2 Sample T-Test Sample Size Calculator

2 Sample T-Test Sample Size Formula:

\[ n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \times (\sigma_1^2 + \sigma_2^2)}{\delta^2} \]

Significance Level (α):

Power (1-β):

Standard Deviation Group 1 (σ₁):

Standard Deviation Group 2 (σ₂):

Effect Size (δ):

Required Sample Size Per Group (n):

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1. What is the 2 Sample T-Test Sample Size Calculation?

The 2 Sample T-Test Sample Size calculation determines the number of participants needed in each group to detect a specified effect size with adequate power while controlling Type I error. It's essential for designing statistically valid comparative studies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \times (\sigma_1^2 + \sigma_2^2)}{\delta^2} \]

Where:

\( Z_{\alpha/2} \) — Z-score for desired significance level (two-tailed)
\( Z_{\beta} \) — Z-score for desired power
\( \sigma_1^2 \) — Variance of group 1
\( \sigma_2^2 \) — Variance of group 2
\( \delta \) — Clinically meaningful difference to detect

Explanation: The formula balances the trade-off between statistical power, significance level, variability, and effect size to determine the required sample size.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures studies have adequate power to detect meaningful effects while avoiding unnecessary resource expenditure. Underpowered studies may miss important findings, while overpowered studies waste resources.

4. Using the Calculator

Tips:

Select standard significance (0.05) and power (80%) unless specific needs dictate otherwise
Use pilot data or literature to estimate standard deviations
Choose δ as the smallest clinically important difference
Results are per group - multiply by 2 for total sample size

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed tests?
A: Two-tailed tests (default) detect any difference between groups. One-tailed tests detect only pre-specified directional differences, requiring smaller samples but being less flexible.

Q2: How do I estimate standard deviations?
A: Use data from pilot studies, similar published research, or clinical expertise. When uncertain, be conservative (use larger estimates).

Q3: What if my groups have unequal sizes?
A: This calculator assumes equal group sizes. For unequal allocation, adjustments are needed (k = n2/n1 ratio).

Q4: How does correlation affect sample size for paired tests?
A: For paired tests (before/after), positive correlation reduces required sample size as it accounts for within-subject variability.

Q5: What about non-parametric tests?
A: Non-parametric tests typically require ~5-15% more subjects than parametric equivalents due to lower statistical efficiency.