Teaching Students How to Spot Manipulated Data

This blog post is part of a series focusing on media literacy.

We love statistics. Specifically, we love raw number statistics: number of students proficient or advanced, number of babies named Emma, number of hot dogs eaten in 10 minutes, and more. We also love percentage statistics: grades; batting averages in baseball, women’s pay as a percentage of men’s pay, and so on. There is a certainty to these. Statistics are made of numbers, and numbers don’t lie.

But while numbers don’t lie, it is easy to use the statistics compiled from them in a biased way. The media literate person needs to understand how statistics can be manipulated—and that's where statistics literacy comes in. Let me offer a hypothetical example—followed by tips for educators and parents to teach students about statistics literacy in either the classroom or at home.

Hypothetical Example: I want my students to turn off all devices for one day—24 hours with no cellphone, no computer, no e-reader, no Xbox, no anything. I want them to see how addicted they are and how life can still continue without screen time. Let’s say I try this experiment with 100 students in three of my middle school classes. I toss out the idea on Monday and ask students on Tuesday how many succeeded. The answer? Only one. I spend some time Tuesday sharing some numbers with students about the average amount of screen time spent daily and the possible negative effects that may have. I repeat the challenge. On Wednesday, five students report that they turned off all devices for a day.

Bias in Selection

Let’s look at two reports using statistics from Tuesday and Wednesday:

The No Device Challenge is gaining traction. In only one day, five times as many students as the day before accepted the challenge. At this rate, in just two more days no students will have devices on.

The No Device Challenge is not gaining traction. After two days, 95% of students have failed to change their behavior.

Both reports are true. Both accurately report the numbers, and the statistics are correct. Yet they lead to opposite conclusions about how the project is going. The reporters selected different numbers to analyze. If you are biased in favor of this project, you will likely use the first report. If you are biased against this project, you will likely use the second.

Sneaking in Biased Words

Beware of descriptive adjectives added to statistical reports. Numbers are embedded in sentences and paragraphs, and the words used to introduce the numbers suggest bias:

The No Device Challenge is gaining traction. In only one day, an impressive five times as many students as the day before accepted the challenge.

The No Device Challenge is not gaining traction. After two days, a disappointing 95% of students have failed to change their behavior.

It is extremely common to see opinions such as these slipped into statistical reporting. Just one or two words can totally influence the way you read the numbers. Did the number of students surge up to five, or did the number of students barely budge from Day 1?

Bias in Graphs

Graphs are used in biased ways, too. Here’s a graph that makes the No Device project look great:

But if you change the graph to include all of the students, the project is going nowhere:

Again, both charts are accurate. They use the same numbers, but somehow, they leave different impressions. Changing the scale is a very common way to make the mundane seem dramatic.

Selecting only a piece of a graph can change the impression, too. I made up these numbers, but let’s say this is a graph of students who need free lunches. This looks scary, right? Our community is falling apart!

How about looking at the entire graph?

The numbers didn’t change, but somehow the community doesn’t look as bad, does it? It looks like lots of progress has been made.

Bias in Percentages

There was a 200% increase in snow days last year in my district. If I had said, “Last year we had one snow day and this year we had two,” you wouldn’t have been impressed, but it is another way of describing what happened. What if I said that last year, about 1% of the days during the school year were snow days? Again, it comes down to which numbers you select to compare. Do you want to be dramatic and shock readers? Make a percentage with one snow day and two snow days. 200%! Do you want to keep things calm? Make a percentage with two snow days and 185 days in the school calendar. 1%. Both are true. Both are biased.

The Bottom Line: Statistics don’t lie. But that doesn’t mean that they can’t be manipulated. The perceived certainty of numbers can make us less critical than we need to be when reading the barrage of figures that come our way daily.

Tips for Teachers

  • Make sure students know that it is possible to be biased and true. Reporters don’t have to lie about the numbers; they just choose the ones they want to use.
  • Have students look for adjectives that describe the numbers. We read “a shocking 15% increase” differently than “a modest 15% increase.” Bias shows up in those adjectives.
  • Encourage students to look for the bigger picture. In an era where the dramatic is used to attract eyeballs, perspective is lost. “One million people may be in trouble!” Is one million a big number? There are 7.7 billion people on the planet, so one million is way less than 1% of the population: about one one-hundredth of 1% (0.01%).
  • Have students look for different ways to put numbers together. For example, in my No Device activity, there was a 500% increase (from 1 to 5), there was five-fold increase (from 1 to 5), there was an increase of four percentage points (from 1% of the students to 5% of the students), there was a 95% failure rate, there were 19 times as many students failing as succeeding (95 divided by 5), and so on. Have them discuss how the different versions suggest different meanings.
  • Tell students to analyze all graphs. Is this the right scale to use? Is this a representative selection? What other graphs could be made with the same numbers?

The views expressed in this article are those of the author and do not necessarily represent those of HMH.


Blog contributor Erik Palmer is an author of the HMH Into Reading and HMH Into Literature programs. Palmer was also a guest on HMH's podcast, Shaping the FutureTM: Future Skills for Fact-Checking Online Fakes.

SHAPING THE FUTURE is a trademark of Houghton Mifflin Harcourt Publishing Company.

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