d_ind_t_t: Cohen's d from t for Independent Samples (Pooled SD)

In MOTE: Effect Size and Confidence Interval Calculator

Cohen's d from t for Independent Samples (Pooled SD)

Description

**Note on function and output names:** This effect size is now implemented with the snake_case function name 'd_ind_t_t()' to follow modern R style guidelines. The original dotted version 'd.ind.t.t()' 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., 'd', 'dlow', 'dhigh', 'n1', 'n2', 'df', 't', 'p', 'estimate', 'statistic') and newer snake_case aliases (e.g., 'd_lower_limit', 'd_upper_limit', 'sample_size_1', 'sample_size_2', 'degrees_freedom', 't', 'p_value'). New code should prefer 'd_ind_t_t()' and the snake_case output names, but existing code using the older names will continue to work.

Usage

d_ind_t_t(t_value, t = NULL, n1, n2, a = 0.05)

d.ind.t.t(t, n1, n2, a = 0.05)

Arguments

t_value	t-statistic from an independent-samples t-test.
t	t-statistic from an independent-samples t-test. Used for backwards compatibility.
n1	Sample size for group one.
n2	Sample size for group two.
a	Significance level (alpha) for the confidence interval. Must be in (0, 1).

Details

Compute Cohen's d_s from an independent-samples t-statistic and provide a noncentral-t confidence interval, assuming equal variances (pooled SD).

For between-subjects designs with pooled SD, d_s can be obtained directly from the t-statistic:

d_s = \frac{2t}{\sqrt{n_1 + n_2 - 2}},

where n_1 and n_2 are the group sample sizes (df = n_1 + n_2 - 2). The (1-\alpha) confidence interval for d_s 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_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.

n1, n2

Group sample sizes.

df

Degrees of freedom (n_1 + n_2 - 2).

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 in MOTE.
    hyp <- t.test(correctq ~ group, data = indt_data)

# Direct entry of the t-statistic and sample sizes:
    d_ind_t_t(t = -2.6599, n1 = 4, n2 = 4, a = .05)

# Using the t-statistic from the model object:
    d_ind_t_t(hyp$statistic, length(indt_data$group[indt_data$group == 1]),
              length(indt_data$group[indt_data$group == 2]), .05)

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