Estimating Sample Size for your Quantitative Research Project
There are several ways to go about estimating the appropriate sample size for your topic. Each method has their own efficacy and issues; however, usually the points considered in deciding sample size are; i. the nature of research questions, ii. types/number of statistical tests, etc. Below are three common methods of estimating sample size apriori (before collecting data). In most cases, this is just an approximate rule of thumb and not a stringent formality.
One of the most standard and objective methods currently used by researchers is the G Power software. It is a power estimation tool, but can be used for apriori sample size estimation also, for a wide range of statistical tests. Check out the two official publications about the software at https://link.springer.com/content/pdf/10.3758/BF03193146.pdf and https://link.springer.com/content/pdf/10.3758/BRM.41.4.1149.pdf. It is a simple and free to download software. Both papers combined have over 70k citations, which show how widely the software is used. After specifying effect size and power of analysis, it calculates a sample size for you.
The traditional method used before were the various estimation tables (such as Krejcie and Morgan tables) where you specify confidence interval (95/99) and margin of error for your specific statistical tests, and it gives you an approximate sample size. Those are less rigorous and bit outdated, but still in use. You can check out the original paper for Morgan’s methods at https://doi.org/10.1177%2F001316447003000308. An example of the pre defined sample size estimates for different population sizes is also given in the table below. A number of online sample size calculators are based on the original theory, check out a few at https://www.calculator.net/sample-size-calculator.html and https://www.surveysystem.com/sscalc.htm
There are other more pragmatic methods to estimate sample size as well. Sometimes, it is more about you justifying your sample size for particular analysis. Checking out sample characteristics of other studies on the same (or similar) topics can be one avenue. Usually, if the measures in use produce scores with high variability (large SD), then large sample size should be considered for subsequent use of the same measure. Check out this paper which describes some of those ways of making sample size judgments; https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3409926/