff_upper_limit`, `sd_diff`). New code should prefer `d_dep_t_diff()` and the snake_case output names, but existing code using the older names will continue to work.

Usage

d_dep_t_diff(mdiff, sddiff, n, a = 0.05)
d.dep.t.diff(mdiff, sddiff, n, a = 0.05)

Value

A list with the following elements:

d

Cohen's \(d_z\).

dlow

Lower limit of the \((1-\alpha)\) confidence interval for \(d_z\).

dhigh

Upper limit of the \((1-\alpha)\) confidence interval for \(d_z\).

mdiff

Mean difference score.

Mlow, Mhigh

Confidence interval bounds for the mean difference.

sddiff

Standard deviation of the difference scores.

se

Standard error of the difference scores.

n

Sample size.

df

Degrees of freedom (\(n - 1\)).

t

t-statistic.

p

p-value.

estimate

APA-style formatted string for reporting \(d_z\) and its CI.

statistic

APA-style formatted string for reporting the t-statistic and p-value.

Arguments

mdiff

Mean of the difference scores.

sddiff

Standard deviation of the difference scores.

n

Sample size (number of paired observations).

a

Significance level (alpha) for the confidence interval. Must be in (0, 1).

Details

Compute Cohen's \(d_z\) and a noncentral-t confidence interval for repeated-measures (paired-samples) designs using the **standard deviation of the difference scores** as the denominator.

The effect size is defined as: $$d_z = \frac{\bar{X}_D}{s_D}$$ where \(\bar{X}_D\) is the mean of the difference scores and \(s_D\) is the standard deviation of the difference scores.

The corresponding t statistic for the paired-samples t-test is: $$t = \frac{\bar{X}_D}{s_D / \sqrt{n}}$$

See the online example for additional context: Learn more on our example page.

Examples

# Example derived from the "dept_data" dataset included in MOTE

# Suppose seven people completed a measure of belief in the supernatural
# before and after watching a sci-fi movie.
# Higher scores indicate stronger belief.

t.test(dept_data$before, dept_data$after, paired = TRUE)

# Direct entry of summary statistics:
d_dep_t_diff(mdiff = 1.14, sddiff = 2.12, n = 7, a = .05)

# Equivalent shorthand:
d_dep_t_diff(1.14, 2.12, 7, .05)

# Using raw data from the dataset:
d_dep_t_diff(mdiff = mean(dept_data$before - dept_data$after),
             sddiff = sd(dept_data$before - dept_data$after),
             n = length(dept_data$before),
             a = .05)