Power Flashcards
Draw a sampling distribution with the representation of Power/type 1 error and type 2 error regions. And equations if you can…
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draw a diagram to show the factors affecting power
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what are p-values in regard to type X errors?
P values are type 1 error rates
We are prepared to accept a certain level of type 1 error – the risk is sufficiently low at .05 to say we’ll tolerate it.
Minimum power ?
.8 or 80%
what is Power?
The probability of correctly rejecting a false null hypothesis
Ð 1-B, where B is the probability of making a type 2 error.
factors affecting power?
Ð Decreasing alpha level will decrease power
Ð Increasing alpha level will increase power, but increase type 1 error rates.
Ð Sample size
Ð Type of statistical test used
Ð Violation of assumptions of parametric tests will decrease power as alpha level is inaccurate (& p values cannot be guaranteed).
Ð Within design
Ð Effect size assuming H1 (mean difference between the groups)
Ð Using a 1 or 2 tailed test – where 1 increases power
what is type 1 error?
Ð Falsely reject the null hypothesis / false positives
Ð (a: alpha) used for significance testing (i.e. p=.05 etc)
what is type 2 error?
Ð Misses
Ð Occur with probability of B (beta)
Power on a distribution?
Ð Power is the probability of correctly rejecting the null hypothesis (true + or, a hit)
The equation is (1-Beta) – it is the area outside the zone on the opposite side of the rejection level. Can increase in size with effect and N.
Type 2 on a distribution?
Ð Type 2 error (missing effect that’s there) would be represented by the size of the triangle on the opposite side to Power.
Type 1 on a distribution?
Ð Type-1 error is the opposite size triangle to this (same direction as power but not whole are under sampling distribution, just that triangle)
what is the relationship between sample size and standard error?
Ð As sample size increases the standard error decreases - SE / sq rt of sample size
Ð it reduces the amount of variation you would get as more and more people = more precise
Ð related to central limit theorem
Ð Standard error is smaller (effectively making the difference larger)
Sample size – Power – Effect size relation?
One can estimate one from two of the others (think Gpower) – NON-LINEAR CURVE
Ð As the effect size gets bigger we need fewer participants
Ð As sample size gets bigger so does power.
3 things to calculate Power?
Ð You need a measure or estimate
1) effect size (guess intelligently)
2) sample size
3) Significance level - alpha (?) at 1 or 2 tails
what is standard measure of effect size?
cohen’s d
how to calculate cohens d?
d=(μ1 –μ2)/σ // Ð Has to be done before the experiment
which ways are there to quantify d?
Ð Meta-analyses of the literature (average effect sizes across lots of experiments)
Ð Look at similar specific experiments and take the effect size
Ð Will vary as a function of statistical test used.
Cohen’s Conventional Labels for EFFECT sizes ?
Not as good but: use Cohen’s Conventional Labels for EFFECT sizes (small .2 / med .5 / large .8)
To calculate power we must first…
Ð Use d and sample size to calculate delta (: a non-centrality parameter)
Ð Key Note: The central distributions we use to test the null (as centered around the null, usually a value of 0, so non-central are ones shifted a certain amount (like effect size). So, if you can estimate , you can calculate power.
second, to calculate power, we must…
delta =d*n [each group p number, better with equal]/2
Ð Then decide and use statistical table
When we get a number for power we can say…
Ð IF power = .56 then we can say the researcher has 56% of correctly rejecting H0, if it is false to the extent expected.
how do we calculate a priori sample size?
Ð This formula for delta can be rearranged to solve for n (the sample size needed to get certain power)
Ð To calculate sample size – n=2(delta/d)2
Ð In independent-groups design this refers to the sample size per group
Ð For unequal sample sizes, we use the smaller of the group n, or harmonic mean.
Ð Unequal sample sizes will result in less power
why a priori not post hoc?
Power calculations for sample size and power needs to be done a priori – using observed power is biased as it uses the sample effect size, not the population effect size.
how do you get a z score?
z = (x – μ) / σ
