Need sample size calculation formula but no previous studies available, only one study available that have only mean, no standarad deviation available so what formula used in Randomized Controlled parallel group design?
Hello Sunil,
The answer depends on several points:
1. Are you more interested in:
(a) ascertaining sample size (N) required in order to estimate some target population parameter within some target tolerance and some permissible error risk, or
(b) ascertaining N required in order to have some target statistical power to detect some target difference/effect size (ES) when testing a null hypothesis?
2. If (a) above is your goal, then you'll some estimate of variation in order to determine an appropriate N. You could conduct a small pilot study. If there are existing studies or actuarial data on the outcome variable, these might be helpful sources as well.
3. If (b) above is your goal, then often the most difficult part is operationalizing the target ES: the smallest degree of difference that you think is clinically/practically noteworthy, and that you'd like your study to be capable of detecting, if in fact it truly exists in the population. Methods of estimating an ES could include consensus of domain experts, results of a pilot study, results of existing studies involving the same outcome variable/s, and cost/benefit (a.k.a. utility/decision theory) analysis.
Without knowing more about your intended study and your specific research question/s, these general remarks are about all that can be offered.
Good luck with your work.
When designing a randomized controlled trial (RCT) study and previous studies only provide the mean, you can use the sample size calculation formula based on the two-sample t-test. The two-sample t-test is commonly used when comparing means between two groups.
The formula for sample size calculation for a two-sample t-test is:
n = (2 * (Zα + Zβ) * σ / Δ)²
Where:
- n is the required sample size per group
- Zα is the critical value of the standard normal distribution for the desired level of significance (usually α = 0.05 for a 95% confidence level)
- Zβ is the critical value of the standard normal distribution for the desired power of the study (usually β = 0.20 for 80% power)
- σ is the standard deviation estimated from previous studies
- Δ is the minimum detectable effect size or the difference in means that you want to detect.
It's important to note that using the standard deviation estimated from previous studies assumes that the standard deviation will be similar to your current study. If the previous study is not similar in terms of the population, intervention, or setting, it may be more appropriate to conduct a pilot study to estimate the standard deviation for a more accurate sample size calculation.
Additionally, there are other factors to consider in sample size calculations, such as the desired power, type I error rate, and potential attrition rate. Consulting with a statistician or using specialized statistical software can help ensure a precise sample size calculation for your specific study design.
Sample size should not be based on the results of previous studies, but on the smallest effect size of practical importance. This is important, because effects that are smaller than published estimates may still be worthwhile effects.
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