Statistics can get pretty complicated, which is one reason why so many people are intimidated by the idea of data analysis.

But even simple analyses can wind up having a big impact on a company's bottom line.

You don't need an elephant gun to take care of a mosquito. Similarly, you don't want to devise a 15-factor, full-factorial designed experiment when a much simpler analysis can take care of the task at hand just as well.

For example, consider the humble 1 proportion test.

The 1 proportion test is a basic statistical test commonly used to confirm or debunk claims. If you want to confirm a supplier's assertion that their electronic components are less than 1% defective, you could take a random sample of components and use the 1 proportion test to determine whether or not the actual proportion defective backs up the claim.

Other examples of proportion data include:

- The proportion of red candies in a jar full of jelly beans
- The proportion of teenagers who pass their driver's test on the first try
- The proportion of manufactured goods that pass inspection
- The proportion of a store's customers who purchase a specific product

The 1 proportion test tells you whether the proportion is equal to a target value. To put it in more starkly statistical terms, the procedure computes a confidence interval and performs a hypothesis test. Your null hypothesis is that the population proportion (p) equals a hypothesized value (H0: p = p0). The alternative hypothesis can be left-tailed (p < p0), right-tailed (p > p0), or two-tailed (p ≠ p0).

So how can that test help an organization?

Suppose you are the manager of the warranty claims department in a company that manufactures TVs. You want to know whether the proportion of your company's TVs that are defective is below the industry average of 0.045. You take a sample of 1,000 TVs and observe 30 defective TVs, or a proportion of 0.03. You use a one-tailed 1 proportion test, with the following null and alternative hypotheses:

H0: p = 0.045

H1: p < 0.045

Let's say your test produces a p-value of 0.010. In this case, you can reject the null hypothesis and conclude that the proportion of your company's TVs that are defective is less than the industry average. There's a statistic that will be great to share with current and prospective customers!

What kinds of benefits have you seen from analyzing data in your organization?