Confidence Intervals (CI)

Sometimes, rather than computing one point estimate, such as a mean,  we want to calculate a range of potential values for whatever statistic we are testing.  Why?  Because we know there is chance of error in our sampling, so our point estimate is likely to "be off" somewhat. A confidence interval is the range of plausible values, within some level of error, for your statistic (point estimate).  We can conduct hypothesis tests on a confidence interval, similar to that of a statistic.

Ex.  We want to know what the range is for the average difference in drinks between men and women.  We know the average difference is 3 in our sample, but what would be a likely range for any potential sample we would pull from that population using the same research methods.

For 95% confidence, the interval would be:  Statistic +/- .025

Formula:  See board


Always divide alpha in half.  CI's are always two tailed. 


The Steps to Computing Confidence Intervals

1.  First you choose your level of confidence: 90, 95, 99  

Ex. You will say you are 95% that the population mean falls between those two values. 


2.  Divide error in half.  Look up critical t for that value.


3. Then use the formula to compute the interval.

n=100, mean difference =3, alpha=.95, s=5

t critical = 1.98

3+/-.99

Confidence interval = 2.01-3.99

We are 95% confident that in the population the average difference in weekly alcohol consumption between men and women is 2.01 to 3.99 drinks.

The higher the confidence, the wider the interval.

We can also use the confidence interval to test your hypothesis: 

If the null hypothesis value is included in the interval than you must accept the null hypothesis. 

In our null hypothesis we state “no difference” or group1-group2 =0.  So if 0 was in the interval, than there was 5% chance or higher that there could be no difference between men and women’s drinking.

If the null value, in this case 0, is not included in the interval, than you can reject the null.  In this case, the interval does not include 0, so we can conclude that men drink more. On average they drink 3 glasses more.

What if the null hypothesis said men drink an average of  0-3 drinks more per week than women, and the research hypothesis said men drink more than that per week than women:

Then we would look for a 3 in our confidence interval.

Interval = 2.01 to 3.99 drinks.

3 is contained in the interval.  So we must accept the null hypothesis.