PSYC2009 Study Guide - Final Guide: Effect Size, Null Hypothesis, Statistic
Effect Size and Power
• Effect size measures how big a difference between a sample statistic and a hypothetical
value should be for it to seem important or worthwhile.
• There are two ways to evaluate how big such a difference is.
1. Scale-based evaluation – relative to the range of the scale itself.
2. Distribution-based evaluation – relative to the dispersion of scores.
• Scale-based effect-sizes use the units of measurement in the scale of the dependent
variable. Eg: A reaction-tie epeiets scale-based effect size might be measured in
milliseconds.
• Distribution-based evaluation measures the difference between means in SD units.
• We can rewrite the t-statistic formula as
where d stands for the
difference between the sample mean and the population mean divided by the sample SD: d
.
• This is known as Cohen’s d, and it measures the difference between the sample mean and
the population mean in SD units.
• Eg: A Cohes d of -2.5 means that the sample mean is 2.5 SD units below the population
mean.
• Cohes d is useful because it provides a measure of the difference between a hypothetical
value for a mean and the sample mean that is independent of the scale used for our
variable.
• I the cotet of a epeiet fo hich the ull hpothesis aouts of a o effect
hpothesis, Cohes d is a scale-fee easue of the epeiets effect size.
• Most of the time, however, researchers just do not have clear-cut criteria by which they can
judge the importance of effect-sizes.
• Cohen offers benchmarks that have proved popular with some researchers
o Small: d = .2
o Medium: d = .5
o Large: d = .8
• Many studies would not enable us to reliably detect small effect sizes, either because their
statistical power is too low or their CIs are too wide.
How big a sample size should we obtain?
• If the researchers are hypothesis-testing, then to answer this question researchers must
decide three things:
1. What confidence level they are going to use?
2. How much power they require?
3. The smallest effect-size they would like to have that power to detect?
How to calculate power and determine sample size
• Eg: Real mean = 106.88, null hypothesis: mean = 100, SD = 15:
1. Gie 95% CL, that eas fo sigificace testig e hae α = .05.
2. Instead of tα/2 we will use zα/2 , the z-score from Table A.2 whose area beyond z is .05/2 =
.025. This turns out to be zα/2 = 1.96.
3. Now zα/2 corresponds to 1.96 SEs up from the null hypothesis mean of 100, which is
(1.95)(15/50) = 4.2, so we would reject the null hypothesis if we got a sample mean of
104.2 or higher.
4. Power is the area beyond 104.2 under the normal curve whose mean is 106.88 and SD =
15/50. TO find out what that is we have to convert 104.2 into the equivalent z-score for
this normal curve. We have zβ = (104.2 – 106.88)/(15/50) = -1.283.
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Document Summary
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