Determining the required number of subjects or observations for a statistical hypothesis test, specifically a t-test, is a crucial step in research design. This process aims to ensure that the study possesses sufficient statistical power to detect a meaningful effect if one truly exists. The calculations involved consider factors such as the desired level of statistical significance (alpha), the anticipated effect size, and the acceptable probability of a Type II error (beta, which is related to power). For example, if a researcher anticipates a small effect size and desires high power (e.g., 80%), a larger number of participants would be necessary compared to a study expecting a large effect size.
Appropriate determination of participant number avoids both underpowered studies, which may fail to detect genuine effects, and overpowered studies, which waste resources and potentially expose unnecessary individuals to research risks. Historically, insufficient attention to these calculations has led to a reproducibility crisis in some fields, as many published findings could not be replicated due to inadequate statistical power. Properly planning the data collection phase maximizes the likelihood of obtaining valid and reliable results, strengthening the conclusions drawn from the research.
