Quantitative Analysis: Inferential Statistics and Multivariate Analysis

This chapter proceeds more deeply into quantitative analysis, exploring more complex inferential statistics and multivariate analysis. In particular, the first half of the chapter focuses on the question of statistical significance. The roots of statistical significance are grounded in the central limit theorem, which posits that the distribution of the sum and mean of random samples taken from a population will approach a normal distribution as sample size increases. That means that you can test the hypothesis that a relationship exists in your data by estimating the likelihood that such a relationship would happen by chance. Establishing a confidence level (commonly 95%) allows you to state whether there is a 95% chance that the relationship is not accidental. Common tests that allow you to determine if a relationship is statistically significant are chi-square, Mann-Whitney U, difference of means, ANOVA, the t-test, and the F-test.

Multivariate analysis involves looking at how multiple variables interact. One way to conduct multivariate analysis is by trying to capture the effect of control variables, which can have no effect on a relationship, make a relationship weaker, make it stronger, or have a different effect for different values. Multiple regression takes into account the effect of multiple independent variables on a single dependent variable. Although regression analysis can only be used with interval-ratio variables, dichotomous (“dummy”) variables can be used to convert nominal or ordinal variables into interval-ratio variables for the purposes of regression.