In coaching a group of smart but unschooled people through solving a problem with normalized median graphs, I learned much about the intersection between analytics and other functions like reporting data, perceiving patterns, presenting results, and setting policy.
The group comprised my students at a for-profit career college: barely literate single parents and eighth- to tenth-grade dropouts. Most of the women were unwed mothers, and more of the men had prison records than had high school diplomas. In one much-dreaded oral communcation assignment, students had to present numeric information orally and visually and explain how it justified a specific conclusion -- a vital skill in starter-level professional jobs.
That same week, the administration had mandated that we use some classroom time to reinforce attendance. Our sessions were deliberately extra long, so students could complete all work in class, since a working single mother or a guy working two jobs and living in a party-prone relative's basement may not have time, space, or quiet to do homework. Not surprisingly, students with perfect attendance tended to get As or Bs. Those with poor attendance failed and dropped out.
So I asked the students, Suppose you're me, and you have to show students like you why attendance is essential. Here's a graph of hours of class attended versus point totals for a previous class. Does this convince you?
"No, it's just dots on a grid."
So what would make it convincing?
"Explain what all the parts are."
I explained the axes and the up-right trend: Students with poor attendance had low points.
"Yeah, but we get a point for every hour attending."
What if we subtract attendance points from total points? Here's a new graph.
Would that convince you?
"It's still just different places on a grid, and there's some higher scores with lower attendance and lower scores with higher attendance."
What if we split things up?
I introduced using the median to divide both axes and using differences from the median, rather than raw scores, so the low group on each axis would all have negative numbers and the high group positive. Graphing difference from the median, and drawing in the medians as heavy dark lines, I asked: Would this get people not to miss class?
"Yeah, but explain all that about the median."
"Yeah, but show how most people were in the high-high or the low-low box."
"Yeah, and the high-low or low-high people are all on the borders, not the middle of their boxes."
Are we done?
"Wait! The way it's drawn, points go 0 to 500, and attendance goes 0 to 48 -- points are about 10 times hours. That's why it looks like one hour makes such a big difference."
I explained normalization -- i.e., rescaling values to make them all fall between negative-1 and 1 -- by dividing by the highest absolute value, so that each graph can be centered on 0.
Here's that graph. Would it convince you?
"You have to explain normalization, too."
I had been writing the need-to-explain points on the board opposite the screen. By class vote, we ordered them into:
A. Axes: 1. Points minus attendance points; 2. Attendance
B. Differences from medians (make negative=low, positive=high)
C. Normalized to avoid exaggerating the point-to-hour relationship
D. Most high point students have high attendance (the high-high box)
E. Most low point students have low attendance (the low-low box)
F. Exceptions are close to the borders
G. So come to class and put yourself into the high-high box.
Then I said: Now, stand by that graph, point when you need to, and give your speech from this outline. Not for grade, just for practice. Mariah, you're up, then Kevin. (I chose the two biggest hams in the class, though I've changed the names.) Everybody else, psych up; you're all going to do it.
They spoke from that outline, pointed to that graph, and accepted crowd advice ("That's the points that ain't from attendance, not the points for not attending!")
Now, all you have to do for a grade is graph some data you think is interesting, see some meaning in your graph, and explain your graph and what it means. (We had already covered finding data and graphing in Excel).
Not only did they do well on the assignment, but for the rest of the term, I had near-perfect attendance. The recipe for their success:
- Tinker with the picture until you can see the relationship and you know it's not bogus.
- Explain the picture.
- Connect your explanation to your recommendation for action.
Sadly, some million-dollar consultants don't always do that.