Checking Assumptions: Testing for Normality
In This Chapter
Putting in place a goodness of fit test
Implementing a Jarque-Bera test
All areas of statistical analysis make assumptions about the data being studied. To ensure the validity of any statistical tests performed on a dataset, determining whether the assumptions made are actually correct is essential.
One of the most common assumptions in business disciplines such as economics, finance, marketing, and so forth is that a variable is normally distributed. In particular, rates of return to financial assets are often assumed to be normally distributed. If this assumption is incorrect, the results of any statistical tests will be questionable.
Many tests are specifically designed to determine whether a dataset follows the normal distribution. This chapter examines two of them in detail: the goodness of fit test and the Jarque-Bera test.
Goodness of fit test
You use a goodness of fit test to test the hypothesis that a population conforms to a specified probability distribution. For example, you can use a goodness of fit test to determine whether a population is normally distributed. The goodness of fit test is based on the chi-square distribution.
Chapter 5 introduces the notion of hypothesis testing. There we test ...