### 7. Confidence Interval

**confidence interval**then is a calculated range of valuesthat is likely to include the population parameter (variable) of interest [in our case, the measure of treatment effect] with a certain degree of confidence. It is often expressed as a % whereby a population parameter lies between an upper and lower set value (the confidence limits).

**confidence level**. One can calculate a CI for any confidence level, but the most commonly used values are 95% or 99%. A 95% (or 99%) confidence interval will give the range of values (upper and lower) that one can be 95% (or 99%) certain contains the true population mean for the measured effect (the variable of interest) in the sample investigated.

**Figure 1: Effect of increased sample size
on precision of confidence interval** *(source https://www.simplypsychology.org/confidence-interval.html)*

Confidence intervals (CI) provide different information from what arises from hypothesis tests. Hypothesis testing produces a decision about any observed difference: either that it is ‘statistically significant’ or that it is ‘statistically nonsignificant’. In contrast, confidence intervals provide a range about the observed effect size. This range is constructed in such a way as to determine how likely it is to capture the true – but unknown – effect size.

The following graphs exemplify how the confidence interval can give information on whether or not statistical significance for an observation has been reached, similar to a hypothesis test:

If the confidence interval captures the value reflecting ‘no effect’, this represents a difference that is statistically non- significant (for a 95% confidence interval, this is non-significance at the 5% level).

If the confidence interval does not enclose the value reflecting ‘no effect’, this represents a difference that is statistically significant (again, for a 95% confidence interval, this is significance at the 5% level).

In addition to providing an indication of ’statistical significance’, confidence intervals show the largest and smallest effects that are likely, given the observed data, and thus provide additional useful information.