How to Calculate Confidence Intervals in Sas

What is a Confidence Interval?

A confidence interval provides an estimated range of values which is likely to contain the population parameter. The most common confidence level is 95%, which means that if the same process were repeated many times, 95% of the calculated confidence intervals would contain the true population parameter.

Key components of a confidence interval:

• Point estimate: The best guess for the population parameter
• Margin of error: The range around the point estimate
• Confidence level: The probability that the interval contains the true parameter

How to Calculate Confidence Intervals in SAS

SAS provides several procedures for calculating confidence intervals. The most common methods are:

1. PROC MEANS for simple confidence intervals
2. PROC TTEST for t-tests with confidence intervals
3. PROC REG for regression confidence intervals
4. PROC SURVEYMEANS for survey data

Using PROC MEANS

For calculating confidence intervals for means:

PROC MEANS DATA=your_data N MEAN CLM;
    VAR your_variable;
RUN;

This will produce a confidence interval for the mean of your_variable using the default confidence level (usually 95%).

Using PROC TTEST

For t-tests with confidence intervals:

PROC TTEST DATA=your_data CI=BOTH;
    VAR your_variable;
RUN;

The CI=BOTH option provides both the confidence interval for the mean and the confidence interval for the difference between means.

Using PROC REG

For regression confidence intervals:

PROC REG DATA=your_data;
    MODEL dependent_var = independent_var;
    OUTPUT OUT=output_data P=prediction CI=ci_lower ci_upper;
RUN;

This will create a dataset with prediction intervals and confidence intervals for the regression line.

Changing the Confidence Level

To change the confidence level (default is 95%), use the ALPHA= option:

PROC MEANS DATA=your_data N MEAN CLM ALPHA=0.10;
    VAR your_variable;
RUN;

This would produce a 90% confidence interval (100% - 10% = 90%).

Worked Example

Let's calculate a 95% confidence interval for the mean of a variable called "height" in a dataset called "people".

SAS Code

PROC MEANS DATA=people N MEAN CLM;
    VAR height;
RUN;

Sample Output

Interpretation

We can be 95% confident that the true mean height of the population is between 67.9 and 69.1 inches. This means if we were to take many samples and calculate 95% confidence intervals for each, approximately 95% of those intervals would contain the true population mean.

Interpreting Results

When interpreting confidence intervals in SAS output:

• Look for the "95% CL Mean" column in PROC MEANS output
• For PROC TTEST, look for the "Confidence Limits" section
• For PROC REG, look at the CI_Lower and CI_Upper variables in the output dataset

Common interpretations:

• If the interval includes zero, the effect is not statistically significant
• Wider intervals indicate more uncertainty in the estimate
• Narrower intervals indicate more precise estimates