1. What is Standard Error for Proportion?

The standard error (SE) of a proportion measures the precision of the sample proportion as an estimate of the population proportion. It quantifies the variability in the sampling distribution of the proportion.

2. How Does the Calculator Work?

The calculator uses the standard error formula for proportion:

Where:

• \( p \) — Sample proportion (between 0 and 1)
• \( n \) — Sample size

Explanation: The formula shows that standard error decreases as sample size increases, and is maximized when p = 0.5.

3. Importance of Standard Error Calculation

Details: Standard error is crucial for constructing confidence intervals and conducting hypothesis tests about population proportions in regression analysis.

4. Using the Calculator

Tips: Enter the sample proportion (must be between 0 and 1) and the sample size (must be positive integer). The calculator will compute the standard error.

5. Frequently Asked Questions (FAQ)

Q1: When is this formula appropriate?
A: When the sample size is large enough that the sampling distribution can be approximated by a normal distribution (np ≥ 10 and n(1-p) ≥ 10).

Q2: What's the relationship between SE and sample size?
A: SE decreases as sample size increases, following an inverse square root relationship (SE ∝ 1/√n).

Q3: How does proportion value affect SE?
A: SE is maximized when p = 0.5 and decreases as p approaches 0 or 1.

Q4: What's the difference between SD and SE?
A: Standard deviation describes variability in data, while standard error describes variability in sample statistics.

Q5: How is SE used in confidence intervals?
A: A 95% CI for the population proportion is typically calculated as p ± 1.96×SE.