*42*

A confidence interval is a range of values that is likely to contain a population parameter with a certain level of confidence.

This tutorial explains how to calculate the following confidence intervals in R:

**1.** Confidence Interval for a Population Mean

**2.** Confidence Interval for a Difference in Population Means

Letâ€™s jump in!

**Example 1: Confidence Interval for Population Mean in SAS**

Suppose we have the following dataset that contains the height (in inches) of a random sample of 12 plants that all belong to the same species:

/*create dataset*/ data my_data; input Height; datalines; 14 14 16 13 12 17 15 14 15 13 15 14 ; run; /*view dataset*/ proc print data=my_data;

Suppose we would like to calculate a 95% confidence for the true population mean height of this species.

We can use the following code in SAS to do so:

/*generate 95% confidence interval for population mean*/ proc ttest data=my_data alpha=0.05; var Height; run;

The value for **Mean** shows the sample mean and the values under** 95% CL Mean** show the 95% confidence interval for the population mean.

From the output we can see that the 95% confidence interval for the mean weight of plants in this population is **[13.4624 inches, 15.2042 inches]**.

**Example 2: Confidence Interval for Difference in Population Means in SAS**

Suppose we have the following dataset that contains the height (in inches) of a random sample of plants that belong to two different species:

/*create dataset*/ data my_data2; input Species $ Height; datalines; A 14 A 14 A 16 A 13 A 12 A 17 A 15 A 14 A 15 A 13 B 15 B 14 B 19 B 19 B 17 B 18 B 20 B 19 B 17 B 15 ; run; /*view dataset*/ proc print data=my_data2;

Suppose we would like to calculate a 95% confidence for difference in population mean height between species A and species B.

We can use the following code in SAS to do so:

**/*sort data by Species to ensure confidence interval is calculated correctly*/
proc sort data=my_data2;
by Species;
run;
/*generate 95% confidence interval for difference in population means*/
proc ttest data=my_data2 alpha=0.05;
class Species;
var Height;
run;
**

The first table we need to look at in the output is **Equality of Variances**, which tests whether or not the variance between each sample is equal.

Since the p-value is not less than .05 in this table, we can assume that the variances between the two groups is equal.

Thus, we can look at the row that uses **Pooled** variance to find the 95% confidence interval for difference in population means.

From the output we can see that the 95% confidence interval for the difference in population means is **[-4.6895 inches, -1.1305 inches]**.

This tells us we can be 95% confident that the true difference between the mean height of plants in species A compared to species B is between -4.6895 inches and -1.1305 inches.

Since 0 is not in this confidence interval, this indicates that there is a statistically significant difference between the two population means.

**Additional Resources**

The following tutorials explain how to perform other common tasks in SAS:

How to Perform a One Sample t-Test in SAS

How to Perform a Two Sample t-Test in SAS

How to Perform a Paired Samples t-Test in SAS