There are two ways of preparing our data to present them to the world.
The first is using numbers and the second is using pictures.
Numbers are descriptive statistics like a frequency table or a mean.
The pictures, called graphs, include such things as bar graphs,
histograms, stem-and-leaf diagrams, and the box plot.
So let's learn how to do graphing.
Graphs are a way to display data with clarity and accuracy. A basic graph is constructed using two intersecting lines:
the x axis (or abscissa) is the horizontal line.
Scores on the x axis are plotted just like a number line, smaller numbers to the left,
larger numbers to the right. The left is the negative direction; the right is the positive direction.
The y axis (or ordinate) is a vertical line.
The scores are plotted from bottom to top with low scores near the bottom and higher scores further up the number line.
In order to display your data honestly, the y-axis should include the range of possible scores.
If you are plotting percentages, for instance, the y-axis should always include 0% and
usually range from 0 - 100%.
The point at which the vertical y-axis meets the horizontal x-axis is called the intersection.
It is the convergence of the two axes that represent a score of 0 on x and 0 on y.
The score is sometimes called the origin.
Scores are plotted based on their values for the x and y variables, and each point on the graph is a data point.
Points can be connected with a line to show the shape of the distribution of data.
Regardless of whether we are creating a bar graph, histogram, or line graph we will follow this convention.
The scores (or the categories) will go on the x axis.
If you have a categorical variable like gender or group, that variable goes on the x-axis.
Frequency (or the outcome variable) goes on the y-axis.
The specific type of graph that we will choose depends upon whether the data we are plotting are nominal, ordinal, interval, or ratio level.
Your most important obligation when graphing is to display the data honestly.
Bad graphs distort data or leave misleading impressions.
Sometimes this distortion is intentional sometimes, it's unintentional.
It is possible to misrepresent data even though what you say is technically true.
For example, here is a bar graph showing the effectiveness of an abstinence-only sex education
program. In their promotional literature the vendors for this curriculum for public school claimed that
students who received "Choosing the Best" were nearly
1.5 times more likely to delay the onset of sexual behavior than the control
students at the end of 9th grade.
When we look at this graph
recreated from their promotional material we see this.
Impressive difference. Now more virgins is better, so the success rate for the blue bar program is
much greater than for the green bar control group.
In fact, the green bar is less than half the size of the blue bar. That looks like a huge difference.
But now notice the origin on the y-axis.
It starts at 61%.
But percentages run from 0 to 100%.
They made a lot of amateur mistakes here. They probably created the graph in Excel.
They used whatever graph the software spit out and clearly did not know that they must anchor their percentage graph at 0.
Not doing so
artificially inflates the magnitude of the difference.
Well, let's see how that difference looks when the data are displayed honestly.
Now the y-axis is anchored at 0, and it includes the full range of the data, and
this is the difference from the previous graph.
That difference of 63% versus 66% does not look quite so impressive when you put it into context.
And furthermore, when you compare the blue bars and the green bars from the beginning of the program to the 3-month follow-up
you see that three months later both groups dropped exactly the same
11.3 percentage points, which is to say that no matter whether students learned Choosing the Best or the control
abstinence-only curriculum, there were 11.3% fewer virgins in both programs three months later.
What conclusions do you draw about program effectiveness now?
Do you see evidence of massive success or
two programs that have exactly the same outcome?
For bar graphs and histograms the y-axis should generally be
anchored at zero and should include the range of all possible scores.
The x-axis should be designed to enhance the presentation of the data and
to display it accurately.
Edward Tufte wrote the definitive book on graphing.
It's called the Visual Display of Quantitative Information.
And this book is a classic. It is on Amazon's list of the best
100 books of the 20th century. It has been called the century's best book on statistical graphics.
They probably have a copy at your school library, and it is worth checking out.
In a section on graphical excellence, Tufte explains the purpose of graphing with elegant simplicity.
he says,
"Graphics reveal data," and then he goes on to explain the qualities of excellent data revelation.
Graphics reveal data.
Graphics reveal data honestly, so that the meaning of the data is clear
without distortion or creating false impressions about the findings such as we saw with the bar graph from the abstinence-only curriculum
focused on
substance. It's all about the data. Don't add color, patterns,
cute graphics, 3D.
That's all chart junk. Keep it simple
Graphics reveal by synopsizing big data into a tidy package.
When you have a huge data set it can become hard to handle.
Show off your data with an excellent graph, and everybody will be impressed.
Graphics reveal by supporting the text description. Adding to it clarifying what you've written,
not duplicating what's already in the manuscript. And finally,
graphics reveal by stimulating thought
comparisons and understanding.
A compelling chart is a delight to all.
It draws you in it, makes you think, it teaches you something, and it leaves you knowing a little more than you did
before you saw it.