PSYC2009 Study Guide - Quiz Guide: Effect Size, Type I And Type Ii Errors, Null Hypothesis
Effect Size and Power
Statistical power:
• Likelihood of detecting an effect/significant difference
• Higher power decreases the likelihood of committing a type II error
Determining power of a study:
1. Determine CL
2. Find the z-score that corresponds to an area beyond z that is equivalent to the level (use
tables in back of textbook, or standard z-score table online):
3. Convert z-score into units of the original scale:
4. Add X to the null hypothesis value to find the minimum sample mean that would allow
rejection of null hypothesis
5. Calculate z-score of this value relative to the distribution of the sample mean
6. Determine the area below Z for using Table A.2.
o This is the power
• Power can be increased by obtaining larger samples or lowering CL in order to make the CI
narrower
o Larger samples preferable: can increase power without increasing risk of type I error
• Can work out how big the sample needs to be in advance once CL is selected and desired
power is determined as well as the smallest possible effect-size that needs to be detected
o Effect size calculated using
and N
o Rearranged to make d subject:
o Rearranged again to make N the subject: this will determine exactly how many
participants needed in order to reach requirements for power and effect size
o Is determined by establishing tge desired power and then finding the corresponding z-
score in Table A.2 with an area beyond z of
Effect size:
• How large the difference is between the null hypothesis value and the sample mean
• Effect size helps us to understand how meaningful the result is
• Measured relative to the range of the scale (scale-based evaluation) or relative to dispersion of
data (distribution-based evaluation)
o Scale-based: measured in same units as dependant variable
o Distribution-based: measured in terms of standard deviations
Cohen's d
• Distribution based evaluation
• Gives the difference between the sample mean and the population parameter in standard
deviation units
o
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