The Most Meaningless Graph I’ve Ever Drawn

Below is the most pointless, meaningless and useless graph I’ve ever drawn in my life.

It plots the % No vote by electoral division on the vertical axis against the percentage of Indigenous residents in each electorate on the horizontal axis.

And by using Indigenous residents on the x-axis, I am overstating the number of Indigenous voters. I didn't get chance to extract the data for aged over 18, or deal with turnout issues, both of which reduce the percentage of Indigenous voters compared to residents.

On first drawing I included a trend line that came up with the ridiculous conclusion that the No vote would reach 100% when the Indigenous population reached 30% of the total. That's because most electorates have a tiny percentage of indigenous residents and there is a vast range of Yes/No results. Only 26 electorates have more than 5% Indigenous residents and only six have more than 10%. If you draw a trend line in this data, you are trying to explain a wide range of No% results against a much smaller range and low number for percentage Indigenous.

The only electorate with an indigenous population large enough to influence the outcome was Lingiari, which has a noticeably lower No%.

I keep hearing that "All electorates with an indigenous population above 5% voted No" as if this says something about indigenous voters. If Indigenous voters make up 5-10% of the population, how can it be responsible for a high No%?

If you argued that experience and proximity to Indigenous Australians influenced the voting patterns of the majority population who are not Indigenous you might be able to mount a case. But you can't draw a conclusion from electorate level data about how Indigenous electors voted because there are just not enough of them to explain the results.

On the chart, as you move from Franklin to Solomon to Kennedy, you get two five percentage point increases in the Indigenous population, but two 15 point increases in No%. If you make the ridiculous assumption that the extra Indigenous voters all voted No, that still leaves you trying to explain the other 10 percentage point increase in No%.

Drawing conclusions from the above chart is a classic case of incorrect statistical inference caused by 'ecological fallacy'. In comparing No% against Indigenous%, you are comparing properties of electorates with an enrolment of 120,000 with Indigenous population which in all but one electorate is under 18,000, and in over half of electorates is under 5,000.

Even if you get a strong relationship between these two variables, you can't automatically make inferences about how individual voters or sub-groups of voters behaved based on the aggregate properties of electorates.

And in this case we have almost no relationship between No% and Indigenous% so drawing conclusions about how Indigenous residents voted is frankly ludicrous.

If you drill down within electorates to voting patterns in communities with a high proportion of indigenous residents, you detect more information about how Indigenous voters in these communities voted. And the majority voted Yes. But even this is difficult to extrapolate to a broader Indigenous vote scattered in smaller proportions across the country.

So let's stop quoting No% figures for electorates with only 5% indigenous residents. The electorate results tell you nothing about how the small number of indigenous voters in those electorates voted.

PS - this is the sort of post that attracts cranky responses. I won't post such responses unless they have a real e-mail address. Go to Twitter if you want to be anonymous.

PPS - the views expressed in this post are entirely my own.

7 thoughts on “The Most Meaningless Graph I’ve Ever Drawn”

  1. Any chance the Australian Election Study or another reputable survey were/are collecting data around the referendum, and therefore that we might be able to do some properly robust analysis down the track?

    COMMENT: I’m not involved in the AES. I know they did a survey in relation to the 1999 Republic referendum. On The Voice I don’t know.

  2. I’ve seen opinion pieces which purported to compare electorates, and state how Chinese-Australians, or Indian-Australians, or Muslim-Australians, voted in the referendum. They strike me as just as meaningless as the various efforts in the media to use selected polling place results to state how the 500,000 Aboriginal-Australians on the electoral roll voted. Do you agree?

    COMMENT: I think using the electorate data for analysis is just hopeless because there just aren’t enough seats with significant concentrations of ethnic or religious groups. The polling place data is more useful, but it draws conclusions about Indigenous voters who live in mainly indigenous communities. It is less useful for a nationwide view of all Indigenous voters.

  3. Antony, a good analysis. The incorrect inference is being drawn by both yes and no proponents. I think that the polling about a week out from the election, given that it was very accurate this time around, would likely have been similarly accurate on the Indigenous vote, meaning that 60% or marginally less of the Indigenous voted Yes.

    COMMENT: I have my doubts there was any reliable polling about Indigenous voting intentions. There were enough problems getting Tasmania right.

  4. The argument appears to be on the lines that a significant indigenous population engenders NO voting among the non-indigenous electors. But are these electors voting against their neighbours or against a proposition that they see in nobody’s best interests.
    I’ve discovered that some Remote mobiles are now catering for non-indigenous rural communities. In O’Connor there were five Remote teams of which the first three had a substantially indigenous voting base. 483 electors with 49.0% voting YES, very different from Lingiari and Durack.

    COMMENT: I stated something similar to your first sentence in the post. That argument could be made for the electorates with higher Indigenous populations, but I’m not sure that’s what the advocates are saying.

    I’ve accumulated Mobiles from across the entire country and the Yes% is 65%. I’m sure something interesting can be done with the data once the roll mark-off to SA1s files are released.

  5. Antony
    I’m very surprised that with your excellent background in handling data you call this graph meaningless. I am a scientist and very used to data with a lot of variability or “noise” (living plants and animals are vet variable). Linguari is very obviously an “outlier” and something very different is happening in that electorate. If that is excluded from the analysis then a number of nonlinear equations would fit the data with a high level of statistical confidence. When you are using nonlinear equations the curve can only legitimstely be used within the data range you can never validly extrapolate outside that data range. I think the data for Australia (minus Linguari) definitely shows a strong effect of % indigenous voters with % No vote up to about 20% indigenous voters. Since %indigenous voters is so low, this says more about how the other voters in the electorate. I think that most electorates with higher % indigenous voters are in country electorates away from capital cities, so this might be the underlying reason. It would be interesting to break these results down by distance from capital cities

    COMMENT: I am sure you can fit a non-linear curve to that data, but what does it mean? That the No% is related to the square or the inverse log of the Indigenous%? Plus this is aggregate data. Maybe you can find a mathematical relationship between No% and Indigenous%, but you still can’t make an inference about how individuals vote.

    You also suggest dropping Lingiari, but it is the only electorate where the proportion of Indigenous voters is large enough to influence the result. The problem is that 80% of electorates are under 5% and there is a massive range of No% results in that area. How can such a tiny social variable have so large an impact on levels of No% for whole electorates? If the distribution had lots of measures between 20% and 60% you might have a variable with a measurable impact on the No%, but with Indigenous% it is just too low in most cases to explain the variance in No%.

    Such a distribution screams out to look at another Independent variable. You’ve suggested distance from capital city, but a social scientist would be much more inclined to look at party levels of support, education, income, age composition, etc of electorates. Having covered elections for over 30 years, the levels of No voting in electorates above 5% Indigenous look perfectly normal to me. Most of them can be explained with reference to levels of party support. For instance, Durack, Kennedy (KAP held) and Parkes are safe Coalition seats on a two-party preferred basis. Solomon and Lingiari are marginal Labor seats and Leichhardt marginal Liberal. There are many better ways to explain the range of No% across electorates than Indigenous%.

  6. Hi Antony
    Are there figures for how many people did not vote?

    COMMENT: On my estimate turnout will finish at about 86%. That’s down on 90% at the Federal election.

  7. Hi Antony
    Any updates on the number who didn’t vote?

    COMMENT: The EC’s turnout estimate is 87-89%, down from 90% at last year’s Federal election. That would correspond to around 2-2.5 million non-voters.

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