Sample Size Power Calculator

Sample Size Power Formula:

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

Z-score (Z_α/2):

z-score

Power Z-score (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 Power Analysis?

Sample size power analysis determines the number of participants needed in a study to detect an effect of a given size with a specified degree of confidence. It ensures studies have adequate statistical power to detect meaningful differences.

2. How Does the Calculator Work?

The calculator uses the sample size power formula:

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

Where:

\( n \) — Required sample size
\( Z_{\alpha/2} \) — Z-score for significance level (typically 1.96 for α=0.05)
\( Z_{\beta} \) — Z-score for statistical power (typically 0.84 for 80% power)
\( \sigma \) — Standard deviation of the outcome variable
\( \delta \) — Effect size or minimum detectable difference

Explanation: This formula calculates the minimum sample size needed to achieve specified statistical power while controlling for Type I and Type II errors.

3. Importance of Power Analysis

Details: Proper power analysis prevents underpowered studies (which may miss true effects) and overpowered studies (which waste resources). It's essential for ethical research design and grant applications.

4. Using the Calculator

Tips: Enter appropriate z-scores for your desired significance level and power, provide the standard deviation from pilot data or literature, and specify the minimum effect size you want to detect.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Z_α/2 and Z_β?
A: For α=0.05 (two-tailed), Z_α/2=1.96; for 80% power, Z_β=0.84; for 90% power, Z_β=1.28.

Q2: How do I estimate standard deviation?
A: Use data from pilot studies, previous research, or literature in your field. Conservative estimates are better than optimistic ones.

Q3: What is a meaningful effect size?
A: This depends on your research field and clinical/ practical significance. Consult previous studies or expert opinion in your area.

Q4: Should I adjust for multiple comparisons?
A: Yes, if conducting multiple tests, consider Bonferroni or other corrections which may require larger sample sizes.

Q5: What about dropout rates?
A: Increase your calculated sample size by expected dropout percentage (e.g., multiply by 1/(1-dropout_rate)).