We need to talk about statistics. Part 1.

 We need to talk about statistics. And I'm not going to start by saying, "I'm no expert" because statistics have found their way into the heart of our job and basic statistical literacy is part of being a professional. And they should be used honestly and usefully. But it's also our job to spot when they are being used dishonestly or destructively.

To start with, if someone says to you, "On average" then alarm bells should ring. In a country where some people are stinking rich and others on the breadline, it doesn't help to say that "on average" everyone is nicely off. And that's before you ask them if they meant mean, mode or median.

Here's an example of how averages can be misrepresented.

My naturally non systematic brain has labelled the axes the wrong way round.
Did anyone notice? Or were you being empathetic?

This is for illustrative purposes only. I have NOT found a way of measuring how much emotional aptitude red people and blue people have for hard maths. You can see that the distribution falls into a familiar curve. With not a lot of people who are very emotionally inept, and not a lot of people who are extremely emotionally apt. Most red people are pretty average. And most blue people are pretty average.

But there is a difference. On average on this hypothetical exemplar graph, red people are more emotionally apt than the blue people. How we explain this, is a different matter. Wouldn't it actually be more surprising if they were exactly the same? Just like people are amazed that one foot is bigger than the other. Wouldn't it be more surprising if they were EXACTLY the same size?

In fact, even with this difference in average, almost everybody is in the part where the curves overlap. So even where red people "on average" were more emotionally apt for hard maths, it would be wrong to state that, "In general red people are more emotionally apt for hard maths, with some exceptions of course." That is the exact opposite of what the graph shows. The graph shows that in general there isn't a difference between most red people and blue people.

In fact a whopping number of blue people are above the average red person. And a huge number of red people are below the average blue person.

If a social mobility tsar were to be pushing the idea that generally on average red people are more emotionally apt for hard maths than blue people, then they are either misusing statistics. Or they are making policy based on the tiny number of exceptions outside the purple area on the graph.

Which would seem to be the opposite of their brief.

But of course it isn't. Look carefully. They are not the tsar for equality or social justice. They are the tsar for social mobility. This is closely related to the current political orthodoxy of The Knowledge Curriculum. (Not to be confused with the Cognitive Science which it is using as a Trojan horse.) This political project claims to give pupils the knowledge they need in order to be inserted into the status quo. It is very careful to maintain society as it is, with its elitist structures. It is about offering well-prepared pupils to be selected by the gatekeepers of the status quo. It favours conformity over creativity. It pushes the works and voices of "the best". It wants to fill pupils with "knowledge" rather than letting them think or express themselves. It is not interested in pupils being able to make of themselves what they want. And it certainly doesn't want to entertain the idea that pupils could remake society.

When the mask slips, it is not about knowledge or evidence or social justice. It is about power, hegemony and orthodoxy.

I do have more to say about statistics, specifically in relation to GCSEs and what we are doing to our young people. But Mrs E is convinced that they will come for me and my job after this post, so we'll see...