July 10, 2014

Summaries of income

I don’t want to get into the general business of election fact-checking, but we have a Stat-of-the-Week  nomination for a statement that is (a) about a specifically statistical issue at the high-school level, and (b) unambiguously wrong.  From Richard Prebble’s “The Letter”:

 Cunliffe is basing Labour’s election campaign around the claim that inequality is growing. Fact check: inequality is falling and New Zealand remains a very equal country. The claim that around a quarter of a million children are in poverty is dubious, to say the very least. Cunliffe says households in poverty have less than 60 percent of the medium income after housing costs. If Bill Gates came to live in New Zealand, the medium income of the country would rise and, according to that logic, more children would be in poverty.

David Cunliffe, as you presumably know, talked about the median, not “medium”; the use of a fraction of median income as a relative poverty threshold is very common internationally. The reason for using the median is precisely that the median income of the country would not rise if a few billionaires were added to the population. The median, the income of the household in the middle of the income distribution, is very insensitive to changes in or additions of a few values. That’s what it’s for.

While I’m writing, I might as well mention the inequality statistics.  Mr Cunliffe isn’t making up his figures on children in poverty; they can be found in the 2014 Household Incomes Report from the Ministry of Social Development [update: that figure is 260000, which matches what The Letter reported was said, but the actual speech said 285000]. The report also gives trends in the Gini index of inequality and in the proportion of income spent on housing.  StatsNZ gives trends in the ratio of 80th to 20th percentile of income, before and after housing costs. The details of trends in inequality depend on how you measure it, but by these measures it is neither falling, nor notably low internationally.

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Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »

Comments

  • avatar
    Wesley Burr

    Is there a reason the article you linked to uses “medium” instead of “median”? I’ve never seen that replacement be a valid one before. Is the author using medium as a synonym for mean, or is it just poor transcription?

    10 years ago

  • avatar
    Kane Bunce

    Fraction of median is not a good measurement for poverty either. One are poor if one cannot afford all the necessities of life, not if one has a set fraction of any income measurement.

    10 years ago

    • avatar
      Kane Bunce

      Ops, I mean “Fraction of median income” and “One is poor”.

      10 years ago

      • avatar
        Thomas Lumley

        It’s a fairly standard measure of poverty related to inequality, and it’s the one Cunliffe was using. Whether it’s the ideal one is not at issue here.

        There’s a good discussion at Wikipedia of the pros and cons of various ways of measuring poverty. It’s worth noting that Adam Smith pointed out the significance of relative poverty — it isn’t just a left-wing idea.

        10 years ago

  • avatar
    Nick Burns

    Thomas, I am glad to see your balanced and sensible comment here. In election years, I am always alarmed at the way statistics are used like a hammer to beat on the anvil of the nation’s heart. Often the statistics end up being the discussion point, and not the scenario from which they are drawn.

    The real discussion point here is the perceived level of poverty in New Zealand’s youth. Statistics can colour this anyway we choose, but this is a debate as to whether poverty is a real social problem and whether the nation is prepared to address it.

    And while this is an outstanding blog for statisticians (and would-be statisticians like myself), do we sometimes forget that the primary role of statistics is to help us convey a story?

    10 years ago