Category Archives: Quotes


Limitations of Statistics

College and university buildings are usually named after the individual(s) who provide all or most of the money needed to design and build them. On rare occasions, however, a building is named in honor of a professor. That’s the case with the Lindquist Center at the University of Iowa. It is named after E. F. Lindquist, a teacher and scholar who made major contributions to the fields of statistics and testing.

In one of the books Lindquist authored, he provided some sage advice to those who analyze data with statistical tools and to those who read or hear the research-based claims made by those who have analyzed data statistically. Here is what Lindquist said:

“Sound statistical judgment involves a keen appreciation of the inherent LIMITATIONS of statistical techniques and of the original data to which they are applied. In the derivation of these techniques, assumptions are frequently made which cannot be satisfied completely in practical applications. The failure to satisfy these conditions necessitates many qualifications in the interpretations of the results obtained.”

In the middle sentence of this passage, notice that Lindquist points out that important assumptions (concerning data and analytic tools) frequently are not satisfied in studies conducted out in the “real world.” As a consequence of these assumptions being violated, Lindquist then asserts, research findings need to be qualified. Being aware of the LIMITATIONS of statistics, he argues, is necessary for sound statistical judgment.

Unfortunately, many applied researchers who publish research reports based on the statistical analysis of numerical data pay little or no attention to the limitations of their data and of the statistical tools they use. Theoretically, the review process used by good journals is supposed to prevent the publication of articles lacking the “sound statistical judgment” called for by Lindquist. In practice, however, not-so-good articles sometimes slip through the review process.

When reading or listening to the summary of a statistically-based research investigation, be vigilant and try to discern whether or not the researcher(s) who conducted the investigation used what Lindquist referred to as “sound statistical judgment.” If so, be more inclined to be influenced by the study’s finding(s). If not, resist the temptation to believe all you read or hear simply because it’s a summary of research.


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“In our case in Rwanda, we are determined to engender a statistics culture…. We are not only talking of professional statisticians in central statistics bureaus; rather, a whole range of policy makers, business operators, civil society, and indeed, engendering a culture of statistics across the board.”

(From a 2007 speech made by His Excellency Paul Kagame, President of the Republic of Rwanda)

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Quality Data vs Fancy Statistics

“…There is a mischievous tendency to suppose that exactitude of statistical handling can compensate for inexactitude or ineptitude of observation [but] neither statistics nor anything else can make a silk purse out of a sow’s ear.” [C. Spearman]

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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:

If you’d prefer to read Gould’s essay yourself, or print it, go here:

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The Motley Fool provides advice on money management and investing. The following 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.”

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