MOTE (version 1.2.2)

d_dep_t_avg: 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)

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.

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.

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)