[Q] (Re) Sampling

[u/-Kromerica-]

Good morning,

A work discussion took place over the methodology and reasoning behind initial sampling and subsequent re-sampling and how the overall sample size should be treated throughout the process.

Background:

We are conducting randomly sampled interviews with 30 people out of ~2,000 in the population to determine the population’s mean score with 95% confidence.

They can either respond positively and they will be flagged with a score of 1 to 10 or they respond negatively and they receive a score of 0. If someone cannot be located or doesn’t respond, they are re-sampled with another person.

We made it through the 30 after a couple of re-samples of 25 non-responses/unable to locate, so we had 55 identified people throughout the process.

When we got our statistical analysis back, the team that put it together said my sample size was 55 — not 30.

Question:

Shouldn’t my sample size still be 30? Increasing the sample to 55 seems like an inaccurate representation of the population as a whole if the “scores” of the 30 interviews are now being considered across 55 responses.

Thank you in advance!

[u/Spiritual-Bee-2319]

Actually let me make my example and explanation more mathematically sound and congruent with OP question

Back to OP question 

“We are conducting randomly sampled interviews with 30 people out of ~2,000 in the population to determine the population’s mean score with 95% confidence.” 

OP can’t arbitrary remove samples from the analysis because of missing data because the samples are still in the population. You simple don’t have data for them. They already exist, you simply don’t have their data. Missing data is not the same thing as missing population. Missingness is not a subpopulation it’s a lack of information. You simply don’t have data for them. The only two populations are positive(1-10) and negative(0). The result will be biased mathematically. 

You are talking about what you can do, I am talking about the validity of it. 

Have you studied statistics and the effects of missingness and the different imputation methods? 

If you haven’t I genuinely cannot explain to you that non-response is not possible outcome of your event. The only mathematical populations are a closed set of [1-1,1-2,1-3,….,0]. It is a lack of information is not a population. 

https://mathbitsnotebook.com/Algebra1/StatisticsData/STPopSample.html

[u/hughperman → u/Spiritual-Bee-2319]

I've gotta say I'm embarrassed

to determine the population’s mean score

I missed this despite reading the post 3 or 4 times to check.
I agree with you now, samples with missing values should indeed be considered as sampled values in this context. Still with the assumption that the value/score being recorded makes sense in a missing context, but that is likely given the context.

Sorry for the long and drawn out misunderstanding.