Relationships Between Two Variables


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Learning objectives for this lesson

Upon completion of this lesson, you should be able to do the following:

Examining Relationships Between Two Variables

Previously we considered the distribution of a single quantitative variable. Now we will study the relationship between two variables where both variables are qualitative, i.e. categorical, or quantitative. When we consider the relationship between two variables, there are three possibilities:

  1. Both variables are categorical. We analyze an association through a comparison of conditional probabilities and graphically represent the data using contingency tables. Examples of categorical variables are gender and class standing.
  2. Both variables are quantitative. To analyze this situation we consider how one variable, called a response variable, changes in relation to changes in the other variable called an explanatory variable. Graphically we use scatterplots to display two quantitative variables. Examples are age, height, weight (i.e. things that are measured).
  3. One variable is categorical and the other is quantitative, for instance height and gender. These are best compared by using side-by-side boxplots to display any differences or similarities in the center and variability of the quantitative variable (e.g. height) across the categories (e.g. Male and Female).

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