Friday, June 27, 2014

Check the Y-axis when reading a chart

Here is an interesting way to make statistics more persuasive without really lying.

Take a look at this chart. It was labeled "Hospital readmissions sharply declined."

Now look at this one. The same data are charted, but the decline does not look nearly as sharp.

A common trick is to abbreviate the Y-axis of a chart. Proponents of this will tell you it makes the chart more compact and easier to read. However, the downside is that a small change is made to appear much larger.

Even though the change was said to be statistically significant in this instance, the casual reader would certainly be impressed much more by the sharp decline depicted in the first chart.

I believe the first chart was produced by the Centers for Medicare and Medicaid Services (CMS) to show that its policy on readmissions was working. I was unable to find the original source for it.

This also works with other graphics as shown in this pair of bar charts from the Visualizing Data blog.

I encourage you to look for this type of manipulation when you read research papers. pharmaceutical ads, or any other depiction of data.


Anonymous said...

Does that include doctors' salaries. LOL.

George Gasman said...

Do I really need to make the "Three kinds of liars" comment?

Nah, didn't think so.

Skeptical Scalpel said...

Don't worry. Someone already made that comment on Twitter.

Anonymous said...

The only thing I really remember from statistics class many decades ago is that figures don't lie, but liars can figure. That was worth the price of the class.

Skeptical Scalpel said...

I wouldn't say abbreviating the Y-axis is lying. It's presenting the data in the most positive way possible. I just think readers should be aware of that.

Anonymous said...

Here's a recent example from a firm I'm all too familiar with:

First convert all the data to percentages.
Then, sum those percentages. Do this for two selected periods (like Q4 of 2013 vs. Q4 of 2014).
Now calculate the overall percentage reduction between the two quarters (in this case, it was a drop from 5% to 4%).
Round up the number, to make it sound a bit more impressive, and announce it proudly! As in:

"There was a 30% drop from Q4 2013 to Q4 2014 ..."

Yes, this actually happened.

Anonymous said...

sorry, meant to say "sum and average"

Skeptical Scalpel said...

That's a neat trick. Can you tell me where it appeared?

Anonymous said...

An interesting variation on this theme is scaling a figure according to some measure. For example, if you showed a 30% bigger dollar sign to indicate a 30% increase in revenue. The area of the sign would be 69% rather than 30% bigger, thus making the increase seem larger.

Skeptical Scalpel said...

That's one I did not think of. Thanks for describing it.

Anonymous said...

Sceptical Scalpel, sadly no. This was internal data, and therefore I cannot point you to a publication. Saying the name of the firm out loud wouldn't be too smart either, given that I work there (still).

Skeptical Scalpel said...

I understand. Thanks.

Anonymous said...

You've heard about the statistician who drowned in a pool an average of 3 feet deep.

Anonymous said...

Look out for the widths of the bars, too.

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