Sample Size Calculation Formula For T-Test

Two-Sample T-Test Sample Size Formula:

\[ n = \frac{(Z_{1-\alpha/2} + Z_{1-\beta})^2 \times (\sigma_1^2 / n_1 + \sigma_2^2 / n_2)}{\delta^2} \]

Significance Level (α):

(0.001-0.2)

Power (1-β):

(0.5-0.99)

Standard Deviation Group 1 (σ₁):

units

Standard Deviation Group 2 (σ₂):

units

Sample Size Ratio Group 1 (n₁):

ratio

Sample Size Ratio Group 2 (n₂):

ratio

Effect Size (δ):

units

Required Sample Size (n):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is The Sample Size Calculation Formula For T-Test?

The sample size calculation for a two-sample t-test determines the number of participants needed in each group to detect a specified effect size with desired statistical power and significance level. This ensures studies are adequately powered to detect meaningful differences.

2. How Does The Calculator Work?

The calculator uses the two-sample t-test sample size formula:

\[ n = \frac{(Z_{1-\alpha/2} + Z_{1-\beta})^2 \times (\sigma_1^2 / n_1 + \sigma_2^2 / n_2)}{\delta^2} \]

Where:

\( Z_{1-\alpha/2} \) — Z-score for significance level (two-tailed)
\( Z_{1-\beta} \) — Z-score for statistical power
\( \sigma_1, \sigma_2 \) — Standard deviations of groups 1 and 2
\( n_1, n_2 \) — Sample size ratios for groups 1 and 2
\( \delta \) — Effect size (minimum detectable difference)

Explanation: The formula calculates the sample size needed to achieve specified statistical power while controlling Type I and Type II error rates.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation is crucial for study design. Underpowered studies may fail to detect true effects, while overpowered studies waste resources. This calculation ensures optimal resource allocation and valid statistical conclusions.

4. Using The Calculator

Tips: Enter significance level (typically 0.05), power (typically 0.8 or 0.9), standard deviations for both groups, sample size ratios (usually 1:1 for equal groups), and the minimum effect size you want to detect. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical significance level used?
A: α = 0.05 is most common, providing 95% confidence level. For more stringent testing, α = 0.01 may be used.

Q2: What power should I aim for?
A: 80% power is standard, meaning 80% chance of detecting a true effect. For critical studies, 90% power is often preferred.

Q3: How do I determine effect size?
A: Effect size should be based on clinical relevance, previous research, or pilot studies. It represents the minimum difference considered important.

Q4: What if standard deviations are unknown?
A: Use estimates from previous studies, pilot data, or literature. Conservative estimates (larger SDs) yield larger sample sizes.

Q5: Can I use this for unequal group sizes?
A: Yes, adjust the n₁ and n₂ ratios accordingly. For example, 2:1 allocation would use n₁=2, n₂=1.