How to Calculate Confidence Interval for Median in Stata

What is a Confidence Interval for the Median?

A confidence interval for the median provides a range of values within which we can be reasonably confident the true population median lies. Unlike the mean, the median is less affected by extreme values, making it a robust measure of central tendency for skewed distributions.

Key points about median confidence intervals:

• They provide a range estimate rather than a single point estimate
• They account for sampling variability
• They can be asymmetric, especially with skewed data
• They require larger sample sizes for reliable results

Why Use the Median Instead of the Mean?

The median is often preferred over the mean when:

• Your data is skewed (not normally distributed)
• You have outliers that would distort the mean
• You're working with ordinal data
• You need a measure of central tendency that's less sensitive to extreme values

For example, in income data, a few very high earners can skew the mean upward, while the median provides a better picture of typical earnings.

How to Calculate in Stata

Stata provides several methods to calculate median confidence intervals. The most common approach is using the bootstrap method with the ci command.

Step-by-Step Process

1. Load your data into Stata
2. Use the summarize command to check your data
3. Calculate the median with summarize or tabstat
4. Use the bootstrap method to calculate the confidence interval

ci median(varname), bootstrap(reps=1000)

For more precise results, you can increase the number of bootstrap replications. However, this will increase computation time.

Alternative Methods

Stata also offers other methods for median confidence intervals:

• ci median(varname), percentile - Uses the percentile method
• ci median(varname), bc - Uses the bias-corrected method
• ci median(varname), bc_a - Uses the bias-corrected and accelerated method

Worked Example

Let's calculate a 95% confidence interval for the median income in a sample of 50 households.

Step 1: Load and Inspect Data

use "income.dta", clear
summarize income

Step 2: Calculate Median

summarize income, detail
tabstat income, statistics(median)

Step 3: Calculate Confidence Interval

ci median(income), bootstrap(reps=1000)

Sample Output

This means we're 95% confident that the true median household income in the population falls between $42,000 and $48,000.

Interpreting Results

When interpreting median confidence intervals:

• Focus on the width of the interval - wider intervals indicate more uncertainty
• Consider the sample size - larger samples provide more precise estimates
• Check for symmetry - asymmetric intervals suggest skewed data
• Compare to other estimates - does the median CI align with other measures?