Extract from Gravetter and Wallnau: Statistics for the Behaviour Sciences
Statistical Power
- Purpose of hypothesis test – determine whether or no particular treatment has an effect
- Risk of reaching wrong conclusion
o Type 1 error
§ Reject true null hypothesis
§ Probability of type 1 error -> level of significance chosen
o Type 2 error
§ Failing to reject false null hypothesis
§ Treatment really has effect, but hypothesis test failed to discover it.
- Power – probability of reaching correct decision
o Probability test will correctly reject false null hypothesis
o More powerful -- more readily it will detect treatment effect when one really exists
- When treatment effect exists à two results
o Fail to discover existing treatment effect (type 2 error)
o Correctly detect – and reject false null)
- Power = 1 – β
- Null hypothesis is rejected whenever sample data is in critical region.
Power & Size of Treatment Effect
- Power depends on size of treatment effect
- Large effect – easy to detect – power will be high
- Rather than refer to power as single value – examine different values of power associated with different magnitudes of treatment effects.
- Critical region
- Alpha level
o Reducing alpha level reduces power of test
§ 0.05 to 0.01
§ Z value changes from 1.96 to 2.58
o Critical boundary moves to the right – therefore this reduces critical region where null hypothesis is rejected
o Less of the treatment distribution
- One tailed vs two tailed
o Changing from regular two tailed test to one tailed test
o With 2 tailed and α = 0.05, critical region on rhs begins at z = 1.96
o Changing to 1 tailed, critical value moves left to a value of z = 1.65
o Therefore increasing critical region
- Sample size
o Larger the sample, the better it will represent sample
o Increased sample size deuces std error
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