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Power and Effective sizeStats/Inferential 2020. 2. 5. 18:29
1. Overview
2. Description
2.1 Power (1−β)
The probability of correctly rejecting a false null hypothesis
Power=P(rejectH0|H1istrue)=1−P(notrejectingH0|H0false)⏟Type2error=1−β=P(notmakingType2error)
Particular Interpretation Sample Size Larger sample more power Effect Size Larger Effect sieze more power Alpha Level Higher Alphas more power Directionality One tail more power 2.1.1 Power Analysis
- Non-centrality parameter
δ=dσ√1n1+1n2
σ is often assumed to be 1 because assumed Variances are same in 2 groups and N's are same in 2 groups.
When n1=n2
δ=d√nk2nk=2(δd)2
When n1≠n2
ˉnh=21n1+1n2=2n1n2n1+n2δ=d√ˉnh2
2.1.2 Problems with low power
- False Negatives
- Inflated effect size estimates
- Lower positive predictive value
2.2 Effect Size
The effect size is the degree of distance between the null hypothesis and alternative hypothesis distributions.
2.2.1 Types
- Cohen's d
Cohen's d is defined as the difference between two means divided by a standard deviation for the data, i.e.
d=ˉx1−ˉx2s=μ1−μ2s=t√n1+n2n1n2
Jacob Cohen defined s, the pooled standard deviation, as (for two independent samples):
s=√(n1−1)s21+(n2−1)s22n1+n2−2
Cohen's d Interpretation 0.2 Small 0.5 Mederate 0.8 Large 3. Reference
https://en.wikipedia.org/wiki/Power_(statistics)
https://en.wikipedia.org/wiki/Effect_size
http://www.psychology.emory.edu/clinical/bliwise/Tutorials/SPOWER/spowesize.htm
http://tysonbarrett.com/EDUC-6600/Slides/u02_Ch8_power.pdf
https://www.youtube.com/watch?v=6_Cuz0QqRWc
https://www.youtube.com/watch?v=6uYNVCy-8NA
https://www.youtube.com/watch?v=tTgouKMz-eI
https://www.youtube.com/watch?v=STO1NtVR2HI
https://effectsizefaq.com/2010/05/31/what-is-statistical-power/
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