up: [[Statistics MOC]] Effect size is a calculation of the size of the difference between the treatment group and the population or sample population. **You would only calculate the effect size if there is a statistically significant difference between the population or sample population and the treatment group.** #### What is Cohen's d? Cohen's d is one of the most common measures of effect size in hypothesis testing. It's calculated by measuring the difference in means between treatment and population or sample population and dividing by the standard deviation. ![[Pasted image 20220921151600.png]] What are the three ds of Cohen's d associated with the three degrees of effect size? :: ![[Pasted image 20220921151636.png]] ### What is estimated Cohen's d for one sample t tests? Finding Cohen's d is different with t statistics. Because we don't have the population standard deviation we instead calculate for the estimated Cohens d. ![[Pasted image 20220922154256.png|700x200]] **The effect sizes are not significantly altered by the sample size but they are altered by the variance.** ### What is estimated Cohen's d for independent sample t tests? Estimated Cohen's d is used when we are measuring effect size for [[Independent Measure T Tests|independent samples]]. Instead of standard deviation like above we use square root of the pooled variance and instead of using the sample mean subtracted by the population mean we subtract the treatment sample mean by the untreated sample mean. Pooled variance equation: ![[Pasted image 20221003152402.png]] Estimated Cohen's d equation: ![[Pasted image 20221003152439.png]] #### Cohen's d for repeated measure t tests ![[Pasted image 20221005144904.png]] ### r^2 r^2 is another method of showing the treatment effect that is the square root of r commonly known as the correlation coefficient. It represents the proportion of total variability in the scores that is explained by the treatment. Equation: ![[Pasted image 20220922155136.png|500]] ###### What r^2 values correspond to what effect size? ![[Pasted image 20220926155336.png]] ### Effect Size for ANOVA #### What is Eta squared? Eta squared is the calculation for effect size under an ANOVA test. Whatever probability you get you can say that x percent of the variance between the samples is because of differences from treatment effects. ![[Pasted image 20221017154854.png]] ### Effect Size for RMANOVA ##### Effect Size for Repeated Measures ANOVA ![[Pasted image 20221021152649.png|500]] #### What does the α, 1 - α, β, and 1 - β represent in Hypothesis testing? ![[Pasted image 20220921153210.png]]