Paired T-Test Size Tool

Formula Used

The sample size calculation for a dependent paired t-test relies on standard normal distribution quantiles for significance and statistical power. The base formula for determining the number of pairs $n$ is derived from:

$$n = \left( \frac{Z_{\alpha/2} + Z_{\beta}}{\text{Effect Size}} \right)^2$$

Where $Z_{\alpha/2}$ represents the critical value for the chosen significance level, $Z_{\beta}$ corresponds to the desired statistical power, and the effect size is quantified using Cohen's d for dependent samples.

How to Use This Calculator

• Enter Effect Size: Input your expected Cohen's d value based on prior literature or pilot studies.
• Select Alpha and Power: Choose your significance threshold (typically 0.05) and statistical power target (typically 0.80).
• Configure Advanced Settings: Adjust parameters like pre-post correlation and predicted participant drop-out rate.
• Submit and Review: Click the calculation button to immediately review required participant counts at the top of the page.

Understanding Paired T-Test Sample Sizes

Conducting rigorous statistical evaluations requires proper planning to avoid Type II errors. A dependent paired t-test evaluates the means of two related measurements taken from the same experimental units, such as pre-test and post-test scores. Ensuring an adequate sample size directly affects the validity and generalizability of your findings.

Why Attrition Adjustments Matter

Longitudinal studies frequently suffer from participant drop-out. Factoring in an attrition percentage prevents underpowered final datasets by inflating initial recruitment targets adequately.

Frequently Asked Questions

• What is a good effect size to start with? A standard medium effect size of 0.5 is commonly used when exact preliminary data is entirely unavailable.
• How does correlation impact the sample size? Higher positive correlation between paired observations reduces the standard error of differences, lowering required sample sizes.
• Is a one-tailed or two-tailed test better? Use two-tailed tests unless directional hypotheses are strongly justified by prior research.
• Can I adjust for high dropout rates? Yes, input your expected dropout percentage in the attrition field to scale up total recruitment goals automatically.