# 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.*

cabinets are not chosen at random. they are chosen by the PM. He deliberately chose a cabinet with one woman in it. How can you argue there’s no gender bias when it’s not a random exercise and is conducted very deliberately by one person?

Dave this is a great analysis. I didn’t understand any of the bits with numbers but I recognised some of the names of the footballers you mentioned. 😉

LHS

So if you take this approach to the UK cabinet what do you get?

Bob, the point is to compare the deliberate choices to what we would expect if things were random (a ‘random sampling’). Basically, the question can be rephrased as follows:

Assume that women are on average as equally capable as men to be in Cabinet – sometimes they might be better, sometimes they might be worse, but ON AVERAGE they are the same. Now, assume for a moment that we have an unbiased Prime Minister. From 100 different trials of picking the Cabinet, in how many would we expect no more than one woman to appear? If the answer is less than 5, we can say that our assumption about an unbiased Prime Minister is wrong, and so Tony Abbott is sexist in his appointments.

In the end, I get an answer of around 7, even when leaving out some of the other characteristics that might have worked in Abbott’s favour. That’s not good enough for me as a researcher to say that the Prime Minister showed a gender bias.

Locky:

Thanks; ironically, it looks like rugby league prop Glenn Lazarus (known as “The Brick”) will be elected to the Senate…

James:

I’m not totally clear on the UK system, particularly the current coalition, but going off Wikipedia and leaving the Prime Minister out, it seems that 4 out of 21 Cabinet Ministers are female and one out of the ten who apparently “also attend Cabinet” is a woman. That’s a higher percentage than in Australia, but without knowing the gender makeup of the candidates for Cabinet I can’t say anything about a deliberate gender bias. Perhaps if I get enthused enough, I might put a bit more work into this project, as it’s getting some attention around the traps.

It must be late and I am really really procrastinating over a paper- I actually read the entire way through your argument and calculations- I’m reminded of the following: For those who believe, no proof is necessary. For those who don’t believe, no proof is possible.” (Stuart Chase). – I’m in the camp of the true believer- Tony Abbot is a misogynist!

One wonders what is at play in Tony’s selection of his Cabinet. Surely a key issue is who among his colleagues voted for Tony when he had the leadership tussle with Turnbull. They would have been rewarded.

Next is who the Liberal Party officials support. These officials keep the Party machine oiled with money from Party donors. They are the link between business and politicians. They provide Tony with advice as to who as ministers and what policies will keep money flowing into Party coffers.

The Liberal Party draws its members principally from the Establishment. I don’t know the female to male ratio on the boards of large enterprises in Australia but I suspect that women are only a small percentage. Cabinet probably simply reflects that ratio.

Aside from the gender disparity, there is an age disparity. One political commentator, Peter van Onselen, writing in “The Australia” newspaper has consistently recommended that Liberal Party refresh its Ministery with young blood. It hasn’t happened. Tony’s first loyalty remains to those who keep him in power.

A not so minor point is that your probability calculations are done assuming replacement. However when picking ministers you can’t go back to the pot so you should perform the calculations for unordered selections without replacement. While this might seem a minor point when choosing from a relatively large pool, in this case your original calculation of 7% comes down to around 5.5%.

The other issue I would take with the analysis is that I would argue that Abbott exercised essentially no choice in picking Julie Bishop in the cabinet. Bishop has been deputy leader longer than Abbott has been leader and so Abbott should not get any credit for her inclusion as a female in cabinet. A similar argument can be easily made for Truss who had to be given a cabinet position. You could argue along similar lines for a few others, but if we say that Abbott was selecting 16 positions (Cabinet less Abbott, Bishop and Truss) without replacement and picked no additional women, the probability assuming random selection of the remaining candidates is 1.5%(!) – well below the 5% threshold.

You can generalise the question and say, well perhaps Abbott really had no say in the picks of Brandis, Joyce, and Hockey. Now he is down to only a selection of 13 positions. In that analysis the P(0) calculation is still only around 3.2%. In fact you have to reduce the number of discretionary positions to only eleven before P(0) = 5.2% > 5%. So for Abbott to not be a misogynist you have to argue that he only got a choice in selecting eleven of his 18 cabinet ministers.

An interesting analysis, but I would strongly dispute this statement:

“Statistically, such numbers mean we can basically rule out any sort of gender effect at all.”

No, all you have demonstrated is that this type of analysis cannot prove that a gender bias exists. It cannot prove that such gender bias does not exist, but that’s hardly surprising since we have only one Tony Abbott cabinet to examine. There just isn’t enough data to prove anything.

You also failed to consider the fact that according to the Liberal party charter the party VP must be a woman, this affirmative action measure was introduced by Sir R Menzies in the 1940s. It’s worth noting the one woman is senior cabinet was not “selected” as such with equal chance as equally qualified colleagues. Given members are not randomly selected, but consciously chosen, the one women chosen has benefitted from affirmative action & several women over looked have significant merit including a senior associate solicitor & have comparable levels of political experience – I maintain that 1 female senior cabinet member is testament to Abbott’s gender bias.

I read through your statistical analysis and had a great laugh at such an inane exercise. Rather than try to prove Abbott is a misogynist – which takes the focus off the issue – let’s ask the real question, ‘Why are women so under-represented in Abbott’s Cabinet and in Parliament?