A survey is to be made on the prevalence of the common diseases in a large population. For any disease that affects at least 1% of the individuals in the population it is desired to estimate the total number of cases with coefficient of variation of not more than 20%.
a.) What size of Simple random sampling is needed assuming that the presence of the disease can be recognized without mistakes?
b.) What is size is need if total cases are wanted separately for males and females with the same precision?
Hi Jane, maybe you could try the program Gpower. You can determine the sample size based on the input parameters in the form of the desired accuracy. Here's a link to download a program http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3/
I hope it'll help. Best Regards
If you are wanting to stratify by males and females, you might want to consider using stratified random sampling instead of simple random sampling. I recommend using gender as your strata.
In regards to calculating sample size needed, I have found the following book helpful...Scheaffer, R. L., Mendenhall III, W., Ott, R. L., & Gerow, K. G. (2012). Elementary survey sampling (7th ed.). Belmont, CA: Thompson.
The website http://www.surveysystem.com/sscalc.htm presents a sample size calculator. You can use it to determine how many people you need to interview in order to get results that reflect the target population as precisely as needed. You can also find the level of precision you have in an existing sample.
Hi Jane. - To Kristin's references, I'd like to add
Cochran, W.G.(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.
On pages 77 and 78, he discusses estimation of sample size. I have noted this in answers to other questions, perhaps here and under Design of Samples. The key assumption is that s/y is approximately fixed for each situation. That is not true if you have data quality problems, so note that the formulas you find for determining sample size assume you won't sacrifice data quality to obtain more quantity. - Jim
Your estimate of sample size has two components: a sample size from the experimental design and a sample size from estimating prevalence.
So you want to estimate prevalence of a disease present in 1% of the population with an accuracy of 0.2% so I assume that the CI would be 0.8% to 1.2%.
A sample size of 10,000 tested individually will give an infection estimate of 1% with a CI of 0.82% to 1.21%. This was estimated using the function pooledBin in the binGroup package in R.
If you want to directly test the question "Is prevalence of disease X in population Y different from the prevalence in population Z?" then you will need multiple samples of 10,000 from each population. There are other analysis options that might not be quite so much work.
If disease prevalence is 10%, then a sample size of 1000 is needed to find 100 positive individuals with a 95% CI of 8.25% to 11.98%.
A prevalence of 50% will be the least amount of work. It takes many more samples if true prevalence is 1% or 99%.
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