Power Flashcards
Type 11 error has a probability of beta what is the probability of power?
1-beta
What is a type 1 error?
Reject the null hypothesis when it is true ( p = Alpha - 0.05)
When null hypothesis is false and you reject the null hypothesis…describe what this is
Correct decision
P = 1 - beta
= power
What is a type 11 error?
When the null is false but you don’t reject it…
P = beta
Explain in terms of the null hypothesis what situation this would occur
A correct decision is made
P= 1- alpha
Null is true and you don’t reject the null
What is a type 1 errors?
False positives
Is the conventional probability value (alpha) used for significance testing ( p = .05)
What are type 11 errors
Misses
Occurs with a probability of beta
What factors affect statistical power?
The probability of a type 1 error (alpha)
The effect size assuming h1 (e.g. Mean difference)
Sample size
Type of statistical test used
One or two tailed test
What is the z critical value for a 1 tailed test?
1.65
What is the z critical for a 2 tailed test?
1.96
What happens to power when the significance level (alpha) is decreased?
Power decreases
What happens to power when the significance level increases & what is a product of this?
Increase in power but also an increase in the probability of a type 1 error
If the effect size between 2 means is increased what happens to power?
Power increases
Increasing sample size will do what to power? (Remember central limit theorem)
Increase sample size reduces the sampling distribution of the mean (standard deviation) (random variation is reduced) so effect size increases and therefore power increases.
If you reduce the variance between two means what happens to power?
Decreasing variance increases the effect size so increases power
Discuss how the assumptions of parametric tests can influence power.
Violation of assumptions underlying parametric tests will often seriously reduce your power
- non- parametric tests may be more powerful in that circumstance.
Why should we worry about power?
We are often interested in knowing he sample size needed to achieve an adequate level of power before we begin a study.
This often has important implications for planning time, resources etc when designing a study
To examine whether a completed statistical test had a fair chance of rejecting an incorrect h0.
What do we need to know to estimate power?
Effect size
Sample size
Significance level (alpha) and whether 1 or 2 tailed test used
What is the formula for cohens d?
D = (m1-m2/ sd)
Where can we find the effect size from?
Previous research (use sample means and SDs obtained from previous studies)
Researcher estimate of important effect: a researcher decides on the minimum important difference between 2 means… Still need to estimate sd)
Using conventional labels of effect size magnitude for d originally provided by cohen
What are cohens d effect sizes for t-test?
.8 = large .5 = medium .2 = small
What is delta?
A noncentrality parameter… For power you a have to assume that h1 is true (in contrast to everything else which is assuming h0 is true, which is centred around the null hypothesis) so power is not centred around the null so it’s noncentral
How do you calculate delta?
Delta = d * square root of n/2
How do you calculate sample size?
n = 2(delta/d) squared
What is the minimum power required
80 % but often people use 90%
Unequal sample size will result in what to power?
Less power
With unequal sample size, we use the smaller of the group n
When can you use power tests?
A priori and post hoc (e.g. determining sample size required)
Remember when testing whether there is a fair chance to correctly reject the null hypothesis population effect size should be used not sample effect size.
What is observed power?
Post hoc power analyses using the sample estimate of the effect size.
What is statistical power?
It’s the probability of correctly detecting an effect when it really is there.
When you draw one of those distribution diagrams to represent power, if you know the population standard deviation (standard error) then what distribution is it? If you estimate the standard deviation from your sample what distribution is it?
Normal distribution & z test
T distribution and a one sample t test
When you convert z scores to percentage of the curve ‘cumulative’ from the left (minus infinity) (x%) what is the name of the function you use?
Cumulative distribution function (CDF) - z to the -1
What function do you use to convert percentage (x%) to z-score in spss?
Inverse distribution function (IDF) - z
The IDF is also known as the probit function
When you have a participant ratio of 2:1 and you are calculating sample size, does this difference make a big impact?
Not too bad actually, you need some more participants but as the ratio gets larger many more are required
