Calculate Sample Size Power Analysis

Sample Size Formula:

\[ n = [Z_{1-\alpha/2} + Z_{1-\beta}]^2 \times \frac{\sigma^2}{\delta^2} \]

Z-score (Z_{1-α/2}):

Z-score

Z-score (Z_{1-β}):

Z-score

Standard Deviation (σ):

units

Effect Size (δ):

units

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 formula:

\[ n = [Z_{1-\alpha/2} + Z_{1-\beta}]^2 \times \frac{\sigma^2}{\delta^2} \]

Where:

\( Z_{1-\alpha/2} \) — Z-score for desired confidence level (typically 1.96 for 95% CI)
\( Z_{1-\beta} \) — Z-score for desired 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 sample size needed to achieve specified statistical power for detecting a given effect size at a particular confidence level.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation is crucial for study design. It prevents underpowered studies (which may miss true effects) and overpowered studies (which waste resources). Adequate power ensures reliable and reproducible research results.

4. Using the Calculator

Tips: Enter Z-scores for your desired confidence level and power, provide the standard deviation of your outcome measure, and specify the minimum effect size you want to detect. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Z-scores?
A: For 95% confidence level: Z = 1.96; For 80% power: Z = 0.84; For 90% power: Z = 1.28.

Q2: How do I estimate standard deviation?
A: Use data from pilot studies, previous research, or literature in your field. If unknown, conservative estimates are recommended.

Q3: What is a reasonable effect size?
A: Effect size should reflect the smallest clinically or scientifically meaningful difference. Consider what magnitude of change would be important in practice.

Q4: Does this work for all study designs?
A: This formula is for continuous outcomes in two-group comparisons. Different formulas exist for proportions, correlations, and other study designs.

Q5: Should I adjust for multiple comparisons?
A: Yes, if conducting multiple tests, consider adjusting alpha levels or using more conservative power calculations to maintain overall error rates.