Sampling Error Calculator
Calculate margin of error and confidence intervals for sample means and proportions
Calculate Sampling Error
Number of observations in your sample
Confidence level for the interval
Proportion as decimal (e.g., 0.8 for 80%)
Sampling Error Formulas
Sample Proportion
e: Sampling error
zα/2: Critical z-value
p̂: Sample proportion
n: Sample size
Sample Mean
e: Sampling error
tα/2: Critical t-value or z-value
s: Sample standard deviation
n: Sample size
Common Examples
Election Poll
Sample: 500 voters
Support: 80% (0.8)
Confidence: 95%
Result: ±3.51%
Product Testing
Sample: 30 products
Mean: 600 units
Std Dev: 70 units
Result: ±26.14 units
Key Concepts
Margin of Error: The range of values below and above the sample statistic
Standard Error: Standard deviation of the sampling distribution
Confidence Level: The probability that the interval contains the true parameter
Sample Size Effect: Larger samples reduce sampling error
Understanding Sampling Error
What is Sampling Error?
Sampling error is the difference between a sample statistic and the corresponding population parameter. It occurs because we're using a sample to estimate population characteristics, and samples naturally vary from the population they represent.
Why Does It Matter?
- •Quantifies uncertainty in statistical estimates
- •Essential for constructing confidence intervals
- •Helps determine required sample sizes
- •Critical for making statistical inferences
Key Relationships
Sample Size Impact
Sampling error decreases as sample size increases. It's inversely proportional to √n.
Confidence Level Trade-off
Higher confidence levels produce wider margins of error but greater certainty.
Population Variability
More variable populations lead to larger sampling errors for the same sample size.
Types of Sampling Error
For Proportions
Used when estimating percentages, success rates, or categorical outcomes.
For Means
Used when estimating averages of continuous variables like height, weight, or income.
Reducing Sampling Error
Increase Sample Size
The most effective way to reduce sampling error is to collect more data points.
Improve Sampling Method
Use stratified or systematic sampling to ensure better representation.
Control Variability
When possible, reduce measurement error and control for confounding variables.