Is Tony Abbott A Misogynist? A Statistical Analysis

[EDIT: Make sure you don’t miss Part II: Comments, Clarifications and Corrections for an update on the analysis.]

 

Like many Australians, I was dismayed to read that the newly elected Prime Minister of Australia, Tony Abbott, had appointed an incredibly male-heavy Ministry to the Parliament of Australia. Most news reports in the mainstream media, both at home and abroad, slammed the announcement by levelling a fairly routine string of sexist labels at our new head of government, the most common being “Misogynist”. However, I was a little surprised by the lack of any quantitative evidence suggesting that the appointments were based on sexism over, say, statistical chance, so I decided to do a rudimentary check myself. Below you’ll find the results of a basic statistical analysis to answer the question:

Is there a gender bias in Tony Abbott’s new Cabinet?

I should point out that this is hardly the first time Tony Abbott has been called this in his life. Throughout his political career, Abbott has regularly been called insensitive to gender equality and the concerns of women, as well as possessing views on gender issues more likely found among Australian males half a century ago. However, to me, none of those reports have been especially convincing, either. As a feminist as well as someone who strongly opposes a lot of Abbott’s policies (particularly with regard to climate change and refugee policy), I was looking forward to the opportunity to finally analyse some ‘hard’ data in coming to a conclusion about our new chief. After reading the initial reports that the new Cabinet contained only one woman out of 19 spots, I felt pretty confident. In the words of Australian of the Year Ita Buttrose, “You can’t have that kind of parliament in 2013. It’s unacceptable.”  How could the data suggest anything other than that the man is a raving chauvinistic pig?

However, it turns out that things are not so simple. For starters, the Australian media has a reputation for being (a) incredibly biased, and (b) terrible at statistics. First, a lot of reports link to the following graph, taken from the Australian Labor Party website:

The most obvious question that comes to my mind is: Why aren’t the values given as percentages? Of course, this doesn’t matter if all the cabinets are the same size…but a quick check shows that this is indeed not the case. For example, India’s cabinet (made up of ‘Union Members’) has 33 spots. My second concern was about the choice of countries, which seemed incredibly arbitrary. The ALP chose to compare Australia to such countries as Rwanda, Liberia and Egypt, but excluded the United Kingdom (our closest parliamentary sibling), most of the G20 countries, and in fact ALL of Europe! Show this graph to anyone with even the vaguest of quantitative training and they’ll start screaming “Data mining! Data mining!” before you can blink.

Comparing ourselves to other countries is a bit fishy in any case. If every country always did this, no women would ever have been elected to high office in any country, ever. No, what I really want to know is whether the election of one single female (Julie Bishop) to Abbott’s new Cabinet could have come about by chance, or whether it suggests deliberate sexist. To ensure that my own biases don’t interfere with the analysis, I established a threshold before I got into the numbers. In any sort of quantitative research, the standard measure is to be at least 95% confident of something in order to draw a conclusion (formally, ‘reject a hypothesis’). I therefore decided that Tony Abbott could be considered guilty of gender bias in his appointments if it could be shown that we could be 95% sure the male/female ratio did not come about by chance. To be perfectly clear, I decided beforehand (ex ante) the analysis would conclude that Tony Abbott’s appointments:

• were gender-biased if the chances of them being random were less than 5%; or
• were random, and the media reports should be condemned for factual inaccuracy, if the chances of them being random were greater than 10%; or
• could not convincingly be shown to be gender-biased if the chances were between 5% and 10%.

So let’s set up the analysis. Now, Abbott was of course elected Prime Minister before he chose his  own Cabinet, so we should exclude him from the list – the relevant statistic is then “One woman out of 18 spots”. Not all of the seats had been officially declared by the time the Cabinet was announced, but according to the Liberal Party website, Abbott had a total of 114 Members and Senators to choose from to fill these 17 spots. Of these candidates, 89 (78.1%) are male and 25 (21.9%) are female. (Note that this excludes the appointment of Bronwyn Bishop as the Speaker of the House of Representatives, so called “the most important position in Parliament” Australia’s premier newspaper The Australian. If she is excluded from the list, the percentage of female candidates falls slightly to 21.2%.)

Further, let’s assume that each female candidate is equally as qualified as each male candidate to serve in Cabinet. Now, this has been a contentious issue in the media, with a lot of the justifications given to the male-dominated appointments revolving around the issue of ‘merit’. Former Liberal Senator and Ambassador to Italy Amanda Vanstone is quoted as saying, “I’d rather have good government, than have more women in the cabinet for the sake of it.” However, let’s ignore merit arguments and focus on the numbers. From a statistical perspective, the question then becomes:

“Assuming all candidates are equally likely to be picked, what is the chance that Tony Abbott appointed no more than one woman (5.6%) to the Cabinet?”

First, note that if we take the ratio of females from the list of candidates and apply it directly to the 18 Cabinet positions, we would expect roughly four women to be appointed (0.219*18 = 3.95). However, we would expect exactly four women to be selected around 20% of the time. We can model the random likelihood of any number of women being selected by what is known as a ‘binomial distribution’. Basically, if Tony Abbott was to put all 114 candidates’ names into a hat and take out 18 at random, and repeat this 100 times, the graph below tells us how many times we would expect each possible gender division to occur.

Therefore, the chances of no more than one woman being appointed – that is, the probability of appointing zero or one woman – looks to be around 7%. Indeed, calculations bear this out (‘P’ stands for ‘Probability’ in what follows):

P(No more than one woman)

= P(0 women) + P(1 woman)

= (0.781)¹⁸ + 18*0.219*(0.781)¹⁷

= 0.012 + 0.059

= 0.07

= 7%

So the answer falls within 5% and 10%, leading us to conclude that the actual Cabinet appointments do not convincingly suggest gender bias.

Still, you might think that finding only a 7% chance that a Cabinet with one woman was randomly selected is still something to think about. This may be true, but taking into account a few other factors dilutes the strength of the result even further. Excluding the new Speaker of the House, Bronwyn Bishop, from the initial sample raises the probability of randomly selecting no more than one woman to 8%.

Furthermore, the one woman who did make it into Abbott’s Cabinet, Julie Bishop, has been appointed Deputy Leader of the Liberal Party as well as taking on the esteemed Minister for Foreign Affairs portfolio. Along with Warren Truss (Deputy Prime Minister) and Joe Hockey (Treasurer), she thus takes one of the three chief roles in Tony Abbott’s leadership team. One woman out of these three key positions is technically something of an overrepresentation, given the candidates available, and so our result weakens further if we weight the spots accordingly. For example, just for argument’s sake, assume that getting appointed to one of these roles is doubly as important as other positions in the Cabinet. That is, assume a woman earns one ‘point’ for each normal Cabinet position and two ‘points’ for one of these chief positions. Then the current Cabinet earns two points through its women (or woman, in this case). The chance of the Cabinet earning no more than two points with a random selection of the candidates is then a whopping 17%. Don’t be scared of the formulas…

P(No more than two points earned by women)

= P(0 points) + P(1 point) + P(2 points)

= (0.781)¹⁸ + 15*0.219*(0.791)¹⁷ + 15*7*(0.219)²*(0.781)¹⁵

= 0.01 + 0.05 + 0.11

= 0.17

= 17%

Even less convincingly, when I use this weighted approach in conjunction with excluding Bronwyn Bishop from the list of candidates, the chance that the current parliamentary Cabinet could occur randomly without gender bias rises to 18%. Statistically, such numbers mean we can basically rule out any sort of gender effect at all.

There are a couple of little caveats I’d like to point out before we jump to any conclusions. This very basic statistical analysis makes a lot of assumptions which may or may not be justified. For example, the men and women in our list of candidates may not be equally capable to serve in the Cabinet after all. For example, what if, all else being equal, older politicians are on average better suited to the Cabinet than younger politicians? This could be relevant because the male and female candidates’ average ages might be different. Judging from the photos on the Liberal Party website, it seems to me that the men are on average older than the women, but of course I should actually get the ages and then compute some sort of weighting scheme if I want to really work out the effect. My intuition tells me, however, that including this feature would produce less sexism in the results.

Secondly, my analysis assumes that Tony Abbott selected all Cabinet positions simultaneously. Of course, it’s more likely that he selected the most important positions first and then worked down the order. I’m not sure how this would change my results; intuitively it shouldn’t make much of a difference, except that Julie Bishop’s position again takes on a little more precedence.

Finally, I’ve assumed that Tony Abbott was essentially just given a list of elected candidates and told to choose a Cabinet. That is, I assume Tony Abbott had no say in selecting the Liberal Party nominees for the electoral seats, which may have led to the gender bias in the candidates in the first place. But that’s a topic for another project.

In the end, then (if you’ve managed to read this far), it does seem that the emotive journalistic style of the Australian media has again got something to answer for in its vilification of Tony Abbott on this issue. I’m not saying our new Prime Minister is taint-free on matters of gender policy – far from it, but my own opinions shouldn’t weigh into it. So here it is, finally: The bottom line, from a basic statistical analysis.

We cannot conclude there is any gender bias in Tony Abbott’s appointment of his Cabinet.