Archive for the ‘statistics’ Category

Girls + Maths ≠ Boys

November 15, 2010

One of the most embarrassing things I have to admit to on a regular basis is that I struggle with maths. I struggle so badly that I suspect I have a learning disability, although I’ve never been diagnosed and am a bit reluctant to categorize my lack of maths skills as such, mainly because it doesn’t really affect my day to day life in the same way that – for example – dyslexia or ADHD affect people living with those conditions.

A recent study I read about in today’s Age has shown that Victorian girls are consistently outperformed by boys in maths at VCE level – in fact, boys achieve better results in all mathematics subjects offered. I can only speculate as to why boys are more successful than girls in these subjects, and I certainly believe the reasons are cultural and not biological or “evolutionary,” as many might argue.  But having completed my entire education in Victorian public schools, and being one of those students who ‘slipped through the cracks’ in every one of my maths classes, I can certainly see how anyone, whether a boy or a girl, might feel completely disinclined to try and learn maths if they constantly lag behind the rest of the class and never seem to be able to catch up.

From Prep to Year 11, I was one of those students who could not catch up. This is despite being reasonably good at everything else – I usually achieved excellent marks in English and aside from maths, I never seriously struggled with any other subjects. If I didn’t have the most coherent understanding of science, I had a keen interest in it and (secretly) loved going to science classes. Mind you, once the science got super mathsy, I lost the thread entirely. Thankyou, Year 10 chemistry!

This is what constantly confuses me about my maths skills – I was a decent student up until Year 11, and an excellent student by the end of Year 12, achieving marks that put me close to the top of my year. How can a student excel at every subject she takes, but not be able to solve basic maths problems? And even now, at the age of 24 and having graduated from uni?

My experience of maths classes in primary and high school was so depressing it still upsets me to think about it. I remember crying during a maths test in Grade 2 because everyone around me was finished and I was still stuck on the third sum. I remember being repeatedly humiliated in Grade 4 while playing a ridiculous game, which involved competing with another student to be the first to answer a sum in front of the class. I was always beaten. One year,when I was about eight or nine years old, I was shunted off to the remedial class with all of the kids who struggled with everything at school (reading, writing, maths, socializing). That might have been alright if it was just a remedial maths class, but it covered everything – I could read at a very high level, had little trouble socializing and could write coherently. I didn’t understand why I had to read books with one word printed on every page when I had a ‘chapter book’ in my schoolbag. Adding insult to injury was the fact that the maths component of those remedial classes made no impact on my maths skills. I continued to struggle in the regular classroom.

Once I got to high school, I was fairly used to being slow at maths, and adopted a sullen, ‘quitter’ style attitude that was apt considering I was a teen. I continued to flounder at the bottom of the maths class, although I compensated by frequently talking back to the teacher and openly laughing at him when he came to school with an eyepatch, after what I can only assume was a cataract operation. Then he got sick and was replaced by a teacher who is now a convicted paedophile. Awesome.

In Year 10, something bizarre happened and I was put in the advanced maths class with all the girls who were good at it. I can only assume that I was placed there because I hung out with girls who were good at maths, or because I was good at everything else and they just assumed my maths marks were an anomaly. Whatever the reason, my teacher soon realized that placing me in the advanced class was a mistake, and I got relocated to the simple maths class. I still couldn’t do the work.

I try to avoid apportioning blame to schools and teachers when students underperform, or have behavioural or social problems. Unfortunately, I don’t think there is any other explanation in my instance. Half of my issues with maths stem from the way I was taught – not through discussion, practical and collective problem solving or logical analysis – but by opening a book full of numbers and symbols that meant nothing to me, and were not adequately explained in the book or by the teacher, unless you count a rehash of the same phenomenon with more bewildering numbers and symbols. If it wasn’t the textbook, it was the teacher who drew some graphs and/or triangles on the whiteboard, with the best explanation they could manage in five minutes, then problem solving from the textbook. And if it wasn’t the teacher trying her best with limited time and resources, it was my best friend writing solutions on her eraser and throwing it at me when I was nearly having a break down on the other side of the table during a test.

Once, my Year 10 maths teacher held my hand before she handed back an exam that I’d failed. I guess she felt sorry for me because she knew that I just didn’t get it, but also knew that I wasn’t stupid. This particular teacher did try really hard to help me, but to no avail – I gave up on maths after Year 11. As well intentioned as she was – and she really gave me a lot of her time – my problems were so far advanced by that stage that honestly, I needed to start again from the beginning.

Had teaching methods been more flexible and constructive when I was in primary school, rather than being based on exclusion and humiliation if you made a mistake, and had my maths teachers given a crap before Year 10, perhaps maths wouldn’t be such an issue for me now. I have no doubt that I was a ‘problem child’ with ‘special needs’ when it came to maths. I accept that I will never be as skilled with numbers and logic problems as I am with words and analysis. But it would be nice not to feel so ashamed when I can’t add up a bill in my head, or work out whether the change I’ve been given in the milk bar is correct. The culture of maths education needs to change if students with the same problems as me are to be given a chance at understanding the very basics, and it’s this same culture that needs to be adjusted if the outcomes of boys and girls are to be equalized at VCE level.

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Some plots of recent changes in birth rates

October 25, 2010

Below I’ve presented some time-series plots of recent changes in fertility rates in Australia. The age-specific rate for a single year gives the number of live births per 1000 females in the specified age bracket. The total fertility rate provides an estimate of lifetime births per woman, based on the sum of age-specific birth rates. I’ve thrown in recent changes in the crude marriage rate for good measure.

Since exponential growth in real capital values depends on a corresponding expansion of either the workforce or labour productivity (with the latter historically dependent on access to high-EROI fuels), these plots tell us something about the likely fate of industrial capitalism.

The changing household consumption bundle

October 21, 2010

In any given time period, an average member of Australia’s employed population buys such-and-such amount of food, clothing, shelter, TVs, Hollywood movies, football matches, medical care etc.

Has this consumption vector changed much over recent decades?

The figures below show the proportion of household expenditure accounted for by various categories of goods and services, and how these proportions changed between 1984 and 2004.

What we see is contrary to the popular, media-fuelled view of affluenza and luxury fever.

The largest relative growth came in categories of spending like household services and operation (phone calls, childcare, housekeeping, cleaning, gardening), housing costs (rent, interest repayments, rates, etc.) and miscellaneous (mostly education fees).

Most new spending was not on items like household furnishings, recreation or personal care (toiletries and cosmetics).

But this is a bit deceptive. It says more about changes in relative prices than the physical volume of items purchased.

The relative price of “goods” to “services” (a crude distinction, it’s true) has fallen over the past 30 years.

Medical practitioners’ fees, for example, increased far more during the period under consideration than did most durable goods. The per-unit cost of components found in electronic equipment (TVs, mobile phones, personal computers) declined due to technical advances.

And of course the average Australian household did not buy fewer shirts, dresses or shoes than it had twenty years earlier. But prices in the textiles and clothing industry barely increased in this time.

Hence the grain of truth in the otherwise fantastic claims of Clive Hamilton, prominent “public intellectual” and one-time Greens candidate:

Average households today are filled with big-screen TVs and DVDs… [We] see backyards dotted with swimming pools. It is nothing for an average parent to spend $1000 on a present for a child or to buy them a personal mobile phone. Ordinary families happily shell out $40,000 for a four-wheel drive play-thing and gamble away a few thousand dollars each year merely for entertainment.

But this is not because, as Hamilton claims, “modern consumers no longer consume the ‘utility’ of goods and services: they consume their symbolic meanings.”

Instead it’s simple technological innovation, working through the substitution effect, that increases demand for certain goods, transforming them “from luxuries to necessities“.

Productivity gains reduce the number of labour hours required to produce many items, lowering their unit price. They can thus be bought at higher volumes and in larger sizes. (Service products are, arguably, less susceptible to technical advances, which may help to explain the recent movement in relative prices.)

Consider some of the major consumer goods (CD, CD-ROM, DVD, MiniDisk, Blu-ray) developed over the past 35 years. These are some of Hamilton’s prime examples of “items that have been transformed from luxuries to necessities in most Australian homes.”

But such products were not developed in response to consumer demand, let alone “ever-rising aspirations in pursuit of lifestyles that would give us an identity.” Consumers didn’t grow tired of the gramophone record and demand something new.

On the contrary, consumer demand was created by Philips, Sony, Pioneer and MCA to meet a technology – Laserdisc – that had been developed in the late 1970s for another purpose: home video. Of course, VHS cassettes proved more successful. To recoup their investment in Laserdisc, these companies created another mass market for the technology: “compact disc”.

This meant placing long-term orders for disc-pressing machinery, laser diodes, and all the intermediate inputs necessary for different stages of production; agreements with record companies to ensure that audio recordings would be released in the right format; and finally the advertising and distribution networks to ensure the product would be bought once it had been launched.

From this beginning followed successive innovations in the production of optical-disc products, similar to those in computing, which increased storage capacity to the extent that a single disc can now hold more than a terabyte of data.

This tendency for technical innovation to allow more efficient delivery of basic needs is a  200-year old feature of industrial capitalism. If the product contributes to the employed population’s consumption bundle, it makes labour cheaper to employ (after nineteenth-century cotton mills made workers’ clothing cheaper, the same real wage, in all industries, could henceforth be met with less money).

It also generates, as Hamilton isn’t the first to point out, the profusion of “non-basic needs”, a “failure to distinguish between what we want and what we need”. (Even though, last anyone heard, Hamilton had declared that the Great Recession meant “the era of affluenza is over”, aggregate demand is in fact sustained more than ever by growth in household debt).

The cause of this cornucopia isn’t the spiritually empty “materialism” of the working population,  and its solution isn’t “downshifting” (“rejecting the values of consumer society”).

The culprit is both mundane and more formidable. It is an invariant structural feature of capitalism: improvements in labour productivity, driven by competition and the search for innovator profit.

As Hamilton makes clear, “growth fetishism”, and its consequent effect on the consumption bundle of the working population, has us on a path to biospheric disaster. But the solution to this social problem isn’t the taking of thought, any more than a remedy for capitalism’s ecocidal, grow-or-die dynamic is the election of Greens members to parliament, or Australia’s “easing back the immigration tap“.

If you’re so smart, why ain’cha rich?

September 22, 2010

If we take a random individual from the population of Australian taxpayers, what’s the probability that her personal income will fall somewhere within the range $20 000-$30 000, or between $120 000-$130 000?

Consider this an inversion of the previous post, in which we used published ATO statistics to examine the income share of various fractiles.

The columns below show the percentage of people whose annual incomes fall within each interval. The probabilities of course sum to unity (100%).

As we can see, individuals cluster within the interval $20 000-$40 000, with the number of taxpayers in each interval declining sharply thereafter as we move upwards along the income scale.  A small number of people receive a huge income.

Income distributions in the United States, Japan, the United Kingdom and Italy closely approximate this Australian pattern.

This is an interesting result. For all their similarities, these five countries differ greatly in labour-market regulation, industry composition, policy settings, degree of ‘social capital’ and spread of ‘human capital.’

Perhaps such details are not, after all, decisive factors in the determination of a country’s income spread.

Indeed there’s good reason to think that this broad pattern of inequality  in which many individuals end up with little income, and very few individuals wind up with a huge income  is a universal feature of market economies, and emerges wherever there is monetary trade by a large number of private agents (and a fortiori whenever a small class of property owners can hire the capacity to labour of those without productive assets).

Ian Wright’s simulation of a market economy involves an agent-based model in which zero-intelligence actors are initially given an equal endowment of resources, then partitioned into classes (employer, employee and unemployed) and led to interact in product and labour markets according to a few basic decision rules.

Just like a real market economy, there are local, micro-level interactions of agents, in which goods and services are exchanged for money. And, just like real market economies, the invisible hand produces macro-level regularities: patterns of income distribution etc.

As in the Australian data shown above, the simulation sees many agents end up with little income, and a small number wind up with a huge income.

Of course, the rich don’t owe their wealth to intelligence or effort (recall that these are zero-intelligence agents, without “strategies” or choice functions, who select a course of action by choosing randomly from a probability distribution).

Merely by the working of chance, a lot of money is bound to end up in the hands of a few.

What’s the upshot of this?

  1. Wherever a large body of private agents (individuals, firms) engages in monetary trade, a highly unequal income distribution is likely to result. This distribution may take a variety of forms (lognormal, power-law, exponential etc.), but its basic shape holds for all reasonable parameter values.
  2. The properties of this income distribution do not arise from individuals possessing unequal endowments of internal talents and capacities (intelligence, responsibility, propensity for hard work). Even with a uniform distribution of initial resources, random interactions and zero-intelligence agents, we end up with a few rich people and large number of low-income people.
  3. So long as market exchange is maintained, inequality of outcome will survive those measures imposing “equality of opportunity”, or “benevolent” welfare and tax policies.
  4. Quotas for disadvantaged groups  e.g. women or ethnic minorities  may increase the “diversity” of the upper strata (through, for example, preferential admission to elite collegiate programmes). But given the essential fixity of the income distribution, the shuffling of social positions is a zero-sum game. The granting of salvation to a special few of the reprobate does not increase the total number of elect; and merely consigns others to damnation in their place.

For left-wing radicals, the implications of this are obvious.

But centrist liberals, too, have cause for thought. Most of them, taking their lead from Ronald Dworkin, incline sympathetically towards a kind of luck egalitarianism. This position holds that inequality arising from unchosen circumstances  as opposed to that inequality which is deserved or for which agents are responsible  is unjust.

Thus Dworkin says:

[Unfair] differences are those traceable to genetic luck, to talents that make some people prosperous but are denied to others… [A just society aims to] neutralize the effects of differential talents… individuals should be relieved of responsibility for those unfortunate features of their situation that are brute bad luck, but not from those that should be seen as flowing from their choices.

John Rawls says that ‘those with similar abilities and skills should have similar life chances.’

But, as we have seen, market societies allocate stupendous wealth, not merely to the innately talented (like Wilt Chamberlain), but also to lucky morons.

Can liberal centrists rise to the challenge of justifying such a distributional order? The example of Dworkin suggests that they can.

In doing so, however, he and his acolytes commit a fallacy of composition. For the vagaries of market exchange and private property, as we have seen, entail the emergence of macro-social inequality even in the presence of identical agents with the same initial endowment of talents and capabilities.

‘Unfortunate features’ of capitalist society must therefore flow not from individual ‘choices’, but from a kind of ‘brute bad luck’: the basic institutions of society.

The young Marx, following the Classical economists, was on solider ground in suggesting that, on a social level, personal merit does not give rise to wealth ex ante. Rather, virtuous attributes intelligence, good taste, attractiveness are retrospectively ascribed to the wealthy because of their wealth.

Here Marx described the ‘power of money’, which Adam Smith had said conferred on its owners the ‘power to command’ labour and the products of labour:

That which is for me through the medium of money  that for which I can pay (i.e., which money can buy)  that am I myself, the possessor of the money. The extent of the power of money is the extent of my power. Money’s properties are my  the possessor’s  properties and essential powers.

Thus, what I am and am capable of is by no means determined by my individuality.

am ugly, but I can buy for myself the most beautiful of women. Therefore I am not ugly, for the effect of ugliness — its deterrent power  is nullified by money.

I, according to my individual characteristics, am lame, but money furnishes me with twenty-four feet. Therefore I am not lame.

I am bad, dishonest, unscrupulous, stupid; but money is honoured, and hence its possessor. Money is the supreme good, therefore its possessor is good. Money, besides, saves me the trouble of being dishonest: I am therefore presumed honest.

I am brainless, but money is the real brain of all things and how then should its possessor be brainless? Besides, he can buy clever people for himself, and is he who has power over the clever not more clever than the clever?

Do not I, who thanks to money am capable of all that the human heart longs for, possess all human capacities? Does not my money, therefore, transform all my incapacities into their contrary?

Homophobia and sport

May 23, 2010

If you believe newspaper reporting,

new research by Victoria University shows that gay men believe Australian rules is the most hostile football code, with many saying they feel too threatened to play the game….The Victoria University research, based on a survey of 308 people and to be published next month, found the most common sports that gay men would like to play but did not, or felt they could not, were Australian rules football (45 per cent), rugby (17.5 per cent) and soccer (10 per cent).

Really? Australian-rules football seems greatly more hostile to homosexual participants than rugby? This made me suspicious, and eager to check out the report, “Come Out to Play: the Sports experiences of Lesbian, Gay, Bisexual and Transgender (LGBT) people in Victoria“. The figures described above in the newspaper, given on page 66 of the report, might catch the eye. But they don’t represent a useful score of perceived hostility, such as the proportion of people who feel they can’t play a particular sport, conditional on them wanting to play that sport. Instead they represent the proportion of people who want to play a particular sport, conditional on them feeling they can’t play a sport. This isn’t so much an index of homophobia as a popularity score! Gay men don’t ‘believe Australian rules is the most hostile football code’ – at least there’s no evidence to say so.

Actually there’s not much evidence for anything in the report, in the sense of unbiased estimates. Intuitively many of the figures make sense, and the dreadful anecdotes of homophobia and abuse deserve weight. But the actual numbers mean little. The survey data comes from a questionnaire hosted online at Demographix, with respondents recruited through both advertising and snowball sampling (researchers forwarded emails to people on their contacts list, who then referred them to friends, and so on). When the target population is hidden or marginalised, of course, this kind of sampling may be unavoidable. But the authors of ‘Come Out to Play’ don’t even acknowledge it, or seem very fussed with what one of them calls ‘rigid quantitative methodologies’. Figures 12 and 15, for example, are completely trivial.

An important issue deserves a bit better than this. Vague impressions and anecdotes are best left to the likes of Jason Akermanis.

Raise your hand if you love statistics and want to do a survey

April 8, 2010

‘I keep saying the sexy job in the next ten years will be statisticians. People think I’m joking, but who would’ve guessed that computer engineers would’ve been the sexy job of the 1990s?’ That was Hal Varian last year in the McKinsey Quarterly.

It’s been hard to miss this kind of talk lately. A few weeks ago The Economist chimed in with a ‘special report’ on ‘the data-centred economy’.

Unfortunately, one prominent growth sector seems to involve hucksters selling meaningless information to anyone dumb, cynical or rich enough to buy. This can be done in several ways, but a few are especially common:

  • Claiming to detect an effect where the coefficient isn’t statistically significant: the observed result could have occurred by chance rather than genuine association (for example, evolutionary psychologist Satoshi Kanazawa purporting to show that ‘beautiful parents have more daughters’ while tall people and engineers have more sons).
  • Failing to control for potential confounds, and thus finding spurious correlations. As previously discussed here, this one is beloved of blowhard journalists who, for example, tie crime figures to ethnicity (look how Sudanese offenders are over-represented! look how Indians are disproportionately victims!) without adjusting for relevant variables like age, gender, occupation and locality.
  • Selection bias, where the sample drawn is unrepresentative of the target population, with some people more likely to be included than others. If you see market research in the popular media, it’s almost guaranteed to have this flaw. Respondents to online surveys usually self-select. They may choose to participate because they have some axe to grind, while people without strong opinions – or older people who don’t use the web – may not bother taking part. 

It’s always been easy to sell equivocal results to a credulous media, which is eager to hype and sensationalise quantitative findings if they involve sex, gender or race. But, increasingly, public and private-sector managers seem willing to pay for noise presented as signal. Consider this week’s report in Melbourne newspaper The Age. Apparently ‘research done for the government’ shows residents of the inner-western suburbs are worried about a proposed freeway tunnel. The research referred to seems to be a local community survey hosted online at SurveyMonkey. Fill it out, if you like; it takes only 15 minutes of your time, and is almost completely worthless. And – hey! – your tax dollars, by way of Sweeney Research, have already paid for it.

Cooking the schoolbooks

January 30, 2010

The Federal Government’s My School website, which shows the NAPLAN results of Australian schools (‘to allow greater transparency and accountability for the performance of schools’), went online on Thursday.

It’s transparently a ploy to win public support for so-called performance-based pay tied to purported ‘productivity’ differentials between teachers.

Putting that aside, though, it’s worthwhile taking a quick look at the methodology used.

It’s widely known that much of the variance in education test results is explained by things like household income and parents’ education levels. These variables are clearly beyond the control of our humble educational service providers, so raw test results don’t accurately reflect their competence or effort.

To allow ‘meaningful and fair comparison to be made across schools’,  each school is assigned a scalar value reflecting its ‘socio-educational advantage’, then grouped with schools of similar values.

Ideally, then, a wealthy private school like Scotch College compares test results with others of its kind, while poorer outer-suburban or non-metropolitan schools have their own cohort, within which comparisons can be made.

All fixed then? Not really.

My School supposedly allows readers to see how the various schools performed on NAPLAN, controlling for their respective students’ socioeducational advantage. But the Index of Community of Socio-Educational Advantage (ICSEA) shows how each school performed controlling instead for the socioeconomic index of the locality from which the students were drawn.

Unless schools draw students randomly from a local population – and the existence of selective government, self-selective private and denominational schools prevents exactly this – these are not the same thing. Scotch College doesn’t enrol a random selection of students from the richest suburbs: it takes the richest kids, while the least-wealthy kids in those rich suburbs disproportionately go the local public school.

My School assumes that each student possesses the demographic characteristics of the average household in their locality. But the process by which parents send their kids to some schools and not others is not random, so there’s a difference between the average characteristics of an area and the average characteristics of students from an area who might go to a certain school.

The flaw becomes most obvious when considering selective entry schools, like Mac.Robertson Girls or Melbourne High, which take the cream of students from all over metropolitan Melbourne.

Behind such official lapses lay the policy goals for ‘reforming’ education provision shared by the state elite.

This project, now pursued by the federal Labor government, was laid out candidly by economist Joshua Gans and Stephen King back in 2004.

Finishing the Job meant supplementing the Labor government’s privatization of state assets between 1983 and 1996 with a new wave of market-based reforms to areas of service provision like education and health:

[There] seems little reason why funding for schools should be distinguished on the basis of ownership. This does not meant that privately-owned and government-owned schools all need to operate in an identical manner. Rather it means that government funding for these schools should be on a symmetric basis, subject to any practical limitations.

Next, consider management. Government-owned schools have traditionally been subject to highly centralised management procedures. While there has been a move to decentralise school management in most states in the past few years, there is no reason why this cannot go further. Recognising that school communities are providing club goods for individual school members, appropriate management will reflect the tastes and preferences of those school members subject to any minimum government requirements.

[…]

The starting point for rethinking education funding is a universal per student allowance. In other words every child of school age would be associated with an appropriate level of funding. The school attended by a child would receive the allowance associated with that child. The payment of the allowance would not be based on either the ownership or the management of the school, subject to the school satisfying the relevant minimum requirements set down by the government. Schools would need to be registered to receive the allowance and would be monitored to guarantee that minimum requirements were being met. However beyond these minimum requirements diversity among schools could be encouraged, particularly in urban areas and at the high school level where each child potentially has a number of relevant and accessible schools.

The benefits of such an approach have been shown by overseas experience. By both freeing up schools and providing competition between schools, such an approach can lead to better educational outcomes that are more appropriate and tailored to students’ individual needs than can be achieved through a more centralised system.

[…]

[The] proposed allowance is associated with further reform of school management and would not discriminate between the private and public systems.

[…]

[An] area based voucher system raises the prospect that richer families might choose to move to poorer areas in order to gain a higher educational subsidy. However to the extent that such a movement occurred this may have good social outcomes.

[A] universal allowance provides families with ‘ownership’ of their children’s education.

‘Race crime’, newspapers and inference

January 13, 2010

From the letters page of Tuesday’s Age newspaper:

Statements by government ministers and police that there is no evidence racism was a factor in Nitin Garg’s murder are to our discredit. India sees through it and is offended. If the spokespeople had been more honest, they would have added there is no evidence that the attack was not racist.

[…]

John Murray, former vice-president, Australia-India Society, Hawthorn

Coincidentally, Ray Solomonoff died last month. I’m yet to see solid evidence that John Murray (or Fairfax columnists Gerard Henderson and Miranda Devine) didn’t kill him.

Whenever fallacious arguments are judged fit for newspaper publication, we mustremember to blame their appearance on cynicism rather than stupidity.

It’s not that the poor editors, short on staff and brainpower, can’t detect faulty reasoning. If that were true, their choices would exhibit no systematic error, and over enough time we’d observe no more than the expected amount of rubbish.

Is that what we see? No, we consistently see regular opinion columns granted to provocateurs, contrarians and Catherine Deveny. It’s no accident. The well-known commercial logic is outrage -> page views -> advertising revenue.

The representation of Nitin Garg’s murder as a story about ‘racist attacks against Indian students’, with little evidence, seems to fit this pattern. Just like ‘French sex murder‘, ‘Italy sex murder‘ and ‘rail chaos‘, it is an opportunistic, rather than stupid, bid for our attention.

But this time there’s more to it.

When trying to explain the string of violent assaults and thefts that’s been committed, over the past few months, across Melbourne against young men of South Asian background, we’re performing a search in hypothesis space. The space is vast: there are many possible reasons for this conjunction of events.

In choosing ‘race-hate crime’ as the preferred hypothesis, we pick a single point in that space. I think there’s a good reason we home in on the solution region marked ‘race’  – and it’s not due to overwhelming evidence.

First, we share an unfortunate tendency to attribute the behaviour of other people to some personal characteristic or disposition, rather than the situation those people are in. To an observer, the ethnicity or group identity of an assault victim (or occupation/clothing of a rape victim) may stand out more than, say, that person’s travelling at night through a park, in a taxi or via public transport.

Second, skin colour, for better or worse, is a very salient phenotypic trait. It’s one of the first things we notice about people. Because skin is by far our largest organ, and its pigmentation exhibits a lot of variation across groups of people, it’s probably the most visible distinguishing personal characteristic. So we naturally use it as a criterion of group classification, far more than e.g. height or eye colour. (Though note many Australians’ discomfort and confusion over whether South Asians are to be considered ‘black’ or ‘Asian’.)

With the victims now defined as ‘Indian students’, a motive is readily imputed to their attackers: evidently, racial hatred.

We’re thus led very quickly, by a few cognitive biases (and official encouragement), to privilege unduly (i.e. without sufficient evidence) a certain hypothesis about these violent attacks.

Sure, it could well be true that anti-Indian sentiment is behind the violence, but without evidence there’s no reason to grant the hypothesis any particular attention. That it does testifies to the hold of racial taxonomies on our thinking.

Some of this is induced by media treatment: if we keep hearing about racial violence, we tend to think it more probable, the same way we can’t help but overestimate the frequency of highly reported occurences like homicides, plane crashes and terrorist attacks.

Newspapers thus prompt our irrationality, while having an interest in provoking hysteria.

I leave open the possibility of whether racial violence could be caused by such reporting.

People like John Murray of Hawthorn are, no doubt, well-intentioned (I’m less sure about Gerard Henderson and Miranda Devine).

But their arguments are merely the inverse of talk about ‘ethnic crime’ and ‘ethnic gangs’ (terms which only apply to non-Anglo-Celts – ‘Aussies’ are not an ethnic group, you see) which sparks up any time someone of Lebanese or Vietnamese background gets in a fight.

Until suggested otherwise by the evidence, race shouldn’t be considered a salient factor in any crime or group of crimes.

The alternative leads us to innumerate hate-speech, like Andrew Bolt or Kevin Andrews claiming that Sudanese people are eight times more likely than others to commit crimes.