Title: The confidence interval
Course: UGQuants (SSPS) > Section: Inference

The confidence interval

In order to be able to make reliable statements based on the data we have from our sample, we need to be aware that there is a certain margin for error: if we do not collect information about everyone, it could be that our sample, no matter how carefully it was selected, is not fully representative of the whole population. The bigger the sample, the more reliable our findings tend to be, but there will always remain a margin of error.

To estimate how likely it is that our findings are faulty (that what we observe in the sample is not true for the whole population), we need to be aware of two measures:

- the confidence interval
- and the significance.

Imagine we are interested in the average mark scored by all students having taken the introduction course of their subject at uni. Because of data protection, we don't have access to the uni records but need to ask a sample of people what mark they scored and infer the likely average from that. The 50 people we asked scored an average of 56 marks, with a standard deviation of 4.5 marks. Based on that, we can easily find an interval in which our population average mark lies, once we settle on a margin of error we are willing to accept.

Type 'confidence interval calculator' into your search engine, and you will find plenty of websites calculating it for you.

In the social sciences, a 95% confidence interval (CI) is usually deemed acceptable, although a higher confidence is of course preferable. In our example, we can say with 95% confidence that the true average mark for all students on the course is somewhere between 54.75 and 57.25.

Put differently, there is a 5% chance that our findings are wrong and the true population average lies outwith this interval.