# d from z-statistic for Z-test

# Description

This function displays $d_{z}$ for *Z*-tests based on the *Z*-statistic. The normal confidence interval is also provided if you have sigma ($\sigma$). If “sig” is left blank, then you will not see a confidence interval.

The formula for $d_{z}$ is: $$d_{z} = \frac{Z}{\sqrt(N)}$$

The formula for $d_{z}$ is: $$d_{z} = \frac{M - \mu}{\sigma_M}$$

# R Function

d.z.z(z, sig = NA, n, a = 0.05)

# Arguments

- z = statistic
- sig = population standard deviation
- n = sample size
- a = significance level

# Example

A recent study suggested that students (N = 100) learning statistics improved their test scores with the use of visual aids (*Z* = 2.50, *SD* = 4.00).

# Function in R:

d.z.z(z = 2.5, sig = 4, n = 100, a = .05)

# MOTE

## Screenshot

## Effect Size:

Effect Size: $d_{z}$ = 0.25, 95% CI [-7.59, 8.09]

## Interpretation:

Your confidence interval does include zero, and therefore, you might conclude that this effect size is similar to zero.

## Summary Statistics:

Not applicable.

## Test Statistic:

*Z* = 2.50, *p* = .012

## Interpretation:

Your *p*-value is less than the alpha value, and therefore, this test would be considered statistically significant.