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.

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These notes have been prepared by Amanda J. Shaker. The copyright for the material in these notes resides with the author named above, with the Department of Mathematics and Statistics and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License CC BY-NC-ND