Calculating Sample Size With Power Analysis

Sample Size Formula for Two-Sample T-Test:

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

Z-Score Alpha (Z_α):

z-score

Z-Score Beta (Z_β):

z-score

Standard Deviation (σ):

units

Effect Size (δ):

units

Required Sample Size (n):

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1. What is Sample Size Calculation With Power Analysis?

Sample size calculation with power analysis is a statistical method used to determine the number of participants needed in a study to detect a meaningful effect with a specified level of confidence and power. It ensures that research studies are adequately powered to detect true effects while controlling for Type I and Type II errors.

2. How Does the Calculator Work?

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

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

Where:

\( n \) — Required sample size per group
\( Z_\alpha \) — Z-score for significance level (α)
\( Z_\beta \) — Z-score for power (1-β)
\( \sigma \) — Standard deviation
\( \delta \) — Effect size (clinically meaningful difference)

Explanation: This formula calculates the minimum number of participants needed in each group to detect a specified effect size with given statistical power and significance level.

3. Importance of Power Analysis

Details: Proper sample size calculation is crucial for research validity. Underpowered studies may fail to detect true effects, while overpowered studies waste resources. Power analysis helps optimize study design and ensures ethical use of research participants.

4. Using the Calculator

Tips: Enter z-scores for your desired alpha and beta levels, the expected standard deviation, and the minimum effect size you want to detect. Common z-scores: 1.96 for α=0.05, 0.84 for 80% power, 1.28 for 90% power.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Z_α and Z_β?
A: For α=0.05 (two-tailed), Z_α=1.96; for 80% power, Z_β=0.84; for 90% power, Z_β=1.28.

Q2: How do I determine the effect size (δ)?
A: Effect size should be the smallest clinically meaningful difference. It can be based on previous studies, pilot data, or clinical expertise.

Q3: What if I don't know the standard deviation?
A: Use estimates from similar studies, pilot data, or published literature. Sensitivity analysis with different σ values is recommended.

Q4: Does this work for one-sample t-tests?
A: For one-sample t-tests, remove the "×2" from the numerator as you only have one group's variance.

Q5: What about different types of tests?
A: This formula is specific for two-sample t-tests. Other tests (ANOVA, correlation, chi-square) require different sample size formulas.