When we discuss whether specific values of one variable are related to specific values of another variable, we are talking about analyzing the relationship between variables. We ask questions like:
- Are high values of variable X consistently linked to high values of variable Y?
- Is there a connection between low values for both variables?
- Are both variables independent of each other? In that case, there would be no relationship between the variables.
To illustrate this concept, imagine the following situation. Suppose you have height and weight data for all the students in your city. You could analyze each variable separately. This would tell you the average height, the lightest weight, etc. However, you could go one step further and ask more complex questions:
- Are taller children usually heavier?
- Is the tallest kid also the heaviest one?
And so on. These are questions about the relationship between two variables - height and weight. You would formulate them as:
- Is height related with weight?
- Do higher values for height correlate to higher values for weight?
We can see the analogy between these two questions and the two more general questions that came earlier.
Discussing the relationship between variables makes sense only when we are analyzing at least two variables simultaneously. So, the basic requirement for this chapter is that we will have two categorical or two numerical variables.