d_z_mean: Cohen's d for Z-test from Population Mean and SD
In MOTE: Effect Size and Confidence Interval Calculator

d_z_mean

R Documentation

Cohen's d for Z-test from Population Mean and SD

Description

Computes Cohen's d for a Z-test using the sample mean, population mean, and population standard deviation. The function also provides a normal-theory confidence interval for d, and returns relevant statistics including the z-statistic and its p-value.

Usage

d_z_mean(mu, m1, sig, sd1, n, a = 0.05)

d.z.mean(mu, m1, sig, sd1, n, a = 0.05)

Arguments

`mu`	The population mean.
`m1`	The sample study mean.
`sig`	The population standard deviation.
`sd1`	The standard deviation from the study.
`n`	The sample size.
`a`	The significance level.

Details

The effect size is computed as:

d = \frac{m_1 - \mu}{\sigma}

where m_1 is the sample mean, \mu is the population mean, and \sigma is the population standard deviation.

The z-statistic is:

z = \frac{m_1 - \mu}{\sigma / \sqrt{n}}

where n is the sample size.

Learn more on our example page.

Value

A list with the following components:

d: Effect size (Cohen's d).
dlow: Lower level confidence interval d value.
dhigh: Upper level confidence interval d value.
M1: Mean of sample.
sd1: Standard deviation of sample.
se1: Standard error of sample.
M1low: Lower level confidence interval of the mean.
M1high: Upper level confidence interval of the mean.
Mu: Population mean.
Sigma: Standard deviation of population.
se2: Standard error of population.
z: Z-statistic.
p: P-value.
n: Sample size.
estimate: The d statistic and confidence interval in APA style for markdown printing.
statistic: The Z-statistic in APA style for markdown printing.

Examples


# The average quiz test taking time for a 10 item test is 22.5
# minutes, with a standard deviation of 10 minutes. My class of
# 25 students took 19 minutes on the test with a standard deviation of 5.

d_z_mean(mu = 22.5, m1 = 19, sig = 10, sd1 = 5, n = 25, a = .05)

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