d_dep_t_avg: Cohen's d for Paired t Using the Average SD Denominator

In MOTE: Effect Size and Confidence Interval Calculator

Cohen's d for Paired t Using the Average SD Denominator

Description

**Note on function names:** This function now uses the snake_case name 'd_dep_t_avg()' to follow modern R style guidelines and CRAN recommendations. The dotted version 'd.dep.t.avg()' is still included as a wrapper for backward compatibility, so older code will continue to work. Both functions produce identical results, but new code should use 'd_dep_t_avg()'. The output function also provides backwards compatibility and new snake case variable names.

Usage

d_dep_t_avg(m1, m2, sd1, sd2, n, a = 0.05)

d.dep.t.avg(m1, m2, sd1, sd2, n, a = 0.05)

Arguments

m1	Mean from the first level/occasion.
m2	Mean from the second level/occasion.
sd1	Standard deviation from the first level/occasion.
sd2	Standard deviation from the second level/occasion.
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_{av} and a noncentral-t confidence interval for repeated-measures (paired-samples) designs using the **average of the two standard deviations** as the denominator.

The effect size is defined as the mean difference divided by the average SD:

d_{av} = \frac{m_1 - m_2}{\left( s_1 + s_2 \right)/2}.

The test statistic used for the noncentral-t confidence interval is based on the average of the two standard errors, se_i = s_i/\sqrt{n}:

t = \frac{m_1 - m_2}{\left( \frac{s_1}{\sqrt{n}} + \frac{s_2}{\sqrt{n}} \right) / 2}.

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

Value

A list with the following elements:

d

Cohen's d_{av}.

dlow

Lower limit of the (1-\alpha) confidence interval for d_{av}.

dhigh

Upper limit of the (1-\alpha) confidence interval for d_{av}.

M1, M2

Group means.

M1low, M1high, M2low, M2high

Confidence interval bounds for each mean.

sd1, sd2

Standard deviations.

se1, se2

Standard errors of the means.

n

Sample size.

df

Degrees of freedom (n - 1).

estimate

APA-style formatted string for reporting d_{av} and its CI.

Examples

# The following example is derived from the "dept_data" dataset included
# in the MOTE package.

# 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)

# You can type in the numbers directly, or refer to the
# dataset, as shown below.

    d_dep_t_avg(m1 = 5.57, m2 = 4.43, sd1 = 1.99,
                sd2 = 2.88, n = 7, a = .05)

    d_dep_t_avg(5.57, 4.43, 1.99, 2.88, 7, .05)

    d_dep_t_avg(mean(dept_data$before), mean(dept_data$after),
                sd(dept_data$before), sd(dept_data$after),
                length(dept_data$before), .05)

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