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

In MOTE: Effect Size and Confidence Interval Calculator

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)

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.

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.

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)

MOTE documentation built on Dec. 15, 2025, 9:06 a.m.