d_single_t: Cohen's d for One-Sample t from Summary Stats

In MOTE: Effect Size and Confidence Interval Calculator

Cohen's d for One-Sample t from Summary Stats

Description

**Note on function and output names:** This effect size is now implemented with the snake_case function name 'd_single_t()' to follow modern R style guidelines. The original dotted version 'd.single.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', 'm', 'sd', 'se', 'Mlow', 'Mhigh', 'u', 'n', 'df', 't', 'p', 'estimate', 'statistic') and newer snake_case aliases (e.g., 'd_lower_limit', 'd_upper_limit', 'mean_value', 'sd_value', 'se_value', 'mean_lower_limit', 'mean_upper_limit', 'population_mean', 'sample_size', 'degrees_freedom', 't_value', 'p_value'). New code should prefer 'd_single_t()' and the snake_case output names, but existing code using the older names will continue to work.

Usage

d_single_t(m, u, sd, n, a = 0.05)

d.single.t(m, u, sd, n, a = 0.05)

Arguments

m	Sample mean.
u	Population (reference) mean \mu.
sd	Sample standard deviation s.
n	Sample size n.
a	Significance level (alpha) for the confidence interval. Must be in (0, 1).

Details

Compute Cohen's d and a noncentral-t confidence interval for a one-sample (single) t-test using summary statistics.

The effect size is defined as the standardized mean difference between the sample mean and the population/reference mean:

d = \frac{m - \mu}{s}.

The corresponding t-statistic is:

t = \frac{m - \mu}{s/\sqrt{n}}.

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

Value

A list with the following elements:

d

Cohen's d.

dlow

Lower limit of the (1-\alpha) confidence interval for d.

dhigh

Upper limit of the (1-\alpha) confidence interval for d.

m

Sample mean.

sd

Sample standard deviation.

se

Standard error of the mean.

Mlow, Mhigh

Confidence interval bounds for the mean.

u

Population (reference) mean.

n

Sample size.

df

Degrees of freedom (n - 1).

t

t-statistic.

p

p-value.

estimate

APA-style formatted string for reporting d and its CI.

statistic

APA-style formatted string for reporting the t-statistic and p-value.

Examples

# Example derived from the "singt_data" dataset included in MOTE.

# A school claims their gifted/honors program outperforms the national
# average (1080). Their students' SAT scores (sample) have mean 1370 and
# SD 112.7.

    gift <- t.test(singt_data$SATscore, mu = 1080, alternative = "two.sided")

# Direct entry of summary statistics:
    d_single_t(m = 1370, u = 1080, sd = 112.7, n = 14, a = .05)

# Equivalent shorthand:
    d_single_t(1370, 1080, 112.7, 14, .05)

# Using values from the t-test object and dataset:
    d_single_t(gift$estimate, gift$null.value,
               sd(singt_data$SATscore), length(singt_data$SATscore), .05)

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