d_ind_t: Cohen's d for Independent Samples Using the Pooled SD
In MOTE: Effect Size and Confidence Interval Calculator

d_ind_t

R Documentation

Cohen's d for Independent Samples Using the Pooled SD

Description

Compute Cohen's d_s for between-subjects designs and a noncentral-t confidence interval using the **pooled standard deviation** as the denominator.

Usage

d_ind_t(m1, m2, sd1, sd2, n1, n2, a = 0.05)

Arguments

`m1`	Mean of group one.
`m2`	Mean of group two.
`sd1`	Standard deviation of group one.
`sd2`	Standard deviation of group two.
`n1`	Sample size of group one.
`n2`	Sample size of group two.
`a`	Significance level (alpha) for the confidence interval. Must be in (0, 1).

Details

The pooled standard deviation is:

s_{pooled} = \sqrt{ \frac{ (n_1 - 1)s_1^2 + (n_2 - 1)s_2^2 } {n_1 + n_2 - 2} }

Cohen's d_s is then:

d_s = \frac{m_1 - m_2}{s_{pooled}}

The corresponding t-statistic is:

t = \frac{m_1 - m_2}{ \sqrt{ s_{pooled}^2/n_1 + s_{pooled}^2/n_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_s.
dlow: Lower limit of the (1-\alpha) confidence interval for d_s.
dhigh: Upper limit of the (1-\alpha) confidence interval for d_s.
M1, M2: Group means.
sd1, sd2: Standard deviations for each group.
se1, se2: Standard errors for each group mean.
M1low, M1high, M2low, M2high: Confidence interval bounds for each group mean.
spooled: Pooled standard deviation.
sepooled: Pooled standard error.
n1, n2: Group sample sizes.
df: Degrees of freedom (n_1 - 1 + n_2 - 1).
t: t-statistic.
p: p-value.
estimate: APA-style formatted string for reporting d_s and its CI.
statistic: APA-style formatted string for reporting the t-statistic and p-value.

Examples

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

# A forensic psychologist examined whether being hypnotized during recall
# affects how well a witness remembers facts about an event.

t.test(correctq ~ group, data = indt_data)

# Direct entry of summary statistics:
d_ind_t(m1 = 17.75, m2 = 23, sd1 = 3.30,
        sd2 = 2.16, n1 = 4, n2 = 4, a = .05)

# Equivalent shorthand:
d_ind_t(17.75, 23, 3.30, 2.16, 4, 4, .05)

# Using raw data from the dataset:
d_ind_t(mean(indt_data$correctq[indt_data$group == 1]),
        mean(indt_data$correctq[indt_data$group == 2]),
        sd(indt_data$correctq[indt_data$group == 1]),
        sd(indt_data$correctq[indt_data$group == 2]),
        length(indt_data$correctq[indt_data$group == 1]),
        length(indt_data$correctq[indt_data$group == 2]),
        .05)

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