effect size and power

What is an effect size?

A standardized measure of the magnitude of the effect between two variables, not biased by sample size.

What is pooled standard deviation?

The average of standard deviations from both groups, reflecting spread around the mean.

How does pooled standard deviation affect effect size?

Smaller pooled standard deviation increases effect size, even if group means stay the same.

What are the general thresholds for Cohen’s d?

0.2 = small, 0.5 = medium, 0.8 = large effect.

What are r effect size thresholds?

0.1 = small, 0.3 = medium, 0.5 = large.

What increases effect size (if other variables are constant)?

Lower within-group variability and greater mean differences.

Does sample size increase effect size

No, but it increases the chance of detecting a significant effect.

What makes a statistical test more powerful?

Larger sample size and larger effect size.

What is a Type 1 error?

Rejecting a true null hypothesis (false positive).

What is a Type 2 error?

Accepting a false null hypothesis (false negative).

What is statistical power?

The probability of detecting a true effect when it exists; equal to 1 - β.

What is the recommended level of statistical power?

80%, which means a 20% chance of Type 2 error.

How can Type 2 error risk be minimized?

Increase effect size, increase sample size, and prefer within-subject designs.

How can Type 1 error risk be minimized?

Lower α level and reduce the number of tests.

Why calculate power a-priori?

To determine needed sample size before the study to ensure adequate power.

What is post-hoc power calculation?

Calculating how powerful the study was after it was conducted.