I was asked to be a statistician in a research (survey). The respondents were hospital personnel from our local hospital with a population size of 173. Respondents were asked (via questionnaire) what they think about the implementation of healthcare waste management practices in the hospital, and they may choose Fully Implemented, Partially Implemented or Not Implemented for each question. The researcher distributed the questionnaires to the whole population but she's being advised by her teacher to just use a sample size for the research. Now I do know of Slovin's formula which is widely used in our country but is now being questioned.

This is the formula

n = N/(1+Ne^2) 
    n = sample size
    N = pop size
    e = margin of error

I don't think i will be using it if it is being questioned. What method would you use to determine the sample size in this case?

  • $\begingroup$ Welcome to CV. Since you’re new here, you may want to take our tour, which has information for new users. Out of curiosity, do you know why the teacher gave such an advice? $\endgroup$
    – T.E.G.
    Oct 12, 2017 at 17:06
  • $\begingroup$ I don't know too. I figured 173 population size is manageable already since all of them are located in the same place, and I already have all the questionnaires filled by the respondents. But, she insist that the professor wants her to perform a stratified random sampling and of course she'll only follow him/her. $\endgroup$ Oct 12, 2017 at 18:01
  • 1
    $\begingroup$ Have there been given a reason to only use a sample when the complete population is available? Seems pretty strange. $\endgroup$ Oct 12, 2017 at 19:07
  • $\begingroup$ Are all the questionnaires completed? No follow-up is required? $\endgroup$
    – RoryT
    Oct 13, 2017 at 0:24
  • $\begingroup$ yeah, all questionnaires are completed. Anyway, I just read that formula above was from Yamane and applicable for dichotomous response only and assumes 95% confidence interval and p=0.5. How do you then get the sample size if the response is polythomous and you don't know the variance? $\endgroup$ Oct 13, 2017 at 1:20

1 Answer 1


You cannot estimate the sample size given only the population size. Indeed, the population size is not usually relevant. To estimate sample size you need to know: 1. Desired power 2. Desired alpha 3. Effect size that you want to be able to detect 4. The statistical method that you will be using.

Given that the population size is so small, you may look into the finite population correction.

However, if all 173 people returned the survey, then taking a sample seems silly. Either the teacher doesn't know statistics (quite possible if he/she is not a statistician) or something is missing in what you are reporting.

  • $\begingroup$ well it seems every mathematics teacher or instructors here are being allowed to teach statistics and getting a masters degree in whatever is so easy, I won't be surprised if research subjects are being handled by non statisticians $\endgroup$ Oct 13, 2017 at 1:43
  • $\begingroup$ Guess I would be using the whole population then. $\endgroup$ Oct 13, 2017 at 1:52

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