# Common words that have particular statistical meanings

I am not a statistician but my research work involves statistics (analyzing data, reading literature, etc.). I was again reminded from a comment on one of my questions posted here that there are some common words that have particularly specific meanings or connotations for those who are well-practiced in the field of statistics.

It will be helpful to have a list of such words and may be phrases along with some comments.

• Sounds like a candidate for Community Wiki. – Glen_b Dec 30 '13 at 4:09
• @Glen_b It could turn into a particularly large one, given that just about any term in statistics or mathematics would qualify. Is there any way to narrow the scope of this question meaningfully? – whuber Dec 30 '13 at 5:18
• @whuber Yes, there's a danger it becomes overly broad. Would something like "which commonly generate confusion" suffice to narrow the scope? – Glen_b Dec 30 '13 at 5:24
• I think that competent statisticians normally have a good command of their native language and would be well aware of when they are using jargon that needs to be properly explained to a lay audience. – Robert Jones Dec 31 '13 at 13:08
• @Glen_b I'm not sure. This is so broad I can barely begin a list of words that should be covered: accuracy, bias, calibration, discrimination, continuous, distribution, hazard, survival, spline, model, response, bootstrap, adjusting, cluster, conditional, confidence, density, estimate, variable, canonical, correlation, predict, inference, censoring, risk, concordance, logistic, limit, coverage, confounding, contingency, convergence, correspondence, freedom, deviance, exponential, extreme, range, normal, drop-in, dummy, explained [variation], factor, failure, fill-in, fit, fitted, function, ... – whuber Dec 31 '13 at 14:46

"significant" -- here the common language use of the word is to mean something like 'important' or 'meaningful'. The statistical meaning is informally nearer to "can be discerned from random variation about the null"; it doesn't signify that the difference is large enough to matter.

Here are some examples where this distinction might have been the cause of some confusion: 1 2

"parameter" -- it often seems to happen - particularly in scientific experiments - that the word 'parameter' is used in the way a statistician would use the word 'variable'. Wikipedia puts it thus:

A statistical parameter is a parameter that indexes a family of probability distributions. It can be regarded as a numerical characteristic of a population or a model

Example where this one may be an issue: 1 - presumably the post that led to this question. (I saw another recently but I can't locate it right now)

"Error" - In statistics it often means any deviation between an observed and predicted value. In real life it means a mistake.

I found a refereed paper from 2010 that looks at this question.

Anderson-Cook CM. Hidden jargon: Everyday words with meanings specific to statistics. ICOTS8, International Conference on Teaching Statistics, Ljubljana, Slovenia, 11-17 July 2010.

The paper is available for free online, so I am only providing a partial list of the terms that the author discusses:

 confounding, control, factor, independent, random, uniform


I've come across the problem of using "falsification" as in "falsify a hypothesis", while others thought I was referring to "making up data". Also "biased" is nearly impossible to mention without causing confusion.

"normal" - In common speech, normal means as expected, not out of the ordinary. In statistics, if a variable is normally distributed, it's referring to the Gaussian distribution. I don't believe it's standard to capitalize the word "normal" to distinguish it from the common speech meaning.

"normalization / standaridization" - In statistics, to normalize a variable means to subtract the mean and divide by the standard deviation.

"standard deviation versus standard error" - Standard deviation usually is calculated using the entire population whereas standard error is calculated using the sample.

• I really doubt that "standard error" is a "common [conventional, non-statistical] word" with a special statistical meaning differing from other uses of that word (phrase, really). Ditto for "normalization" and "standard deviation." – whuber Dec 30 '13 at 5:20
• Maybe not "normalization," but "normal" is a good point, and so would be "standardize," which is also used to describe tests intended to establish national standards (e.g., in education, such as in the USA after No Child Left Behind). I agree that "standard deviation" is unlikely to cause confusion, though "deviation" by itself in common parlance may be more likely to carry a negative connotation (especially as a synonym for "deviance"). – Nick Stauner Dec 30 '13 at 9:59
• Here is another way to distinguish SD and SEM.Standard deviation quantifies variation or scatter. A standard error quantifies precision of a computed value. – Harvey Motulsky Dec 31 '13 at 2:09
• @HarveyMotulsky I think the best way is think of an asteroid (irregular shape). What is the center of mass of the asteroid? It is the point that is equidistant from all other points. That's the mean. What is the standard deviation? It is the "average" distance of each point from the center, a measure of size. What is the SEM? It tells you how sure you are about the location of the center of the asteroid. – Flask Dec 31 '13 at 8:03
• I find saying that standard error is the standard deviation calculated using the "sample" a bit unfortunate. That would be the square root of the sample variance for me, while the standard error is the standard deviation of a test statistic. Also, from the above terms only "normal" seems really common. But I guess that's normal... – means-to-meaning Jan 6 '14 at 0:45

"Parametric" versus "Non-Parametric": categories of tests that either require "Normal" or "not Normal" data. Parametric tests are preferred to non-parametric.

Common tests: T-test (paired), Mann-Whitney U, ANOVA, Anderson-Darling, etc.

Other terms include "significant". This is a measure of if the data indicates your hypothesis to be valid or not. When you test your hypothesis to a certain degree of likelihood (normally 95%), a "p-value" of less than 0.05 would indicate that you would reject your "null hypothesis" (i.e. data sets are not different) and accept your "alternative hypothesis" (i.e. data sets are different).

Skewed in statistics implies asymmetric in distribution.

In ordinary language, and even within science, skewed is often used (and increasingly?) to mean what statistical people would usually called biased, as in "Results for mean height are skewed by including so many basketball players".

Estimate -- In statistics it is the result of a calculation. For example, the sample mean is an estimate of the population mean, and the confidence interval of a mean is an interval estimate of the population mean. These are both results of exact calculations. The "estimation" is a precise generalization of trying to make an inference about a population from data in a sample.

In ordinary use, the word estimate means an informed guess or hunch, or the result of an approximate calculation.

Likelihood - in ordinary parlance the synonym of probability, but in statistics having a particular inverse relation to probability, in that, for any parameter set $\theta$ and data set $X$, $\mathcal{L}(\theta|X)=\Pr(X|\theta)$.

Representative - has a number of sometimes conflicting meanings in both everyday and scientific parlance. Refer to Kruskal & Mosteller 1979a, 1979b, 1979c and 1980. Most statisticians I know would consider a sample representative if it was sampled with known probability; most laypeople I know would consider it representative if the marginal distributions were akin to the population.

• Sample: while in statistics this refers to a set of cases, in many other disciplines a sample is one physical specimen. Of course, sample size is also ambiguous, refering either to the number of cases in the statistical sample or the physical size (mass, volume, ...) of the specimen.

• Sensitivity: for medical diagnostics the fraction of diseased cases that is recognized by the test. In analytical chemistry: the slope of the calibration curve (see below).

• Specificity: in medical diagnostics the fraction of non-disease cases this correctly recognized by the test. In analytical chemistry, a method is specific if there are no cross-sensitivities.

• Calibration: actually, two meanings are listed already for statistics in the Wiki article. In chemistry and physics, the reverse regression meaning is the usual one. Confusion arises, though:

• In chemometrics, (forward) calibration models the measured signal $I$ dependent on the concentration $c$: $I = f (c)$. Prediction then solves for concentration $c$: $c = f^{-1} (I)$. Inverse calibration models $c = f (I)$. Thus, the forward model agrees with the causality (concentration of analyte causes signal, not the other way round), but the inverse models the direction that is used for the predictions.
(In practice, it is often possible to say that the error on $c$ or the error on $I$ is much larger than the other, and the appropriate modeling direction is/should be chosen from that)
• I've seen plots of predicted probability over true probability called "calibration plots" (stats people). In analytical chemistry, the corresponding calibration plot would be predicted probability over measured signal (usually some other unit). The plot of predicted over true dependent variable would usually be called recovery curve.
• Validation set: here I'd like to draw the attention to a potentially confusion use of terms which I think already arises within the different statistics-related fields, even though I again contrast . In the context of nested/double validation or optimization vs. validation/testing, one line of terminology splits training - validation - test and uses the "validation" set for optimization of hyperparameters.
E.g. in the Elements of Statistical Learning, p. 222 in the 2nd ed.:

... divide the dataset into three parts: a training set, a validation set, and a test set. The training set is used to fit the models; the validation set is used to estimate prediction error for model selection; the test set is used for assessment of the generalization error of the final chosen model.

In contrast, e.g. in analytical chemistry validation is the procedure that demonstrates that the model (actually, the assessment of the final model is only part of the validation of an analytical method) works well for the application, and measures its performance, see e.g. John K. Taylor: Validation of analytical methods, Analytical Chemistry 1983 55 (6), 600A-608A or guidelines by institutions like the FDA. This would be "testing" in the other line of terminology, where the "validation" is actually used for optimization.
The crucial difference is, that the "optimization-validation" results are to be used to change (select) the model, whereas changes in a validated analytical method (including the data analytic model) mean that you have to revalidate (i.e. prove that the method still works as it is supposed to work).

If you happen to have to talk to chemists, a good reference of the analytical chemistry terminology is Danzer: Analytical Chemistry - Theoretical and Metrological Fundamentals, DOI 10.1007/b103950