This is the fourth of six special TOK posts to directly assist students and teachers in appreciating vital nuances associated with each of the May 2021 Prescribed Titles. For each title, I will identify some initial key concepts and highlight some specific approaches to address them along with specific Ideas Roadshow’s IBDP Portal resources that can concretely assist in the development of a strong TOK essay for that particular title.

This piece discusses PT4: *“Statistics conceal as much as they reveal.” Discuss this claim with reference to two areas of knowledge.*

**Key Concepts:**

The claim in this title is a pretty strong one, and unlike some of those in other titles, represents a summary judgement that in my view is a lot harder to justify. But regardless of whether your knee-jerk impulse is to agree or disagree with it, clearly a key to successfully grappling with its implications involves coming to terms with the **subjective aspects of the acts of “concealment” and “revelation” that lie at the heart of the claim.** Statistics in themselves, of course, are merely objective mathematical expressions, but the very act of interpreting and presenting these expressions to others—expressed here by the words “conceal” and “reveal”— clearly has the potential to veer decidedly towards the subjective side of things in a way that could well involve an array of both inadvertent and deliberate errors.

The idea that fundamentally specious conclusions could be “dressed up” and somehow rendered more authoritative using deliberately skewed statistical arguments is hardly a new thought, and lies at the heart of Mark Twain’s oft-quoted remark that he attributed to Benjamin Disraeli:

There are three kinds of lies: lies, damned lies, and statistics.

So the first thing to recognize is simply that any statistical argument necessarily involves an *interpretation* of the mathematics, which will often bring in an array of subjective factors and judgements that we need to make explicit and question, ranging from which conclusions are valid to larger structural issues such as how the statistical study was initially designed.

That seems clear enough. But a quick glance at the title reveals that that is not, in fact, what it says. The claim is not that “interpreting statistical arguments invariably involve a certain degree of subjectivity” or even “there are times when statistics can be used to support a number of distinct, and even contradictory, conclusions”, but rather “statistics conceal as much as they reveal”.

To be able to justify such a claim, you not only have to explicitly tackle the thorny issues of what it means to “conceal” and “reveal” concepts related to statistics (which you have to do anyway if you decide to take on this title, and among other things, will likely involve an explicit mention of the concept of beginning an investigation without any initial convictions as to the outcome), but—even more problematically—you are forced to demonstrate that in *all* instances of statistics, and presumably for *any* conclusion that is based upon them, there is an equal amount of concealed or hidden information to somehow “counterbalance” what is alleged to be demonstrated by the statistics.

Once again, that seems a pretty hard position to maintain, and certainly not one I subscribe to. But that’s not the point of a TOK title, of course. I can’t just write: I disagree. I have to demonstrate exactly *why* I disagree in terms of what, specifically, I find objectionable about the claim.

**In this case, there appear to be two separate issues to tackle no matter what your final position is:**

- Discuss what exactly could be meant by the words “conceal” and “reveal” in terms of related concepts we’ve discussed above (interpretation, subjectivity, objectivity).

- Evaluate to what extent you agree, or disagree, with the claim that the amount of “concealment” and “revelation” is
*always*equivalent in statistical arguments, which I would argue is tantamount to declaring that statistical arguments can never give rise to objectively true statements.

In my view the best way to go about making your case is to invoke specific examples of statistical reasoning, highlighting associated interpretative (subjective) aspects together with more objective ones. In what follows, I’ll present several helpful resources from Ideas Roadshow’s IBDP Portal that involve explicit mention of statistical arguments and can be used to build an excellent essay.

Below we highlight a number of specific resource examples from *Ideas Roadshow’s IBDP Portal* to build a world-class TOK Essay for exclusive use at our subscribing schools.

Ideas Roadshow’s IBDP Portal is an IB-specific video and digital print database which offers a strong pedagogical framework where TOK is the backbone of interdisciplinarity throughout *all* resources. Visit our website for further details and to request a free, no-obligation trial (teachers & librarians only).

In *Divining the Date*, University of Michigan classicist Richard Janko reveals how he used statistical arguments to date an ancient manuscript by looking at the frequency of certain linguistic expressions, giving additional support to the notion that objectively verifiable conclusions can be deduced from careful, independent-minded statistical studies.

In *Circular Reasoning*, University of Oxford physicist Roger Penrose gives an explicit example of how a statistical argument that purports to give an account of “a random sky” wrongly incorporates pre-existing informations, although it’s worth emphasizing that he believes this to be a misinterpretation rather than an active attempt to promote an alternative scientific agenda.

In *Defining What You’re Looking For* and *Subjective Distortions*, award-winning violinmaker and acoustician Joseph Curtin relates his pioneering “double-blind” experiments to determine whether or not expert musicians can identify the sound of a Stradivari violin, presenting a compelling argument for how a rigorous statistical analysis could filter out many subjective biases commonly held throughout the world of professional musicians.

In *fMRI* and *Assessing Consciousness*, neuroscientists Kalanit Grill-Spector and Martin Monti demonstrate how contemporary brain-scanning experiments that involve explicit statistical algorithms can give rise to an array of well-grounded insights.

In *Autism and Vaccines*, UCL psychologist Uta Frith describes the various statistical arguments that went into establishing the conclusion that the development of autism was not causally connected to being vaccinated with the childhood vaccine for measles, mumps and rubella. I suggest that students investigate to what extent potentially “concealed” conclusions could be reduced by increasing the number of such studies and how, in general, the volume of studies impacts the statistics themselves.

In *Scientific Credibility*, business professor and environmentalist Andy Hoffman describes how, notwithstanding significant amounts of scepticism from those who are convinced that climate scientists are “concealing contradictory data”, he believes that at the end of the day most people will recognize the objective validity of their many statistical models.