**The Wilson score confidence interval for the single proportion**

We love to run sophisticated statistical analyses. However, sometimes research questions are just plain simple. For example, what's currently the percentage of Dutch schoolchildren using an electrical bicycle for transportation?

In both applied and scientific research, we are often interested in simple percentages. Another example: How many people in The Netherlands are left-handed? This question too is about prevalence and may be answered here by calculating the proportion (or %) of left-handed persons in a representative sample.

Imagine we take a sample of 56 Dutch persons of which we count 5 left-handed. In that case we estimate that 5 / 56 = .09 or 9% of the Dutch are left-handed. Before we jump to conclusions and start mass-producing Dutch Design left-handed computer mouses, it may be a good idea to consider that this is just an estimate sprinkled by a good pinch of sampling fluctuation. There is much uncertainty and therefore we need a good all-round confidence interval (CI). This confidence interval provides a range of plausible values of the proportion of left-handed persons in the Dutch population.

Well let’s get this basic confidence interval from the Analysis menu in SPSS! Forget it. For some reason the confidence interval for a proportion has not been implemented in SPSS.

The SPSS syntax below will calculate the Wilson score confidence interval for a single proportion. Using the example data, you will find that the proportion of left-handed Dutch persons is estimated to be 9% with a 95% CI of 4% to 19%. In APA style we could write:

*P*= .09, 95% CI [.04, .19].

Feel free to download the SPSS syntax and example data file.

**The Newcombe-Wilson hybrid score confidence interval for the difference between independent proportions**

****A very common practice is to compare two groups on the prevalence of some outcome. In this case the research question is whether there is a difference between two proportions. Of course, we can test the statistical significance of the association between independent and dependent variables by means of contingency table analysis, but that does not provide us with a well-performing confidence interval of the difference.

An example: How many people in The Netherlands are left-handed? Is there a difference in prevalence between man and women?

The SPSS syntax below will calculate a confidence interval for for the difference between two proportions.

Feel free to download the SPSS syntax and example data file.