An area graph is a multi-line graph, where none of the lines cross and the difference between the frequency of each variable for each value is important.
The differences in frequency are highlighted by adding different shadings between the adjacent lines of the graph. Note the confusing terminology:
an area chart is a histogram, with only one variable, while an area graph is a line graph with multiple lines where the areas between the lines are important.
We could have used an area graph for our Fig. 7-11, Why Isn’t My Business Making Money? We would have left out the black line (net income) and shaded the area between the two other lines black, to show that it’s height did not vary. This would focus attention on the area with the unchanging height, net income, which is the problem we want our readers to focus on. For an example of an area graph, see Fig. 7-17.
Comparing Two Variables: The Scatter Plot
The scatter plot is a type of graph used to show the relationship between the distributions of two different numeric variables. (Scatter plots are most valuable when both variables have real number, rather than just integer, values.) Scatter plots are different than the other graphs we have looked at so far, because each and every unit is shown as a dot on the graph. For each individual subject unit, a point is placed on the graph. Each point is placed directly above the position on the x-axis equal to the unit’s value on the first
Fig. 7-11. Multiple-line graph: Why isn’t my business making money?
variable and directly to the right of the position on the y-axis equal to the unit’s value on the second variable. The result is a graph with N points scattered over the chart.
What does a scatter plot show? A scatter plot shows how being high or low on one numeric variable relates to being high or low on a second numeric variable. This sort of relationship is very important to statistical techniques such as correlation and regression, which we will discuss in Chapter 12
‘‘Correlation and Regression.’’ If two variables measure features of the world that are involved in some of the same causal processes, then that can result in relationships that can show up in a scatter plot. To illustrate this, here are two scatter plots of Judy and her friends, Fig. 7-12, showing the relationship between their weights and their heights, and Fig. 7-13, showing the relationship between their weights and their I.Qs.
Note that the cloud of points in the first scatter plot is oval shaped and the cloud in the second plot is rounder. An oval cloud is an indication that there is a relationship between the two variables. As we might expect, taller folks
Fig. 7-12. Scatter plot of weight and height of Judy’s friends.
Fig. 7-13. Scatter plot of weight and I.Q. of Judy’s friends.
tend to weigh more. That means that, across a population, there are fewer folks who are tall and light (points on the upper left) or short and heavy (points on the lower right). (Even tall, skinny people weigh a fair amount because they are tall. And short, overweight people do not weigh as much as a tall overweight person might.) Because there are fewer points on the upper left and lower right, the overall cloud of points looks more oval. In short, the relationship between weight and height shows up in terms of the shape of the cloud of points in the scatter plot. We have gone one step further and created a line, called a regression line, on this scatter plot. Microsoft Excel automatically performed a linear regression for us and inserted the line.
The regression line is a description of the relationship between the variables, and is discussed in Chapter 12.
In the case of weight and I.Q., where there is no relationship, we get a roughly circular cloud of points. This indicates that there is no visible correlation between the two variables; that is, they seem to be independent. If that happens, we do not draw a regression line. The set of points in Fig. 7-13 may not look very circular due to our small sample size. But it certainly does show that there is no indication of a correlation.
In some data sets, the regression line could slope downwards instead of upwards. Picture this chart: If we have two variables such as hours of television watched per week on the X-axis and grade-point-average on the Y-axis, we will see an oval cloud that starts high on the left (less TV, higher grades) and ends low on the right (more TV, lower grades). The regression line would slope from the upper left to the lower right, indicating a significant negative correlation between the two variables.
Don’t Get Stuck in a Rut: Other Types of Figures
There are many more types of statistical charts than can be shown in this one chapter. There are box-and-whisker plots, pictograms, ideograms, digitdot plots, cross diagrams, bubble charts, contour plots, diamond charts, and statistical maps, among others. Some are specialized developments from one particular industry, or for one particular statistical application. It is good to have a nodding acquaintance with many different types of charts and graphs.
It is important to be familiar with all of the types of charts and graphs used in our own industry. And, most important of all, we must understand how to use the basic charts well, and how to use the sophisticated charts of our industry making full use of all their features.
When the occasion arises, we should be able to scout around for the best type of graph to use. Often, the best chart doesn’t fit into any of the standard categories, but may be a mixture of different standard chart types, or inspired by aspects of standard types we have seen. Here, we will look at mixing chart types, using 3-dimensional graphs, and creating statistical maps.