## 3.1 Effect size for a one-sample $$t$$-test

Recall the cholesterol example where we tested the hypotheses

$H_0:\mu = 5\;\;\text{versus}\;\;H_1:\mu \neq 5,$

where:

• $$\mu_0$$ denotes the mean under the null hypothesis,

where the associated $$t$$-test results were:


One Sample t-test

data:  heartattack\$cholesterol
t = 2.2063, df = 71, p-value = 0.0306
alternative hypothesis: true mean is not equal to 5
95 percent confidence interval:
5.012405 5.245325
sample estimates:
mean of x
5.128865 

The results of the associated effect size calculation are as follows:


Cohen's d (single sample)

d estimate: 0.2600188 (small)
Reference mu: 5
95 percent confidence interval:
lower      upper
-0.2119399  0.7319776 

As we can see, the effect size was 0.26 (this can be thought of as 0.26 standard deviations) and is considered small.