Two Proportion Sample Size Calculator Raosoft

Two Proportion Sample Size Formula:

\[ n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \times (p_1(1-p_1) + p_2(1-p_2))}{(p_1 - p_2)^2} \]

Zα/2 (Critical Value):

unitless

Zβ (Power Value):

unitless

Proportion 1 (p1):

proportion

Proportion 2 (p2):

proportion

Sample Size (n):

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1. What is the Two Proportion Sample Size Calculation?

The Two Proportion Sample Size calculation determines the required sample size to detect a statistically significant difference between two proportions with specified power and significance level. This is essential for designing studies comparing two groups.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \times (p_1(1-p_1) + p_2(1-p_2))}{(p_1 - p_2)^2} \]

Where:

\( Z_{\alpha/2} \) — Critical value for desired confidence level
\( Z_{\beta} \) — Critical value for desired statistical power
\( p_1 \) — Expected proportion in group 1
\( p_2 \) — Expected proportion in group 2
\( n \) — Required sample size per group

Explanation: The formula accounts for the variability in proportions and the effect size to determine the minimum sample size needed to detect a significant difference.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures studies have adequate power to detect meaningful differences, prevents wasted resources on underpowered studies, and helps avoid false negative results.

4. Using the Calculator

Tips: Enter appropriate Z-values for your desired confidence level and power (typically 1.96 for 95% confidence and 0.84 for 80% power). Proportions must be between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Zα/2 and Zβ?
A: Common values are 1.96 (95% confidence) for Zα/2 and 0.84 (80% power) or 1.28 (90% power) for Zβ.

Q2: How do I choose p1 and p2 values?
A: Use estimates from previous studies, pilot data, or clinically meaningful difference you want to detect.

Q3: What if my proportions are very close together?
A: Smaller differences require larger sample sizes to detect. The calculator will show this relationship.

Q4: Does this assume equal sample sizes per group?
A: Yes, this formula calculates the sample size needed for each group when groups are of equal size.

Q5: When should I use this calculation?
A: Use for clinical trials, A/B testing, survey research, or any study comparing proportions between two independent groups.