Lecture 28- Power Flashcards
In hypothesis testing what does the amount of data needed to correctly reject/ retain the null dependent on?
On how large the difference is between the null hypothesized value and the truth.
If there is a big difference it is easy to distinguish so can have less data and still be confident in our claims.
What happens if we increase sample size?
With small samples there is lots of random variation/ noise as sample size increases we get less of this and so the CI width decreases. This means we can get conclusive results and make accurate claims in regards to the null.
What is likely with a small sample size in terms of the errors made?
Likely to not have enough evidence to confidently reject the null therefore will retain it and a type 2 error will result (retain null when false).
What type of error is it when you reject the null when it is actually true?
Type 1
What is the same as a type 1 error?
Alpha, therefore we control type 1 errors when we set the significance level.
What are type 2 errors denoted by?
Beta.
Draw the graph on slide 540 showing how errors can arise in hypothesis testing and explain what each of the areas are…
Answer on slide 540
What is the power of a test? What is it given by?
Power is the correct decision of rejecting the null when it is false. It is the alternative to a type 2 error (retaining null when false) and the probabilities of these two events therefore add to 1 (either or situation) therefore power is given by 1-beta.
What four factors does power depend on?
- the size of the difference
- the variability in the data (σ2)
- the sample size (n)
- the level of significance (α).
What happens to power when you change the significance level?
- Red areas shrink (type 1 error reduced)= good
- But price is the blue area (type 2 error) has increased and therefore power reduces
What happens to power when you change the effect size?
As you increase the effect size (increase the true difference between means) you shift the alternative hypothesis curve to the right. This ultimately means there is less overlap between the two curves decreasing beta/ type 2 error and increasing power. This makes sense when you think about it logically you are making the distributions very different so it is easy to distinguish between them.
What happens to power under a small sample size?
There is great overlap between the distributions, increasing beta/ type 2 error and decreasing power.
What happens to power as sample size increases?
With larger sample sizes the spread of the sampling distributions is much
less so overlap is less, and the power is greater.
What happens to power as we change the standard deviation?
If increase SD i.e. make the data more variable both the distributions of the null and alternative hypothesis’ will be wider. The overlap between the curves will therefore be greater and so type 2 error/ beta will increase and power will decrease.
What occurs in the ultimate study design?
Both α and β are small, so there is good separation between the sampling distribution under H0 and the sampling distribution under HA. We will therefore have the most chance of making the correct decisions (retaining null when true and power).
