Yesterday's post attracted a few good comments.

Several readers don't like the data used in the NAEP score chart. The authors labeled the metric "gain in NAEP scale scores" which I interpreted to be "gain scores," a popular way of evaluating educational outcomes. A gain score is the change in test score between (typically consecutive) years. I also interpreted the label "2000-2009" as the average of eight gain scores, in other words, the average year-on-year change in test scores during those 10 years.

After thinking about what reader *mankoff* wrote, which prompted me to download the raw data, I realized that the designer did not compute gain scores. "2000-2009" really means the difference between the 2009 score and the 2000 score, ignoring all values between those end points. So * mankoff *is correct in saying that the 2009 number was used in both "2000-2009" and "2009-2015" computations.

This treatment immediately raises concerns. Why is a 10-year period compared to a 7-year period?

Andrew prefers to see the raw scores ("scale scores") instead of relative values. Here is the corresponding chart:

I placed a line at 2009, just to see if there is a reason for that year to be a special year. (I don't think so.) The advantage of plotting raw scores is that it is easier to interpret. As Andrew said, less abstraction. It also soothes the nerves of those who are startled that the lines for white students appear at the bottom of the chart of gain scores.

I suppose the reason why the original designer chose to use score differentials is to highlight their message concerning change in scores. One can nitpick that their message isn't particularly cogent because if you look at 8th grade math or reading scores, comparing 2009 and 2015, there appeared to be negligible change, and yet between those end-points, the scores did spike and then drop back to the 2009 level.

One way to mitigate the confusion that *mankoff* encountered in interpreting my gain-score graphic is to use "informative" labels, rather than "uninformative" labels.

Instead of saying the vertical axis plots "gain scores" or "change in scores," directly label one end as "no progress" and the other end as "more progress."

Everything on this chart is progress over time, and the stalling of progress is their message. This chart requires more upfront learning, after which the message jumps out. The chart of raw scores shown above has almost no perceptive overhead but the message has to be teased out. I prefer the chart of raw scores in this case.

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Let me now address another objection, which pops up every time I convert a bar chart to a line chart (a type of Bumps chart, which has been called slope graphs by Tufte followers). The objection is that the line chart causes readers to see a trend when there isn't one.

So let me make the case one more time.

Start with the original column chart. If you want to know that Hispanic students have seen progress in their 4th grade math scores grind to a halt, you have to shake your head involuntarily in the following manner:

(Notice how the legend interferes with your line of sight.)

By the time you finish interpreting this graphic, you would have shaken your head in all of the following directions:

Now, I am a scavenger. I collect all these lines and rearrange them into four panels of charts. That becomes the chart I showed in yesterday's post. All I have done is to bring to the surface the involuntary motions readers were undertaking. I didn't invent any trends.

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