summary statistics and methodology part 2

Summary statistics and methodology, methodology

Lecture 6, Power
Scientific studies are sometimes bound to fail (wrong resources, not reading literature
beforehand)

Definition of statistical power: The probability to detect an effect that is actually there
Or: The probability to reject H0 when it is incorrect
- Under-powered studies are bound to fail

The probability to reject H0 when it is incorrect is determined by:
- Sample size
- Effect size
- Experimental design
- Etc.

,Example 1:
Do men and women from the regular population score differently on an IQ test?
Given: H0 is true: there is no difference




Mostly we find a T-value of 0




However, when we find a high t-value: Type I error→ incorrect conclusion that M and F
differ

,Example 2:
Do men and women from the regular population score differently on an IQ test?
Given: H0 is false: there is a difference




Of what are these distributions?
- Distribution of the test statistic (in this case the t-value) under H0 and H1
- NOT the distribution of data

, All things being equal:
If alpha gets smaller, beta gets larger
If alpha gets larger, beta gets smaller




Alpha is mostly 0.05