5.1 - Graphs for Two Different Measurement Variables

In a previous lesson, we learned about possible graphs to display measurement data. These graphs included: dotplots, stemplots, histograms, and boxplots view the distribution of one or more samples of a single measurement variable and scatterplots to study two at a time (see section 4.3).

Example 5.1 Graph of Two Measurement Variables Section

The following two questions were asked on a survey of 220 STAT 100 students:

  1. What is your height (inches)?
  2. What is your weight (lbs)?

Notice we have two different measurement variables. It would be inappropriate to put these two variables on side-by-side boxplots because they do not have the same units of measurement. Comparing height to weight is like comparing apples to oranges. However, we do want to put both of these variables on one graph so that we can determine if there is an association (relationship) between them. The scatterplot of this data is found in Figure 5.2.

The scatterplot with weight as y axis and height as x axis shows positive association between these two variables since weight increases as height increases.

Figure 5.2. Scatterplot of Weight versus Height

In Figure 5.2, we notice that as height increases, weight also tends to increase. These two variables have a positive association because as the values of one measurement variable tend to increase, the values of the other variable also increase. You should note that this holds true regardless of which variable is placed on the horizontal axis and which variable is placed on the vertical axis.

Example 5.2 Graph of Two Measurement Variables Section

The following two questions were asked on a survey of ten PSU students who live off-campus in unfurnished one-bedroom apartments.

  1. How far do you live from campus (miles)?
  2. How much is your monthly rent (\$)?

The scatterplot of this data is found in Figure 5.3.

The scatterplot with rent as y axis and distance from campus as x axis shows negative association between these two variables since rent decreases as distance increases.

Figure 5.3. Scatterplot of Monthly Rent versus Distance from campus

In Figure 5.3, we notice that the further an unfurnished one-bedroom apartment is away from campus, the less it costs to rent. We say that two variables have a negative association when the values of one measurement variable tend to decrease as the values of the other variable increase.

Example 5.3 Graph of Two Measurement Variables Section

The following two questions were asked on a survey of 220 Stat 100 students:

  1. About how many hours do you typically study each week?
  2. About how many hours do you typically exercise each week?

The scatterplot of this data is found in Figure 5.4.

The scatterplot with study hours as y axis and exercise hours as x axis shows no association between these two variables since the number of study hours does not increase or decrease as the number of exercise hours increases.

Figure 5.4. Scatterplot of Study Hours versus Exercise Hours

In Figure 5.4, we notice that as the number of hours spent exercising each week increases there is really no pattern to the behavior of hours spent studying including visible increases or decreases in values. Consequently, we say that that there is essentially no association between the two variables.