1. What is Standard Error for Two Proportions?

The standard error (SE) for two proportions measures the variability in the difference between two sample proportions. It's used to construct confidence intervals and perform hypothesis tests comparing two proportions.

2. How Does the Calculator Work?

The calculator uses the standard error formula for two independent proportions:

Where:

• \( p_1 \) — Proportion in sample 1
• \( n_1 \) — Size of sample 1
• \( p_2 \) — Proportion in sample 2
• \( n_2 \) — Size of sample 2

Explanation: The formula combines the variability from both samples to estimate the standard error of the difference between the two proportions.

3. Importance of Standard Error Calculation

Details: The standard error is crucial for determining the precision of your estimate of the difference between proportions. It's used in z-tests for proportions and constructing confidence intervals.

4. Using the Calculator

Tips: Enter proportions as values between 0 and 1, and sample sizes as positive integers. The calculator will validate your inputs before computation.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this standard error formula?
A: Use this when comparing two independent proportions, such as success rates in treatment vs control groups.

Q2: What's the difference between SE and SD?
A: Standard deviation (SD) measures variability in data, while standard error (SE) measures precision of an estimate (like a proportion difference).

Q3: Can I use this for dependent samples?
A: No, this formula is for independent samples. For dependent samples (e.g., before-after measurements), use McNemar's test.

Q4: What sample size is needed for accurate SE?
A: Generally, both samples should have at least 10 successes and 10 failures for the normal approximation to hold.

Q5: How is this SE used in hypothesis testing?
A: The SE is used in the denominator of the z-test statistic: \( z = (p_1 - p_2)/SE \).