Illuminating Statistical Analysis Using Scenarios and Simulations

AData Types and Some Basic Statistics

Statistical Scenario

Which method would you use to measure happiness?

We often try to make sense of the world by trying to make sense of data about the world—naturally quantitative data such as heights, weights, incomes, and prices; quantitative indices of things such as inflation and unemployment; and, quantifications of qualitative things such as peoples' attitudes, beliefs, and opinions.

A fundamental aspect of data is its measurement type. The type of measurement determines how we can interpret the associated data, how we can manipulate and analyze it, and, in general, how much information it can relate. Figure A.1 outlines the commonly used types.

1. Nominal data, also called categorical data, have values that signify different categories. As examples, sex and political affiliation are both nominal variables: Sex is a binomial when there are only two categories allowed, “female” and “male”; political affiliation is a multinomial when there are more than two categories allowed, “Democrat”, “Republican”, and “Independent.” The values of a nominal variable simply signify category membership.

   The basic computation we can do is counting: We can count the number of occurrences in the various categories and analyze the counts. Related to counts, we can also determine proportions. For example, based on counts of the number of people who ...