I am working on a sampling exercise which involves both random and stratified sampling. The sampling is for a series of experiments run on multiple populations. Some experiments may run on the same population either during non-overlapping time periods or might overlap at the same time.
When the test don't overlap then i do simple random sampling but if they do overlap at the same time then for the first test i do random sample and for the second experiment i perform stratified sampling to ensure there is no bias and also to study the incremental value of the 2nd experiment.
I am facing troubles with the stratification in terms of the number of treatment groups. This particular population group has 99 people in it. A case that i am currently facing is as below:
Experiment 1: Control-50 people; Test-49 people Experiment 2: Control-6%; 16 Test-groups adding upto 94%
For experiment 2, the 6% for control is a mix of 6% of the population each from control and test from the first experiment. And the same for each of the treatment groups. When the # of treatments is low, this is not the issue but when there are cases like above where there are 16 treatments i end up with a unbalanced group like below
Split of test-control is control: 6%, T1-6%,T2-6%, T3-6%.......T15 & T16-5%. Thus adding up to 100% Experiment 2: Control = 6% of Exp1.Control + 6% of Exp1.Test T1 = 6% of Exp1.Control + 6% of Exp1.Test . . . T15 = 5% of Exp1.Control + 5% of Exp1.Test
Expected Split of people across the control and 16 treatment is :
Even though the split for 1st experiment is 50-50 since there are only 99 people, control gets 50 people and test gets 49 ppl or vice versa.
But during stratification 6% or 5% of 50 & 49 people results in decimals and hence i using the lower function. And because of that i am getting this split instead of what is expected:
So instead of using
Ceiling would most likely solve the problem in this case but it will cause a problem if the # of groups is more than 17. At some point there wont be any for the last group if i go with
ceiling and there will be skewed split if i got with
So is there a way to find at how many number of splits will it mathematically not be possible to do stratification?