Confidence intervals
Confidence Intervals (CI) are calculated to show the range of likely values for a parameter. The CI can be set at any level, but is typically reported at the 95% confidence level. The confidence interval shows us that if we repeated the experiment on multiple samples, the true population parameter would be within the values of the CI, 95% of the time (not that 95% of the values are within the range).
Example applications
Confidence intervals are most commonly reported on bar charts, where the mean is reported in the bar chart, and the sample CI is reported using lines (error bars) that extend to the lower and upper bounds of the CI. Having a larger CI (e.g. 95%) means that the bars will be larger, but that we can be more confident of the difference and effect size if the bars do not overlap between samples. A CI should be reported if you report the average of a sample: such as the average height of students, or the average income of an engineer.
Steps
Assuming that you know the standard deviation (σ) is known, then:
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Identify the sample mean (x̄)
- Identify the z* to use as the critical value: for 95% CI, 1.96 is used
- Put the values into the formula on the right
- Plot and interpret the results
As you can see, one easy way to reduce the confidence interval is to increase the number of samples in a population (n).
Key concepts
- an explanation of what a confidence interval is, and when it should be used
- an example that walks through how to establish the confidence interval
- advice to the student engineer on how to interpret the results
Core resources
- John McDonald has authored an online textbook Handbook of Biological Statistics, which has a very clear entry on Confidence Limits (limits are for our purposes the same as intervals){: .link-ext target=”_blank” }.
Similar tools…
Confidence intervals are an alternative method to using p-values to establish the differences between two groups. If you’re feeling inclined, you could explore the difference between the two.