TRY THIS SAMPLE ON FOR SIZE 

by Dale Atkinson 

Have you ever dreamed of working in the Sample Design Section? Probably not! However, 

you may have wondered how sample sizes are determined. Well, you're in luck, because the 

topic on our talk show today is one even Oprah Winfrey hasn't thought of – sample size 

estimation. Our special guest is that famous sampler, Mr. Sam Puller. Let's get right to the 

phones and hear from our listeners. 

Caller 1: The sample size for one of our State surveys has just been increased from 250 

to 1,000. Why was such a large increase necessary? 

Mr. P: The biggest factor in determining sample size is the level of precision desired in 

the survey indications. Precision is measured by something called the coefficient of 

variation - CV, for short. The smaller the CV, the better the precision. In your case, it 

was determined that a lower CV is needed. Quadrupling the sample size will reduce the 

CV by half. If the CV had been 20 percent with a sample size of 250, it will probably be 

about 10 percent with a sample size of 1,000. If your sample size were increased even 

more - for example, quadrupled to 4,000 - then the CV would be reduced to 5 percent. 

Sample size is determined by the required precision of the survey indications. 

Caller 2: The sample size for our labor survey is 400, but the sample size for our 

December Crops/Stocks Survey is 2,000. Why the big difference? 

Mr. P: Estimation objectives differ from survey to survey. For the labor survey, sample 

sizes are determined with the objective of producing regional estimates, not State 

estimates. Thus, when the sample size for your State is lumped in with the other States 

in the region, fairly precise regional estimates can be obtained. The December 

Crops/Stocks Survey sample sizes are designed to provide precise State estimates. 

Caller 3: Well, our labor survey has a sample size of 500, and our Agricultural Resource 

Management Survey (ARMS) has a sample size of 1,000. We do not do State estimates for 

either survey in our State, only regional estimates. So why is there a difference in these survey 

sample sizes? 

Mr. P: Different types of data demonstrate differing amounts of variability. The labor 

sample sizes are designed to provide precise estimates of number of workers and wage 

rates. These data tend to be less variable than total farm expenditures - the primary 

item of interest in the ARMS. The more variability in an item, the larger the sample size 

needed to estimate it well. 

Caller 4: Our State has a sample size of 1,500 for the December Crops/Stocks Survey. 

Our neighbor State to the north also has a sample size of 1,500 although they have twice 

as many farms. Why is that? 
Mr. P: Sample size is usually not affected by population size (i.e., number of farms). 

Thus, if a sample size of 1,500 is needed to obtain a certain CV, it doesn't usually matter 

if there are 50,000 or 100,000 farms in the State - the sample size still needs to be 1,500. 

It is a common misconception to think that if you have a smaller population size, your 

sample size will be less. NASS has larger sample sizes in some States because they 

produce a larger share of the U.S. production, and NASS wants a lower CV in those 

States. Of course, States which are more agricultural tend to have more farms, but it is 

the lower CV that is usually affecting the sample size - not the number of farms. 

Sampling experts take population sizes into account only when more than 10 percent of 

the population will be in the sample, or the State sample size must be allocated to a set 

of strata. 

Caller 5: The list sample size for our December Crops/Stocks Survey was increased, and 

although the crop acreage CV's decreased somewhat, we did not see any change in our grain 

stocks CV's. Why was this? 

Mr. P: For multiple frame surveys, the area frame component, or nonoverlap (NOL) domain, 

must be taken into account – both the CV for NOL and the percentage of the indication that 

comes from the NOL. The stocks estimates in your State probably have a large NOL 

component, so that simply increasing the list sample size did not result in a noticeable 

improvement in the multiple frame CV. Rather than increasing the list sample size, your State 

probably needs to improve the list coverage for stocks (capacity) so that less of the total estimate 

comes from the NOL domain. 

Caller 6: Does stratification have any effect on sample sizes? 

Mr. P: Stratification is a tool that gives us some control over data variability. Stratified 

samples usually produce estimates with much better precision (in other words, lower 

CV's) than would be realized if the sample size were used in an unstratified design. The 

quality of the control data used to construct the strata is an important point in effective 

use of stratification. High quality, current control data on the sampling frame will result 

in better stratification and lower CV's. 

Caller 7: We need to obtain a 5 percent CV on our hog indication, but we cannot afford 

the sample size which is required to get a 5 percent CV. 

Mr. P: Resources do have some effect on sample size. For your situation, you must 

decide if the sample size that you can afford will result in a level of precision that will 

make the survey worth doing. Survey organizations often find themselves using the 

sample sizes they can afford rather than the sizes they desire. However, a survey 

organization would be better off not doing a survey if the affordable sample size will 

produce such large CV's that the survey indications are not usable. 
Well, this has been very interesting. I hate to end the discussion, but I have to run. So, until next 

time, happy sampling!