Standard Error Calculator - SE for Mean Proportion

Calculate the standard error of a sample proportion for statistical analysis. Essential for students and researchers working with categorical data and confidence intervals.

Assumes simple random sampling and normal approximation (np ≥ 10 and n(1-p) ≥ 10).

Sample Proportion (p)

Enter between 0 and 1 (e.g., 0.45 or 45%)

Sample Size (n)

Results

Enter values to calculate

About Standard Error of Proportion

The standard error (SE) of a sample proportion measures the variability between sample proportions from different samples. It's crucial for constructing confidence intervals and hypothesis tests for proportions.

Calculation Formula

SE = √[p(1-p)/n] where p is the sample proportion and n is the sample size.

Example Calculation

For a sample proportion of 0.6 with sample size 250:
SE = √[0.6 × (1-0.6) / 250] = √[0.6 × 0.4 / 250] = √0.00096 ≈ 0.0310

Reference Table

Proportion	Sample Size	Standard Error
0.5	100	0.0500
0.5	400	0.0250
0.7	250	0.0290

Sample Size Effect Visualizer

Proportion (p)

0 0.5 1

Frequently Asked Questions

What is the standard error of a proportion?

The standard error measures how much the sample proportion is likely to vary from the true population proportion.

When is the normal approximation appropriate?

When both np and n(1-p) are greater than or equal to 10, the sampling distribution can be approximated by a normal distribution.

Can I use this for small sample sizes?

For small samples (np < 10 or n(1-p) < 10), consider using exact methods like the Clopper-Pearson interval instead.

Disclaimer

For informational and educational purposes only. Not professional statistical advice. Results depend on input assumptions and sampling methods.

References:

1. Sampling Distribution of Sample Proportion

2. Central Limit Theorem for Proportions

3. Confidence Interval Construction for Proportions

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Standard Error Calculator - SE for Mean Proportion

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