In many ways, Benford's Law seems like the perfect test for fraud and other misdeeds. It's intriguing, simple, and computationally cheap. However, as we've seen, it's not always reliable; Χ² tests can be finicky, and as evidence, it doesn't stand on its own. It really needs to be buttressed by other data and helps to support cases of fraud.

However, it is a piece of evidence. It provides a distribution that is difficult to mimic, and it describes a wide class of number sequences accurately. In combination with other information and evidences, it can provide support in the cases of misdeed.

We've also learned about Χ² tests, a very useful statistical procedure. Although they are sensitive to the sample size, these tests still have a lot to offer and are highly recommended. They're cheap to perform., and they work well with the categorical data or data that counts a limited, fixed number possibilities, such as sex or color. When used with appropriate sample sizes, they're straightforward to interpret.

In the end, we're again reminded that working with data is messy. Having a wide range of tools and techniques that we can apply to our researches and questions is critical to being able to successfully track down the information and analyses that we need.

In the next chapter, we'll look at using sentiment analysis to find positive and negative hotel reviews automatically. This turns out to be a more problematic and a more interesting problem than you might suspect at first.