Sample Size Calculation Using Power Analysis

Sample Size Formula:

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

Z-score (1-α/2):

(typically 1.96 for α=0.05)

Z-score (1-β):

(typically 0.84 for 80% power)

Standard Deviation (σ):

units

Effect Size (δ):

units

Required Sample Size (n):

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1. What Is Sample Size Calculation Using Power Analysis?

Sample size calculation using power analysis determines the number of participants needed in a study to detect a statistically significant effect with a specified level of confidence and power. It ensures studies are adequately powered to answer research questions.

2. How Does The Calculator Work?

The calculator uses the standard sample size formula for continuous outcomes:

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

Where:

\( n \) — Required sample size
\( Z_{1-\alpha/2} \) — 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
\( \delta \) — Minimum detectable effect size

Explanation: This formula calculates the sample size needed to detect a specified effect size with given statistical power and confidence level, accounting for variability in the data.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation is crucial for study validity. Underpowered studies may miss true effects (Type II errors), while overpowered studies waste resources. Power analysis ensures optimal study design and resource allocation.

4. Using The Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What Are Common Z-score Values?
A: For 95% confidence (α=0.05): Z=1.96; For 80% power (β=0.2): Z=0.84; For 90% power (β=0.1): Z=1.28.

Q2: How Do I Estimate Standard Deviation?
A: Use pilot data, previous studies, or literature values. If unknown, conduct a small pilot study to estimate variability.

Q3: What Is A Reasonable Effect Size?
A: Effect size should be clinically meaningful. Consider what difference would change practice or be important to patients.

Q4: Should I Adjust For Multiple Comparisons?
A: Yes, if testing multiple hypotheses, consider adjusting alpha level or using more conservative power calculations.

Q5: What About Dropout Rates?
A: Increase calculated sample size by expected dropout rate (e.g., if 10% dropout expected, multiply by 1.1).