Let's say that we are doing an online survey among a group of people with the same profession - cross-sectional study. The population size identified, and sample size calculation is done. And since the sample size is small (n=588), a census is planned (universal sampling). Along the way, population size was underestimated and the sample size calculated. The real population size is N=1070, and sample size, n=780. Therefore, sampling needs to be done. Because of time constraints, my question is - can we do sampling and randomization after the data has been collected? And if so, is there a research article that has done it before? One way to avoid bias, is that the data has no identifiers except name of workplace. Can that be done?
Bootstrapping offers a statistically valid method to randomize a set population. Please see the article "A Bootstrap Method for a Finite Population: describing bootstrapping in a context similar to yours. The article can be found at the below link.
https://www.jstor.org/stable/pdf/25050557.pdf
Doing randomization after results are known is akin to putting a cart in front of the horse!
Randomization of the subjects in a randomized study has to be done before a treatment is allocated to two or more groups, whether the trial is placebo controlled or comparative between different treatment groups. Purpose is to remove bias from the results. Doing randomization after getting the result will mean a flawed biased study results akin to putting a cart before the horse.
For further information please have a look at these articles:
1. Article Randomization made easy for small size controlled clinical trials
2. Article Fundamentals of Randomization in Clinical Trial
3. Article An overview of randomization techniques: An unbiased assessm...
Is it your objective to generalize? Do you need a probability sample? Ideally sample size and technique has to be decided a priori. Using formula for finite sample for a survey study your sample size for 95% Confidence levels will certainly be less than 588, so you are ok as far as power is concerned but a systematic random sample selection could be better. Depends on your objectives.
Preamble (scenario): You are carrying out a survey, in which the target population (or sample frame of a profession) is known(identified), and along the line in the survey, you realised you need more sample (without replacement), using the same sampling technique and randomization method to obtain more units which have not been collected before.
My Opinion: It's in order. But as others have noted, randomization after sampling is like "putting the cart before the horse" {or "eating off the spoon before dipping it in a bowl of rice for a spoonful, then stop". My dear, obviously you haven't randomize nor a design o just select respondent(bias introduced) without documenting their names or identifyable number, hence you need to start all over, :) }
*Not over! If this is the scenario and you believe (with good reasons) your "power" is not enough, hence resampling becomes an option but in a time saving way then:
1. Use same randomization process (i.e., generated random number, systematic or block randomization (workplace as block))...you haven't before... not even a design .
2. Use the results to select from your sampling frame and sample framework which is the workplace (without replacement, or if they will be honest not to respond twice or identify those who haven't )
3. Add the survey reports to your reports for the original sample surveyed.
Have a good day.
No. Statistics assumes that the sample design is what is specified prior to data collection. if you didn't collect data according to that design then you have something other than that design. my guess is that you are worried about power. why not just collect some additional data using your specified samoling method. unless your results are time depenent for some reason i believe this will work better than another round of sampling that is not specified in the design. Be sure to include whatever you do in the description of your methods. Best, David Booth
PS as others have mentioned your sampling is already on shaky grounds because you were attempting a census originally. In addition you might be able to treat this as a two stage sample with the first stage a census and the second stage a probability sample on the added individuals. I would certainly consult: Cochran, W G., Sampling Techiques, 3rd edition on these things. N.B. This is considerably more complicated than you seem to think. Good luck, D. Booth
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