Determining the sample size in a quantitative research study is challenging. There are certain factors to consider, and there is no easy answer. Each experiment is different, with varying degrees of certainty and expectation. Typically, there are three factors, or variables, one must know about a given study, each with a certain numerical value. They are significance level, power and effect size. When these values are known, they are used with a table found in a statistician's manual or textbook or an online calculator to determine sample size.
Choose an appropriate significance level (alpha value). An alpha value of p = .05 is commonly used. This means that the probability that the results found are due to chance alone is .05, or 5%, and 95% of the time a difference found between the control group and the experimental group will be statistically significant and due to the manipulation or treatment.
Select the power level. Typically a power level of .8, or 80%, is chosen. This means that 80% of the time the experiment will detect a difference between the control and experimental groups if a difference actually exists.
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Estimate the effect size. Generally, a moderate to large effect size of 0.5 or greater is acceptable for clinical research. This means that the difference resulting from the manipulation, or treatment, would account for about one half of a standard deviation in the outcome.
Organize your existing data. With the values for the three factors available, refer to the table in your statistician's manual or textbook; or enter the three values into an online calculator made for determining sample size.
Survey the existing literature on the research topic to explore different values used for the three factors.
You may want to use a larger sample than recommended to ensure power.