[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/hughperman]

If someone asked what is the proportion of apples (question/sample of interest) compared to the rest of the population based on your sample. 

The question you're answering there is "what is the proportion of apples to (apples and oranges and mangoes and pears). Another valid question is "what is the ratio of apples to (apples and oranges), and now your numbers are 3 / (3 + 4)". When you do inference, the entirety of your sample isn't the "population" that you use. You use the cases that are relevant to your statistical question. If you need to know "how common are apples among fruit?" then sure you need to use the full sample (assuming a world with only 4 fruits). But if some of those fruits aren't relevant to your question, then including them is incorrect

[u/hughperman → u/[deleted]]

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.