When determining an appropriate sample size, researchers need to consider the study objectives and design, the characteristics of the population, and the type of variables being measured. The expected effect size, level of significance, and statistical power are also critical, along with the potential for nonresponse or dropout. Practical aspects such as available resources and ethical considerations should be balanced to ensure the sample is neither too small to yield meaningful results nor unnecessarily large.

Sacuration and redundancy are the key factors. That is, when you don't get new results, this means that you reached the point of redundancy to which new data or a bigger sampleadds nothing new to your analysis.

Adding to Dr. Ridho's excellent response above, if the study involves testing a hypothesis, then often a mathematical model can be made that includes the magnitude of the expected outcome/response in the variable(s) of interest. If the expected response is hypothesized to be large, for example, then the sample size can be small while still maintaining statistical significance in distinguishing the differences in relative magnitudes of a response variable of interest.

Type II error is a key factor which should influence the decision on an appropriate sample size at the stage of designing the experiment. There is a book by M. M. Desu and D. Raghavaro, Sample size methodology, Academic Press, 1990. The table of contents one may find here https://www.perlego.com/book/1897921/sample-size-methodology-pdf

Contact me, if you need a pdf version of the book.

Determining an appropriate sample size requires consideration of several key factors, including the research objectives, the size and variability of the population, the desired margin of error and confidence level, the expected effect size and statistical power, the study design, and practical constraints such as time, cost, and anticipated non-response.

Aqeel Mery Mohammad First, define what you want to test (the hypothesis), then plan how to test it (the study design), and finally calculate how many participants (sample size), needed based on what outcome you are analyzing.

You may go through this link to calculate sample size. https://mythreyaherbal.com/quickly-calculate-the-sample-size-for-your-clinical-study/

Below factors need to be considered in determining an appropriate sample size for a study.

1. Study Objective and Design

2. Effect size: How much difference you want to detect between groups or conditions. Smaller effect sizes require larger sample sizes to detect statistically significant differences. Should be based on clinical relevance or prior studies.

3. Significance level (α): Typically set at 0.05 (5%), representing the probability of a Type I error (false positive). Lower α (e.g., 0.01) increases the required sample size.

4. Statistical Power (1−β): Commonly set at 80% or 90%, representing the probability of detecting a true effect. Higher power reduces the risk of Type II error (false negative) but increases sample size.

5. Variability in the data: Measured by standard deviation (SD) or variance in the outcome.

Greater variability demands a larger sample to achieve the same precision.

6. Expected dropouts or missing data: Adjust for attrition, especially in longitudinal or clinical studies. Add a buffer (e.g., 10–20%) to maintain statistical power.

7. Population size (for finite populations): Important in surveys or epidemiological studies. For large populations, this factor becomes negligible.

8. Regulatory and ethical considerations: Avoid underpowered studies that waste resources or expose subjects unnecessarily. Avoid overpowered studies that use more animals or participants than needed.

Use prior studies or pilot data to estimate variability and effect size. This strengthens the assumptions behind your sample size calculation.