Statistical Misconception Removal
20 March 2012
Operations Research and Statistics: BFF
30 March 2012

I received a phone call from the company that leases us our equipment. I got quite excited when the salesman told me they would waive the purchase price of a new iPad. Then I decided it was time to clarify things. “Ok,” I said, “You are using the term ‘purchase price’. To me that means the amount you pay for something when you buy it. You are telling me that if I get a new iPad on the same lease as the old iPad you will waive the purchase price. This sounds great to me, but I can’t imagine I’ve got it right.”
I didn’t have it right.
He was using the term “purchase price” to describe an extra payment at the end of the two-year term to allow me to “purchase” the two-year-old iPad. Darn.
Similar confusion arises when common terms are used in specialized ways within a discipline. Statistics and Operations Research have plenty of confusing specialised language. A Google search on “confusing statistical terms” uncovers a goldmine.
“Significant”, “Random, “Regression” and “Normal” have common meanings quite distinct from their technical meaning. “Linear Programming”, though not a term in common use, implies programming, probably in a linear fashion, which does nothing to aid comprehension. There are problems with the term “problem” and even greater problems with the word “solution.” In Operations Research a solution is nothing like an everyday solution. It doesn’t even have to be possible!
Sometimes, like my friendly salesman, we can forget how confusing these terms are. And not only are the terms confusing, but they are sticky. The students have lived their lives with one vague meaning for random, so it will take many attempts to internalize a different meaning.
In writing this post I found numerous references to this problem, and explanations of tricky terms. Here are some links:

Solutions (Hopefully feasible, but unlikely to be optimal)

Here are some thoughts on how to address the problem when teaching.

Be aware

A comprehension problem could stem from misunderstanding of language, like my communication problem with the loan clerk.

Be explicit

Say to students – “Whatever meaning you have for ‘random’, you need to put it to one side when we are talking about random in this discipline.” Get them to explain what it means to them, and explain what it means in the discipline. Find similarities and differences.

Use a modifier if it makes sense

When talking about significance in statistics, I try to call it “statistical significance”, which is a reminder that it means something different from the everyday (and newspaper) use of significant.


State the meaning alongside the term often as you can – until they are so sick of it they recite with you. For example, “This statistically significant result, meaning we have evidence that the result in the sample exists in the population, indicates that men and women do differ in their chocolate eating habits.”

Assess for it

Students learn best what is tested. Have questions about statistical language that separate out the meaning of the term from the statistical concept. A student could say that a sample contains probable bias, by being confused about the term and the application of the phenomenon and the two errors cancel out, giving them a correct answer.

Provide examples

Give examples of the terms used in the “everyday” way and in the specialized way for them to sort.

Student participation

  • Give students opportunities to use the terms in their speaking and writing.
  • Include comprehension activities as part of the class. (“But Miss, this is a Maths lesson, not an English lesson!” “Actually, Angus, this is a Statistics lesson, not a Maths lesson.”)
  • Students to identify whenever there is a conflict between everyday use and statistical use – make their own list like the one below.

Confusing terms in Statistics and Operations Research

This is not comprehensive. Get the students individually or as a class to come up with their own list, possibly humorous! (Nice list at Stats with cats)

  • Significant
  • Random
  • Normal
  • Regression
  • Representative
  • Reliable
  • Average
  • Error
  • Bias
  • Residual
  • Outlier
  • Power
  • Interaction
  • Confidence
  • Risk
  • Solution
  • Uncertainty
  • Linear programming
  • Operations Research
  • Optimal
  • Heuristic
  • And not quite in the everyday category, but annoying nonetheless : ANOVA (why is it called analysis of variance when its purpose is comparing means?)

Compared to the challenge of helping students comprehend inference, the language issue is a small one. But unless it is dealt with, it can be a barrier to the complex ideas.
And I did get the iPad. For business use of course!


  1. […] Teaching statistical language – how I didn’t get a free iPad […]

  2. […] have written earlier about the minefield of statistical terminology, particularly when the statistical word also has an everyday meaning which is not quite the same. […]

  3. […] There are several issues with regard to statistical terminology, and I have written a post with ideas for teachers on how to teach terminology. […]

  4. Peter Chapman says:

    To make things even worse, the word error has two different meanings depending on context. A type 1 or 2 error is a probability. An error is the difference between an observed and a fitted value in a model. We then add more complexity by having two versions of some concepts, one denoted by Greek letters (a theoretical or unknown value), the other denoted by Roman letters (the observed or measured value). No wonder statistics is such a difficult subject. In my experience (of working with applied scientists of various persuasions) we spend far too much time teaching the mathematics underlying statistics, how to do a t-test etc., and not nearly enough time explaining the underlying concepts and how the jargon words aid communication.

  5. […] Language is an issue in teaching and learning statistics. There are many words that have meanings in statistics, different from their everyday meaning, and even with multiple meanings within the study of statistics. Examples of troublesome words are: error, correlation, regression, significant, model. I wrote about addressing this in Teaching Statistical Language. […]

  6. […] In this post I will look at these issues, and ask some questions about how we can better teach students about randomness and random sampling. This problem exists for many domain specific terms, that have colloquial meanings that hinder comprehension of the idea in question. You can read about more of these words, and some teaching ideas in the post, Teaching Statistical Language. […]

  7. […] of statistics is rife with misleading terms. I have written about this before in such posts as Teaching Statistical Language and It is so random. But the terms sampling error and non-sampling error win the Dr Nic prize for […]

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