24. A supermarket chain has 100 equally-sized stores. It is desired to estimate the proportion of vegetables that spoil before being sold. The following sampling designs are considered:
(a) Sample 10 stores, then sample half the vegetables within each of these stores; or
(b) Sample 20 stores, then sample one-quarter of the vegetables within each of these stores.
Which of these designs has the lowest variance? Why might the higher-variance design still be chosen?
Solution to question 23
From yesterday:
23. Suppose you are conducting a survey in which people are asked about their health behaviors (how often they wash their hands, how often they go to the doctor, etc.). There is a concern that different interviewers will get different sorts of responses—that is, there may be important interviewer effects. Describe (in two sentences) how you could estimate the interviewer effects within your survey. Can the interviewer effects create problems of reliability of the survey responses? Explain (in one sentence). Can the interviewer effects create problems of validity of the survey responses? Explain (in one sentence).
Solution: You can do a survey experiment and randomly assign different respondents to different interviewers. Then look at the average (and s.e.) of responses for each interviewer, and compare (ideally using a graph!).
Yes, interviewer effects can create problems of reliability (different interviewers getting different results) and validity (responses being different from the truth).
I believe it’s a trick question, since there is variation both within and between stores. And if you knew where the greatest variation occurred then you could exploit that with a model to examine factors which influence the variation.
Dan:
I never give trick questions! Life is too short for that sort of thing.
On second thought, I don’t see why either design would result in a lower variance with all else being equal. But I can’t tell whether your denial of trick questions is facetious!
Does a single chive or pea count as “one vegetable”? Or is the set of all chives in the store “one vegetable”? I am just asking what is meant by “sample half the vegetables”: Sample half the *types* of vegetables, or half of the individual objects known as vegetables?
Oh and on Q 23: What kinds of “interviewer effects” are known? Can you give us astronomers an example?
I’m very green on stats but the only thing we know that is equal is the size of the stores in the supermarket chain. I’d go with the 20 store option because I’d think it would expose more non-equal (variable) factors, such as shipping, logistics, store-level management/staff practices, customer differences, et al. Even so, with half the sample locations, the 10-store option would likely be less expensive and quicker, and be an easier project for a smaller audit staff. 10-store option would be the higher variance sample, with only store size being controlled as equal, I’d think. :) I need a stats refresher course…and maybe some memory therapy because I can’t recall how I even landed on this page.
Of course, (a) will give lower variance since more similar vegetables within a store are selected. However, for better representativeness of the population, (b) should be chosen.
20 stores = lower variance, 10 stores = easier/cheaper
David, interviewer effects can be e.g.
– a hot interviewer makes it more likely that respondents give supposedly “cooler” answers
– an interviewer might ask questions in a certain way that influences respondents (“and about that politics thing – you probably favor party X, too, right?”)
– an interviewer might fake the whole data set (not totally uncommon)
– an interviewer might be in a situation where she has to classify an answer in a given classification and might tend towards a certain interpretation of the classification, making one class more likely than the others
@Matthias: Thanks