Statistical Power Sample Size Calculator

Sample Size Formula For Power Analysis:

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

Significance Level (α):

(0.05 for 5%)

Statistical Power (1-β):

(0.8 for 80%)

Standard Deviation Group 1 (σ₁):

units

Standard Deviation Group 2 (σ₂):

units

Sample Size Group 1 (n₁):

subjects

Sample Size Group 2 (n₂):

subjects

Effect Size (δ):

units

Required Sample Size (n):

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1. What Is Statistical Power Sample Size Calculation?

Statistical power sample size calculation determines the number of participants needed in a study to detect a specified effect size with a given level of confidence and power. It ensures studies are adequately powered to detect meaningful differences while controlling Type I and Type II errors.

2. How Does The Calculator Work?

The calculator uses the sample size formula for power analysis:

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

Where:

\( n \) — Required sample size per group
\( Z_{1-\alpha/2} \) — 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 sizes of groups 1 and 2
\( \delta \) — Effect size (clinically meaningful difference)

Explanation: This formula calculates the minimum sample size needed to achieve specified statistical power while maintaining the desired significance level.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation is crucial for study design validity. Underpowered studies may fail to detect real effects, while overpowered studies waste resources. It ensures ethical research conduct and reliable results.

4. Using The Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is statistical power?
A: Statistical power (1-β) is the probability of correctly rejecting a false null hypothesis, typically set at 80% or 90% in research studies.

Q2: What is a good effect size?
A: Effect size depends on the research context. Small effects (δ = 0.2), medium (δ = 0.5), and large (δ = 0.8) are common benchmarks, but clinical relevance should guide selection.

Q3: Why use two-tailed testing?
A: Two-tailed testing is more conservative and detects effects in both directions, making it the standard for most research unless there's strong theoretical justification for one-tailed testing.

Q4: What if standard deviations are unknown?
A: Use estimates from pilot studies, previous research, or literature reviews. Sensitivity analysis with different SD values is recommended.

Q5: How does unequal group size affect power?
A: Unequal group sizes generally reduce statistical power. The most efficient design has equal group sizes (n₁ = n₂).