Sample Design A pharmaceutical company wants to conduct a surv...

Question

Sample Design A pharmaceutical company wants to conduct a survey of 30 individuals who have high cholesterol. The company has obtained a list from doctors throughout the country of 6600 individuals who are known to have high cholesterol. Design a sampling method to obtain the individuals in the sample. Be sure to support your choice.

Accepted Answer

Hi everyone. Let's move on to our next problem together. A medical research firm obtained a nationwide registry of N equals 4800 adults diagnosed with type 2 diabetes and needs a sample of n equal to 40. The registry contains counts by age strata. 18 to 39 has N1 equals 1200, 40 to 59 has N2 equals 2000, and 60+ has capital N 3 equals 1600. Which sampling design and selection procedure is most appropriate to obtain a representative sample of N equals 40? A use convenience sampling at 3 large clinics until each age group has approximately 1/3. Multiplied by lowercase n respondents. B, use a single simple random sample of N equals 40 from the entire registry without stratification. C. Use cluster sampling by randomly selecting 40 doctors and surveying all their diabetic patients, or D use proportional stratified sampling with lowercase n subh equal to, and then a fraction of N H divided by capital N multiplied by lowercase n. And then perform a simple random sample without replacement within each stratum. Giving n1 equals 10, n2 equals 17, 3 equals 13. So, this one looks very technical and maybe a bit intimidating at first. But let's think through what this description means about this population, and how we would find the most representative sample. So we've got this big sample, 4800 adults who have type 2 diabetes. And our registries is divided by age strata. So we know that there will be variances in the age strata as to how prevalent type 2 diabetes is, that might be important. We'd want that to be reflected in our Overall random sample, if we're choosing only 40 patients. So, our sample should represent age variants. So, we will want to subdivide our group by age before picking random samples. And when you subdivide a group and then randomly sample, that's called stratified sampling. However, notice that the numbers are uneven here. In our youngest group, we have 1200, in our middle age group, 40 to 59, we have 2000, while our 160 over group has 1600. So, with such different numbers to be most representative of the whole sample, We'd want to further modify that to be proportional, representing the size of the different groups. So, we'd like to modify further and be proportional stratified sampling. Which is going to be representative of different group sizes. So that helps us zoom in on choice D. I'll put a little dot here in case we find a better answer after we look more thoroughly, because it specifically mentions using proportional stratified sampling. Let's just look through the rest of this answer to make sure it's correctly describing proportional stratified sampling. Well, we know we want a sample of n equals 40. Our small sample will be 40 out of the entire 4800. So, if we calculate what fraction of the whole is made up of each age strata, we can multiply that by 40 to find out how many participants we should be choosing from each age strata. And that's indeed what we describe here. We're described getting in uh lowercase n sub H, which is our number that will go into number from the age strata that will go into our sample population. And that equals a fraction. That we calculate of the age strata's size, divided by the entire population, N sub H divided by N. and then we're multiplying that by lowercase n, multiplying that by 40. So, calculating how many of the 40 should be from each age strata. So, that calculation is indeed correct. Then it says perform a simple random sample without replacement within each stratum. And that is indeed the next step. So, we've calculated what proportion of our samples should be from each stratum, and then we go to each of those strata and do a random selection from that age group. And then you see that these numbers we get, and 12, and 3, are then representative of the relative prevalence of each age group. So choice D is indeed correct. It's not as complicated as it might look at first glance. To be thorough, let's go over our other answer choices. Choice A, use convenient sampling at three large clinics until each age group has approximately 1/3 of lowercase n respondents, but this would not be representative. First of all, convenience sampling, risks selection bias. Is there something about those clinics that make the population not representative of the larger population? And if the age group is, you know, each age group is 1/3 of the respondents, this is not representative of their prevalence in that larger population. Choice B, use single random sample of N equals 40 from the entire registry without stratification. Again, we've gone into why this is not as representative as a proportional stratified sampling. And then Cho C, use cluster sampling by randomly selecting 40 doctors and surveying all their diabetic patients. Again, we're not um Making our age groups representative, we're not calculating that into taking that into account, and we risk um selection bias on the doctors. So, risk selection bias. And surveying all their diabetic patients. Not representative. Of different. Age prevalence. Or we could just say age variants. So, once again, we have this problem where we've been given a registry of adults who have type 2 diabetes. We're told to pick a sample of them containing 40 people. Our registry has been subdivided by age strata, and those age stratas have different numbers of people in them. So, which sampling design and selection procedure is most appropriate? To obtain a representative sample group of N equals 40. And the answer is choice D use proportional stratified sampling with. We read that formula several times, very long, the proportional formula, and then perform a simple random sample without replacement, where they need stratum, giving us and sub 1 equals 10, and sub 2 equals 17, and sub-3 equals 13. Hope to see you in the next video.

Key Concepts

Sampling Methods

Simple Random Sampling

Sample Size Determination

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