Statistics in high schools: Towards more accessible conceptions of statistical inference

(by Andrew Gelman)

C. Wild, M. Pfannkuch, M. Regan, and N. J. Horton have a long article. Here’s their abstract:

There is a compelling case, based on research in statistics education, for first courses in statistical inference to be underpinned by a staged development path. . . . We discuss the issues that are involved in formulating precursor versions of inference and then present some specific and highly visual proposals. These build on novel ways of experiencing sampling variation and have intuitive connections to the standard formal methods of making inferences in first university courses in statistics. Our proposal uses visual comparisons to enable the inferential step to be made without taking the eyes off relevant graphs of the data. . . . Our approach was devised for use in high schools but is also relevant to adult education and some introductory tertiary courses.

The article appears with many comments by discussants. Here’s what I wrote:

I agree that, wonderful as informal plots and data summaries are, we also should be teaching students formal statistical inference, which is a big part of what separates statistical thinking from mere intelligent commentary. I like the authors’ formulation that statistical inference

addresses a particular type of uncertainty, namely that caused by having data from random samples rather than having complete knowledge of entire populations, processes or distributions.

The authors write

we also need to start from a clear distinction between when we are playing the description game and when we are playing the inference game.

I would go one step further and get rid of the concept of ‘description’ entirely, for two reasons.

(a) Ultimately, we are almost always interested in inference. Catch-phrases such as ‘let the data speak’ and rhetoric about avoiding assumptions (not in the paper under discussion, but elsewhere in the statistics literature) can obscure the truth that we care about what is happening in the population; the sample we happen to select is just a means to this end.

(b) Description can often—always?—be reframed as inference. For example, we talk about the mean and standard deviation of the data, or the mean and standard deviation of the population. But the former can be presented simply as an estimate of the latter. I prefer to start with the idea of the population mean and standard deviation, then introduce the sample quantities as estimates.

Similarly, some textbooks first introduce linear regression as a data summary and then return to it later in the context of statistical inference. I prefer to . . . introduce the least squares estimate, not as a data summary, but as an estimate of an underlying pattern of interest.

In giving these comments, I am not trying to imply that my approach is the best way or even a good way to teach statistics. I have no evidence to back up my hunches on how to teach. But I would like to suggest the possibilities, because I think that statisticians are so stuck in a ‘description versus inference’ view of the world which can lead to difficulty in teaching and learning.

The article and many of the discussions are worth reading. (Check out what Sander Greenland has to say!)

We welcome your reactions here. Any comments you post at this forum will certainly be noticed by the authors of the article.

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6 Responses to “Statistics in high schools: Towards more accessible conceptions of statistical inference”


  1. 1 Kaiser April 12, 2011 at 3:56 am

    I’m still making my way through that LONG article and will post more detailed reactions later.
    I’m a bit bewildered that this great idea is being treated as a high-school problem. I’d argue that the approach of Wild, et. al. could be the path through which we teach the first college course too. There is ample evidence that college students have a tough time comprehending sampling distributions and inference concepts the way they are currently taught.
    I don’t know if “skipping description” is the right prescription but I agree with Andrew’s diagnosis. There is really no value in pure description without inference. In the business world, description is often called “directional” analysis as if it is an acceptable analysis, just less reliable than statistical (i.e. inferential) analysis. Directional analysis is our enemy.

  2. 2 The Statistics Forum April 13, 2011 at 1:25 am

    Kaiser:

    I have huge difficulties teaching sampling distributions. I still don’t know what to do about it. I don’t think I can really teach straight Bayes in an intro course. (I cover some Bayes, but as a method of combining prior info and data using a weighted average. I don’t do it using conditional probability.)

  3. 3 Kaiser April 13, 2011 at 9:57 pm

    Exactly, everyone gets mixed up between the sampling and population distributions. I think the issue is that the sampling distribution is a theoretical consequence, it’s imaginary and so it’s hard to grasp. I use an example with a small population so there is a finite number of possible samples.
    Somehow I think our materials must look alike. I also only do a simple Bayes example, pointing out prior v. posterior, and updating with data. Also, on regression, similar to your point above, I emphasize that the coefficients are subject to sampling variability, that regression also fits into the framework of trying to generalize samples to the population.

  4. 4 jimmy April 15, 2011 at 2:14 am

    andrew, thanks for pointing out this article and in particular sander greenland’s comments. i very much agree with his lamenting the relative neglect of nonrandom sources of uncertainty in statistics education. (maybe something to incorporate in the andrew gelman intro stats book!) however, looking over the greenland 2005 paper, i’d like to echo your comments, “accounting for bias in causal inference is hard work …” despite that, i do think the ideas are important to convey, because people take these results from standard methods, interval estimates and hypothesis tests, far too seriously.

  5. 5 Michael Lavine April 19, 2011 at 3:08 pm

    David Bornstein, in the New York times of April 18, http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach-math/, writes about a math education program that succeeds with one of the strategies described by Wild et al: breaking concepts down into smaller parts.

  6. 6 Kaiser April 28, 2011 at 12:26 pm

    Now that I have read the whole article, including the discussion, I have a question. Many discussants complained about the “unrealistic” nature of teaching students about the random sampling framework, preferring to expose students to self-selected biased non-independent samples of observational studies from the get-go.
    Can I ask what materials you use to teach such an intro stats class as I’m unaware of any textbooks at the introductory level that takes such a perspective?


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The Statistics Forum, brought to you by the American Statistical Association and CHANCE magazine, provides everyone the opportunity to participate in discussions about probability and statistics and their role in important and interesting topics.

The views expressed here are those of the individual authors and not necessarily those of the ASA, its officers, or its staff. The Statistics Forum is edited by Andrew Gelman.

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