d_dep_t_diff_t: Cohen's d from t for Paired Samples Using the SD of...

In MOTE: Effect Size and Confidence Interval Calculator

Cohen's d from t for Paired Samples Using the SD of Difference Scores

Description

Compute Cohen's d_z from a paired-samples t-statistic and provide a noncentral-t confidence interval, using the **standard deviation of the difference scores** as the denominator.

Usage

d_dep_t_diff_t(t_value, t = NULL, n, a = 0.05)

Arguments

t_value	t-statistic from a paired-samples t-test.
t	for backwards compatibility, you can also give t.
n	Sample size (number of paired observations).
a	Significance level (alpha) for the confidence interval. Must be in (0, 1).

Details

For paired designs, d_z can be obtained directly from the t-statistic:

d_z = \frac{t}{\sqrt{n}},

where n is the number of paired observations (df = n-1). The (1-\alpha) confidence interval for d_z is derived from the noncentral t distribution for the observed t and df.

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.

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 before and after an intervention.
# Higher scores indicate stronger endorsement.

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

# The t-test value was 1.43. You can type in the numbers directly,
# or refer to the dataset, as shown below.

    d_dep_t_diff_t(t_value = 1.43, n = 7, a = .05)

    d_dep_t_diff_t(t_value = scifi$statistic,
        n = length(dept_data$before), a = .05)

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