Design of experiments Flashcards
What is the principle for increasing sample size?
If looking at means from two different groups, want to see if there is a difference. Must get SE small enough i.e. sample size large enough that any difference is noticeable. This is because T test uses m1-m2/SE
Which problems will replication not solve?
Will reduce SE all you want, but if groups are differing by something else e.g. a confounder then will remain biased. Can compensate for one with the other.
If sample size is adequate, should you make it larger?
No!
Premise of power calculations?
If know that there is a difference (μ1 not equal μ2) i.e. 2.8mm and 3.0mm, and agree that detecting a difference is P<0.05 on T test, then with sample size of (20) may find that only 1/6 experiments comes out with significant P value. Power of test is % of experiments that would have a significant P value for a given difference (specify what would be significant) and changes as N changes.
What affects power calculation?
If increase sample size, power gets higher. If decrease σ, then power gets much higher for given sample size i.e. need smaller sample to detect differences with less variation. Crucially, if the difference itself (μ1-μ2=0.4 not 0.2) then need much smaller sample. If double μ and double D, then power will stay much the same. In summary, power depends on σ, d and n.
Using power graph thing, what is chance of a difference being detected if (μ1-μ2/σ) = 0 (the standardised difference?
5% - this is premise of hypothesis testing.
Using power calculation to plan?
Think about what difference you want to detect, then use (μ1-μ2/σ) (use smallest difference that you think is important). Estimating σ not easy - can try several and see how power changes.
Difference in power calculations for binary?
For continuous, d alone matters. For binary, x and d matter (where x is the mean for one group).
When is randomisation not random enough?
If, say, have two breeds of chickens on two different feeds, and randomisation leads to 5/6 of one type being randomised to one feed.
What is restricted randomisation?
For chicken example, randomise chickens within breed to one feed or another. In trials, this is known as stratification or BLOCKING. Called restricted because some options are not allowed.
Advantage of blocking?
Removes confounding because get less biased estimate. Means differences within “breeds” get cancelled out by the same differences in the other groups. Good in biology studies because cannot ethically have huge groups.
Lessons from foreskin experiment?
“Blocked” by testing increasing doses on each foreskin so that comparing doses is unaffected by foreskin differences. But also means must do paired T test when looking at differences between doses 0, 1 and 3 as this removes variation between foreskins. Not actually paired T test but is analogue for three groups called two-way ANOVA
Analogues of paired and unpaired T tests for three groups?
Unpaired = one way ANOVA; paired = two-way.
