Tag Archives: Median

WHAT SEEMS TO BE TRUE OFTEN ISN’T

Many People Get Fooled

The Motley Fool provides advice on money management and investing. However, its recommendations can and should be used by people in other fields. For example, the following 20-word tip, from the “Fool’s School,” should be memorized by everyone who encounters statistically-based claims or findings in politics, medicine, psychology, education, and all other arenas of our lives:

“Never blindly accept what you read. Think critically about not just words, but numbers. They’re not always what they seem.”

Here are 5 examples illustrating how numbers in statistics often do NOT mean what they seem to indicate:

Example A

If the 14 players on a basketball team have a median height of 6 feet 6 inches, it might seem that 7 of those athletes must be shorter than 6’6” whereas 7 must be taller than that. Wrong!

Example B

If the data on 2 variables produce a correlation of +.50, it might seem that the strength of the measured relationship is exactly midway between being ultra weak and ultra strong. Not so!

Example C

If a carefully conducted scientific survey indicates that Candidate X currently has the support of 57% of likely voters with a margin of error of plus or minus 3 percentage points, it might seem that a duplicate survey conducted on the same day in the same way would show Candidate X’s support to be somewhere between 54% and 60%. Bad thought!

Example D

If a null hypothesis is tested and the data analysis indicates that p = .02, it might seem that there’s only a 2% chance that the null hypothesis is true. Nope!

Example E

If, in a multiple regression study, the correlation between a particular independent variable and the dependent variable is r = 0.00, it might seem that this independent variable is totally useless as a predictor. Not necessarily!

The Motley Fool’s admonition, shown above in italics, contains 20 words. If you can’t commit to memory the entirety of this important warning, here’s a condensed version of it:

“Numbers. They’re not always what they seem.”

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Filed under Mini-Lessons, Misconceptions

HOW OLD ARE THE MEDIAN, MODE, & ARITHMETIC MEAN?

Mean Median Mode (Oldest)

According to one source, the word “mode” was first used (by Karl Pearson) in 1895. The concept of the “median” is a bit older; it was used for the first time by the Frenchman Antoine Cournot in 1843. The notion of the “arithmetic mean” is even older.

QUESTION: When do you think the concept of the “arithmetic mean” was born?

ANSWER: A long, long, LONG time ago. The Pythagoreans studied it in the 5th century B.C.

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Filed under History of Statistical Terms

DO YOU KNOW SOMEONE WITH CANCER

Dr. Stephen Jay Gould, a world-famous scientist who taught at Harvard, was 40 when diagnosed with cancer. He discovered that people with his kind of cancer live for a median of 8 months. Gould’s down-to-earth essay, “The Median Isn’t the Message,” deals with his “survival expectancy.” It’s considered by some to be “the wisest, most humane thing ever written about cancer and statistics.”

In his thoughtful commentary, Gould offered some important advice to those who hear (for themselves or a loved one) grim diagnoses based on median survival rates. As Gould so correctly pointed out,

What does “median mortality of eight months” signify in our vernacular? I suspect that most people, without training in statistics, would read such a statement as “I will probably be dead in eight months”––the very conclusion that must be avoided, since it isn’t so….

Dr. Gould’s essay contains important food-for-thought not just for those concerned about cancer or other life-ending diseases, but also for those who produce or receive statistically-based research claims in any disciple. In a nutshell, his admonition says: Don’t focus so heavily on means and medians that the important underlying variability is totally overlooked. As Gould put it,

We still carry the historical baggage of a Platonic heritage that seeks sharp essences and definite boundaries. … This Platonic heritage, with its emphasis in clear distinctions and separated immutable entities, leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua. In short, we view means and medians as the hard “realities,” and the variation that permits their calculation as a set of transient and imperfect measurements of this hidden essence.

If the median is the reality and variation around the median just a device for its calculation, the “I will probably be dead in eight months” may pass as a reasonable interpretation. … But all evolutionary biologists know that variation itself is nature’s only irreducible essence. Variation is the hard reality, not a set of imperfect measures for a central tendency. Means and medians are the abstractions.

If you’d like to hear Gould’s essay read while you see a series of photos of him at work and play, click this link: http://www.youtube.com/watch?v=cH6XuiOBbkc

If you’d prefer to read Gould’s essay yourself, or print it, go here: http://cancerguide.org/median_not_msg.html

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Filed under Applications, Mini-Lessons, Quotes

STATISTICIANS ARE UNUSUAL YET QUITE AVERAGE

On the one hand, statisticians are a bit weird. On the other hand, they are altogether average. Here’s the proof:

  1. They often break the law and drive their cars on the MEDIAN.
  2. At dinner, they invariably want more desserts than anyone else, and they always want them ala-MODE.
  3. If you sum up their deviations, they lose their cool and get incredibly MEAN.

(This little effort at statistical humor comes from S. Huck)

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