# What does non overlapping confidence intervals mean?

## What does non overlapping confidence intervals mean?

If those intervals overlap, they conclude that the difference between groups is not statistically significant. If there is no overlap, the difference is significant.

**When a 95 confidence interval does not overlap?**

When 95% confidence intervals for the means of two independent populations don’t overlap, there will indeed be a statistically significant difference between the means (at the 0.05 level of significance).

### What is the 95% confidence interval for the proportion of smokers in the population?

For 2015, the percentage of adults aged 18 and over who were current cigarette smokers was 15.1% (95% confidence interval = 14.46%–15.72%), which was lower than the 2014 estimate of 16.8%. The prevalence of current cigarette smoking among U.S. adults declined from 24.7% in 1997 to 15.1% in 2015.

**Do the confidence intervals overlap?**

The short answer is: not always. If two statistics have non-overlapping confidence intervals, they are necessarily significantly different but if they have overlapping confidence intervals, it is not necessarily true that they are not significantly different.

#### When do 95% confidence intervals do not overlap?

When 95% confidence intervals for the means of two independent populations don’t overlap, there will indeed be a statistically significant difference between the means (at the 0.05 level of significance). However, the opposite is not necessarily true. CI’s may overlap, yet there may be a statistically significant difference between the means.

**What is the lower and Upper Confidence limits?**

The lower confidence limit is 45.3 (70.0−24.7), and the upper confidence limit is 94.7 (70+24.7). Confidence limits are the numbers at the upper and lower end of a confidence interval; for example, if your mean is 7.4 with confidence limits of 5.4 and 9.4, your confidence interval is 5.4 to 9.4.

## How to calculate confidence limits of nominal data?

There is a different, more complicated formula, based on the binomial distribution, for calculating confidence limits of proportions (nominal data). Importantly, it yields confidence limits that are not symmetrical around the proportion, especially for proportions near zero or one.

**How are confidence limits and standard error of the mean related?**

Confidence limits and standard error of the mean serve the same purpose, to express the reliability of an estimate of the mean. When you look at scientific papers, sometimes the “error bars” on graphs or the ± number after means in tables represent the standard error of the mean, while in other papers they represent 95% confidence intervals.