Statistical Power

What is the complement of beta error (Type II)

I-beta, is the statistical power of a test

Power

The probability that a test will lead to rejection of the null hypothesis (probability of attaining statistical significance)

If beta is 0.20, what is power

0.80

If your test has 80% power, then

There is 80% probability that we would correctly demonstrate a statistical difference and reject Ho

The more powerful a test

The less likely one is to make a Type II error

What is a conventional standard for protection against Type II

Beta = 0.2 (power of 80%)

What are the 4 functions that determine statistical power

1. Significance criterion (alpha)

2. Variance

3. Sample size

4. Effect size

Is there a direct mathematical relationship between alpha and beta

Nope, but there is a trade off

As probability of committing Type I error decreases,

The probability of committing Type II error increases

What is significance criterion

An inverse relationship between alpha and beta

If variance is large

Difference between groups will be less obvious

How do we control for variability by experimental design

• repeated measures

• Homogenous subjects

• Controlling measurement error

• Increasing sample size

As variance decreases

Power increases

As sample size increases

Power increases

Why is a bigger sample better

Closer rep of pop

What is effect size

How big of an effect do you expect from your independent variable? How big is the difference between sample means?

Large changes or correlations are more likely to produce what

Significant outcomes

As effect in size increases

Power increases

What does the power analysis take into account

Alpha value, effect size, and sample size

How should power be calculated

Calculate sample size needed to detect a particular effect at a particular power level BEFORE conducting the study