How to define population proportion (prevalence) for sample size determination?
We often see the equation as: Sample Size= Z2.p.(1-p)/d2
in this particular sample size determination equation which is also called as Fisher's equation, I often see researchers to use 0.5 as prevalence. my question is should it be used always as 0.5 in all aspect? Some friends of mine also said it is rather probability of getting a response for any particular question which defines the value. But I was wondering if I can get an appropriate answer from this platform which can stop me for searching any further.
Here, p is the prevalence, not a p-value. To calculate the sample size for a binary variable, we need to know the prevalence of the variable. Here, p is that prevalence. Usually, we get this prevalence from the literature. When we do not have such information from the literature, we consider it 0.5, as it gives the largest sample size than considering other prevalences.
To calculate adequate sample size, there is a simple formula, however it needs some practical issues in selecting values for the assumptions required in the formula too and in some situations, the decision to select the appropriate values for these assumptions are not simple.
The following simple formula would be used for calculating the adequate sample size in prevalence study Z2.p.(1-p)/d2 ; Where n is the sample size, Z is the statistic corresponding to level of confidence, P is expected prevalence (that can be obtained from same studies or a pilot study conducted by the researchers), and d is precision (corresponding to effect size).
The level of confidence usually aimed for is 95%, most researchers present their results with a 95% confidence interval (CI). However, some researchers wants to be more confident can chose a 99% confidence interval.
Researcher needs to know the assumed P in order to use in formula. This can be estimated from previous studies published in the study domain or conduct a pilot study with small sample to estimate the assumed P value. This assumed P is a very important issue because the precision (d) should be selected according to the amount of P.
The value of 0.5 is often used because it maximizes the sample size. It is therefore this value that we take if we have no idea a priori of the desired proportion.
For the best answer to this question see this link: https://b-ok.cc/book/2324520/acf6e2
The answer depends on how you plan to take your sample.
Best wishes, D. Booth
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size