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Math The Media Science

The Public Do Not Understand Logarithmic Graphs Used To Portray COVID-19 (lse.ac.uk) 349

Mass media routinely portray information about COVID-19 deaths on logarithmic graphs. But do their readers understand them? Alessandro Romano, Chiara Sotis, Goran Dominioni, and Sebastian Guidi carried out an experiment which suggests that they don't. From a report: The fact that the framing of information can dramatically alter how we react to it will hardly surprise any reader of this blog. Incidentally, the canonical example of framing effects involves an epidemic: a disease that kills 200 out of 600 people is considered worse than one in which 400 people survive. Whereas this imaginary epidemic was just a thought experiment, an actual global pandemic turns out to be an unfortunate laboratory for framing effects. In a recent experiment, we show how framing crucially affects people's responses to one of the most important building blocks of the COVID-19 informational puzzle: the number of deaths. We show that the logarithmic scale graphs that the media routinely use to display this information are poorly understood by the public and affect people's attitudes and policy preferences towards the pandemic. This finding has important implications because during a pandemic, even more than usually, the public depends on the media to convey understandable information in order to make informed decisions regarding health-protective behaviours.

Many media outlets portray information about the number of COVID-19 cases and deaths using a logarithmic scale graph. At first sight, this seems sensible. In fact, many of them defend their decision by showing how much better these charts are in conveying information about the exponential nature of the contagion. For history lovers, the popular economist Irving Fisher also believed this, which led him to strongly advocate for their use in 1917 (right before the Spanish Flu rendered them tragically relevant). Fisher was ecstatic about this scale: "When one is once accustomed to it, it never misleads." It turns out, however, that even specialized scientists don't get used to it. Not surprisingly, neither does the general public. We conducted a between-subjects experiment to test whether people had a better understanding of graphs in a logarithmic or in a linear scale, and whether the scale in which the chart is shown affects their level of worry and their policy preferences. Half of our n=2000 sample of US residents was shown the progression of COVID-19 related deaths in the US at the time of the survey plotted on a logarithmic scale. The other half received exactly the same information -- this time plotted on a good old linear scale. [...]

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The Public Do Not Understand Logarithmic Graphs Used To Portray COVID-19

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  • by spun ( 1352 ) <loverevolutionary&yahoo,com> on Wednesday May 20, 2020 @05:34PM (#60084022) Journal

    A&W wanted to one up the Quarter Pounder, so they introduced the 1/3 Pound Burger back in the early '80s. Sales were abysmal. In customer surveys, the most frequent response was "why would I pay more for a smaller burger? Three is less than four, right?"

    Basic numeracy is sadly lacking, expecting the public to understand log scales is completely naive.

    • by PuddleBoy ( 544111 ) on Wednesday May 20, 2020 @06:22PM (#60084250)

      About 20 years ago, I worked for a telco and we tried to offer less-expensive phone lines with all surcharges included in one flat price. Competition advertised $26 phone lines... and with surcharges, they came out to about $45. We offered a flat $40 per line with all surcharges included.

      No one bought our lines. When we asked, customers always said 'but $26 is less than $40'. We tried to explain about all the other charges, but it never sunk in. So we advertised our lines as $24 plus surcharges (which often added up to *more* than $40) and we sold a ton of them.

      • by im_thatoneguy ( 819432 ) on Wednesday May 20, 2020 @07:26PM (#60084568)

        No one bought our lines. When we asked, customers always said 'but $26 is less than $40'. We tried to explain about all the other charges, but it never sunk in. So we advertised our lines as $24 plus surcharges (which often added up to *more* than $40) and we sold a ton of them.

        This is the perfect example of why non-predatory companies want regulation. If you try to do the right thing but people only support predatory companies which are defrauding their customers, the free market rarely works. Or it takes so long to work that the competition has gone bankrupt and new predatory companies have sprung up to collect the people slowly catching on.

        A minimum wage means we can pay a reasonable wage to employees without our next door competitor swooping in and underbidding us on everything. Environmental regulations mean we can competitively sell product and not dump the waste down the storm drain poisoning people and hope nobody notices.

        • If you try to do the right thing but people only support predatory companies which are defrauding their customers, the free market rarely works

          There are several assumptions in free market theory. One of which is complete information. Predatory companies withholding pricing information is a violation the basic assumptions of free market economics, and warrants government regulation.

      • Most of the retail sector operates on similar principles. Market your product as 20% off and customers feel that they got a bargain, even though the 20% off offer never ends.

        • Sure it does. For about 1-2 weeks a year, Kohls will sell their crappy $25 shoes for about $50. Just so they can't get sued for false advertising for claiming it's discounted the other 50ish weeks a year...
    • by cusco ( 717999 )

      "Math is hard!" - Barbie

    • by gweihir ( 88907 )

      US education is _this_ bad now? Fascinating.

    • Re: (Score:3, Funny)

      by freeze128 ( 544774 )
      This just proves that Burgers should be Metric.
  • by hubang ( 692671 ) on Wednesday May 20, 2020 @05:37PM (#60084036)
    If I was shown the figure from the article, I don't think I'd get that it's log scale; at least at first glance. Usually, I look for logarithmic grid lines. Without them, it doesn't exactly jump out at you. And the title of the graph is probably the worst place to put relevant information.
  • by thesupraman ( 179040 ) on Wednesday May 20, 2020 @05:39PM (#60084042)

    The fact that they endlessly use absolute numbers of deaths between countries when trying to claim comparisons is orders of magnitude ( ;) ) worse..
    Seriously, the number of graphs with a bunch of countries charted with absolute number of deaths and/or infections, and we are supposed to be grabbed by some 'meaning' in it, when often the populations are different by an order of magnitude or more.

    Then there is the complete lack of context to where the numbers sit in comparison to other causes of death. Of course every single avoidable death is bad, but hey, where are the global shutdowns for HIV, for normal flu... Hell, banning smoking and alcohol would probably save more lives - but that is certainly not done.

    Context IS desperately needed, however apparently we are too dumb to understand it, or perhaps it would just get in the way of 'the message'

    So yes, people don't understand logarithmic graphs, but that is hardly the primary problem here.

    • by Nidi62 ( 1525137 ) on Wednesday May 20, 2020 @05:44PM (#60084066)

      Hell, in Georgia they got caught putting days in different order on graphs to show downward trends. The graph would go from May, to April, and back to May

    • Re: (Score:2, Insightful)

      by spun ( 1352 )

      The problem is assholes who think some abstract notion of "the economy" is more important than lives. Here's the thing, bud. We have records from 1918. We know what works and what doesn't in a pandemic. Counties that stayed locked down longer recovered quicker, economically. It's a simple fact: dead people don't buy goods and services. You can put people back on the job, but more will die and the ones who survive will be scared for longer, not out actually buying goods and services.

      Just remember folks, when

      • by LynnwoodRooster ( 966895 ) on Wednesday May 20, 2020 @06:06PM (#60084178) Journal

        Seems that lockdown meant something different [bbc.com] back then. Public walks, bars and restaurants and churches still open, no changes in work spaces, etc.

        As far as the economy, it IS jobs. If you were a barber - you haven't made a dime for 2 months (and pushing for 3 more, if you're in Los Angeles). That pretty much bankrupts anyone. Saying "it's just stocks" is pretty rude and dismissive of millions of small and independent businesses and workers.

      • by SuperKendall ( 25149 ) on Wednesday May 20, 2020 @06:08PM (#60084182)

        The problem is assholes who think some abstract notion of "the economy" is more important than lives

        The problem is assholes who think losing 30+ million jobs is fine, while implementing questionable changes that hardly save any lives.

        You claim to care about lives, but in the end it turns out not really because you are willing to destroy lives after the data shows clearly what you are doing is not really saving very many people over doing nothing.

        If we had locked down the nursing homes and totally isolated them, and did no other shutdowns the NYC COVID death rate alone would be something like 80% of the current total.

        All without losing 30 million jobs...

        I mean really, why do you not care about 30 million people losing work? That to me is truly baffling. I myself care about both - I wanted to see deaths minimized, but I ALSO realize the effect of that many people losing jobs is equally as destructive to society as a whole.

        • If we had locked down the nursing homes and totally isolated them, and did no other shutdowns the NYC COVID death rate alone would be something like 80% of the current total.

          This is not true, the hospitals would have been overwhelmed.

        • by Opportunist ( 166417 ) on Wednesday May 20, 2020 @07:26PM (#60084566)

          You know, in civilized countries the governments stepped in and made sure that these businesses survive. But it seems in the US, to get bailed out you have to be too big to fail ... and make relevant bribes to your relevant political whores.

        • by dryeo ( 100693 )

          Well, it sure isn't working out for Sweden. https://nationalpost.com/news/... [nationalpost.com]
          Where I am, the government is helping those barbers and their workers with money and help with the rent. It's costing, with borrowing close to what America was borrowing before the pandemic. Seems America would rather support the stock market rather then workers.

      • by phantomfive ( 622387 ) on Wednesday May 20, 2020 @06:16PM (#60084224) Journal
        It's not new, there were mask protests in 1918, too [sfchronicle.com]. I'm sure you're not surprised. Quote:

        "“A week ago I laughed at the idea of the mask,“ John A. Britton told a reporter. “I wanted to be independent. I did not realize that the cost of such independence was the lives of others.”

        --Some guy in 1918

      • by Anne Thwacks ( 531696 ) on Thursday May 21, 2020 @04:24AM (#60085750)
        It's a simple fact: dead people don't buy goods and services

        people keep saying ths but where is the data on the undead?

    • by quonset ( 4839537 ) on Wednesday May 20, 2020 @05:58PM (#60084136)

      Then there is the complete lack of context to where the numbers sit in comparison to other causes of death.

      No, there is not. The original mantra was, "It's not as bad as the flu". Then people started using other examples of death such as heart disease, car accidents and smoking. Here's one for you. If covid-19 was a war, it would be the fourth deadliest for Americans.

      Hell, banning smoking and alcohol would probably save more lives - but that is certainly not done.

      Those involve choices people make. You can choose not to smoke. You can choose not to drink. You don't choose whether or not to get infected with covid-19.

      Further, just because you smoke does not mean there is any large chance I will smoke. The same with drinking. If you get infected with covid-19 there is a large chance you will infect someone else.

    • Attempts to outright lie to push a more sensational headline to generate web site traffic and ad revenue.

      Example of a desired narrative [dailymail.co.uk] ("COVID infections are getting worse in the United States") was out there on The Daily Mail last week. We're talking grade school level deception - but hey, it looks like exponential growth and DANGER...

    • Re: (Score:3, Insightful)

      by Anonymous Coward

      So here you are complaining about a lack of scientific literacy and then you go and write "where are the global shutdowns for HIV, for normal flu", and you get marked insightful. I mean, jesus fucking wept. How ignorant can you possibly be? The reason this is not worse than a typical flu season or the HIV pandemic is *because* there has been a lockdown. If it's already passed through the population, and killed a quarter of the over-70s and lots of the rest of us too, it's a bit fucking late for a lockdown,

  • by phantomfive ( 622387 ) on Wednesday May 20, 2020 @05:39PM (#60084046) Journal
    I've also found that communication has been really lacking around re-opening. All those protestors seem to think that the plan is to be locked down for a long, long time.

    I've found when I show people charts like this one [imgur.com], that show a well-thought-out plan for re-opening, it calms them down and gets them out of their conspiratorial ways of thinking.

    We have techniques we can use to start the economy again without killing 1% of the population, and people need to know that.
    • I've also found that communication has been really lacking around re-opening. All those protestors seem to think that the plan is to be locked down for a long, long time.

      I can't imagine where they'd get that idea from... https://www.cnn.com/2020/04/09... [cnn.com] https://www.foxnews.com/scienc... [foxnews.com] https://www.washingtonpost.com... [washingtonpost.com] https://www.yourlocalguardian.... [yourlocalguardian.co.uk]

      • Yeah, there is a communication problem. It's not clear if the problem is intentional, or if reporters are just being dumb (and by dumb, I mean completely ignorant of any of the math tools required to have any understanding of the situation. Like "averages" or "y-axis").
        • by cusco ( 717999 )

          This is what happens when we go from "the press" to "the media". Once upon a time a newspaper or major TV or radio outlet would have a "science reporter", a journalist with some background and understanding of science, a "business reporter" with some background in business, etc. Now the primary requirement to be a "reporter" is to look good on camera and be able to read a corporate press release as though it were actual news. /rant

  • The problem for most people is, i suspect, the fact that the scale on one axies is linear and the othe logarithic, so a hcange of s alog the x axies ( as in the timspan of 2 days) sudenky means a factot of 200 on the y (number of deths) but the number stil onlu changes from 0 to 2 in both cases, and you know the fact that a large number of people find any math scary. Caveat: my examle can be off logaritmic js one thing butvare ve talking about natural logarithems or base 10 logarithms?
  • Graphs are supposed to be intuitive, you can glance at one and get a quick grasp of what the numbers are telling you. Logarithmic graphs are not, if you don't read the fine print it's very easy to interpret them wrong. That doesn't mean they should never be used, they can be very useful in some contexts. But probably not in an article intended for a mass audience.
    • by zieroh ( 307208 )

      I would go so far as to argue that the media should NOT be showing logarithmic graphs to the general public, unless their intent is to mislead.

    • by thegarbz ( 1787294 ) on Wednesday May 20, 2020 @07:16PM (#60084524)

      Logarithmic graphs are not, if you don't read the fine print it's very easy to interpret them wrong.

      By "fine print" you mean looking at the scale? It sounds like the only thing you're interested in if you ignore that "fine print" is up or down, in which case either logarithmic or linear will do the job for you just fine. There's nothing "intuitive" about reading logarithmic data on a linear graph which is why they invented the damn logarithmic graph in the first place. TFA makes that point nicely, on the linear graph presented it looks as though Italy and USA are trending identically, but that graph counter to your assertion actually isn't intuitive given the data presented on it.

      In much of the world we teach kids the importance of labeling their axis and deduct points if its not done correctly, is that not part of common core maths?

    • That fine print is called the scale. Yes, you actually have to read a graph, you can't just look at the pretty picture.

      And yes, if you want to compare growth rates, a logarithmic scale is actually more useful because when you're dealing with exponential growth it can far better display the difference in magnitude.

  • The scale is not very important here. Showing cumulative deaths or cumulative cases is not informative in assessing the dynamics. Also, registered deaths lag the infections by 2-3 weeks. Daily new cases should have been used.

  • Imagine a world ... (Score:4, Interesting)

    by OrangeTide ( 124937 ) on Wednesday May 20, 2020 @05:53PM (#60084116) Homepage Journal

    Imagine a world where a majority of voters are borderline illiterate.
    Now here's the twist, they don't even know they are illiterate.

    • by gweihir ( 88907 )

      I don't have to imagine that world. If we take functional illiteracy (basically, people can read but do not understand what they read), we are living in that world.

  • Title should really be, The Public including the Media do not understand log graphs and statistics.
  • ... an intuitive understand of exponents.

    But to be fair, I find that looking at a logarithmic graph with only one curve on it is not nearly as useful as looking at a logarithmic graph that compares several curves which might have different orders of magnitude.

    • by gweihir ( 88907 )

      ... an intuitive understand of exponents.

      Or of exponential growth. That is why most people do not understand that on something like Covid-19, a week or two can be the difference between the medical system still works and everything collapses. Or that a timely response in retrospect makes a safely avoided catastrophe look pretty harmless.

  • Surprised? (Score:4, Insightful)

    by Freischutz ( 4776131 ) on Wednesday May 20, 2020 @05:59PM (#60084138)
    The public not understanding logarithmic graphs is something that could only surprise a scientist or an engineer. If scientists themselves don't get used to logarithmic scales the public does not stand a chance. On top of that, for Corona virus, Log graphs make things look better to the untrained eye than linear graphs. To the untrained eye this graph: https://aatishb.com/covidtrend... [aatishb.com] makes the situation in the US look a lot less serious than this: https://aatishb.com/covidtrend... [aatishb.com] and if you are interested in trying to downplay the seriousness of the COVID-19 pandemic then this bug is a feature.
  • Ok, I never got the purpose of this - when I read an actual article, I expect there to be links to point to additional context about the subject at hand the article discusses (usually within that paragraph), as an "see this for additional info, but not required".

    But in a summary about an article or story? WTAF?! I don't even know which one of the nine links in this summary is the 'main' one to go to...

    • by Guignol ( 159087 )
      I'm totally with you on this one
      This is really getting annoying
      After a bunch of totally not nerdy articles, we, slashdotters (science guys around, probably almost famous in our 10+ people circles) finally get an article where we can make fun of dumber than us people that don't understand logarithmic scales
      I was almost thinking about actually getting up to grab the pop corn but then, WTF ? 9 links ? wait, what was the topic about ? I can't even imagine how non older slashdotters not yet trained to not fol
  • Itâ(TM)s probably something that those who made the graphs have little understanding of as well.

  • The greatest shortcoming of the human race is our inability to understand the exponential function -Al Bartlett "Arithmetic, Population and Energy"
  • ... looks a lot less intimidating logarithmically.

  • All the best conspiracy theories at the moment seem to involve believing "the media" is "exaggerating" the problem. "If a million people have this, how come I don't know nobody who got it? This is just some bullshit". In a country of 330M, odds are still that you don't know anyone who has it, unless you are just a very social person. But odds are also that you have visited a place a sick person has been through at least once in the past few weeks. That's why you should care anyway.

  • by hcs_$reboot ( 1536101 ) on Wednesday May 20, 2020 @06:20PM (#60084240)
    the Richter scale, +1 magnitude is 10 times more amplitude, or 31 times more energy.
  • logarithmic scale is deceiving.
    it is often used for such purposes too (not covid, other things).
    • by gweihir ( 88907 )

      logarithmic scale is deceiving.
      it is often used for such purposes too (not covid, other things).

      Bullshit. Only somebody utterly deranged would see a log-scale plot as a deception. It is merely a different way to display things. For an exponential phenomenon (and an epidemic is very much that), it is the natural scale for things.

      • by zieroh ( 307208 )

        Only somebody utterly deranged would see a log-scale plot as a deception

        I don't think you've been paying attention. For example: https://en.wikipedia.org/wiki/... [wikipedia.org]

        • by gweihir ( 88907 )

          No, I can actually read graphs, whether linear or log-scale. Linear is wrong here or only useful as additional graph.

          Sure, the general public reading data aimed at scientists and misunderstanding them is a problem, but in only becomes deception when it is not labelled correctly. (Of course, it needs to be labelled correctly, why is that even a question? Anything not labelled clearly is a problem, that is not limited to log-scale at all.) For experts, these log-scale plots are helpful and needed. A non-expe

  • It really does not matter whether they learned it at school either. People go with emotion and with what they want to see. They (with rare exceptions, which usually turn out to be the 10-15% independent thinkers) are not interested in facts and do not even understand what a fact is. They think the world works how they want it to work. Many are even willing to apply violence to anybody and anything that threaten their fantasies of how things are.

    • by ceoyoyo ( 59147 )

      It's worse than that. When confronted with evidence that contradicts their beliefs, people generally not only hold onto those beliefs, but they strengthen them.

  • by hey! ( 33014 ) on Wednesday May 20, 2020 @06:27PM (#60084268) Homepage Journal

    One of the problem with linear scale graphs is that the largest number represented on the graph dominates your impression, which can be misleading.

    Suppose I'm plotting COVID-19 cases for two states, A and B, during the initial exponential phase of the epidemic when cases are roughly doubling every four days. The graph is dominated by the biggest number on the graph -- say the latest number of cases from A. I might look at the graph and conclude the problem is much smaller in B, which is *accurate*, but *misleading*. It's possible that A and B are following exactly the same trajectory, but A simply got started a week earlier than B.

    A logarithmic scale would make that much clearer. But it *is* misleading about the relative size of the problem *right now*.

    The answer is, you look at *both*. In fact, you look at as many different *kinds* of visualizations of the data as possible, with different independent variables too.

  • by drh1138 ( 6194498 ) on Wednesday May 20, 2020 @06:27PM (#60084272)
    Scientists and science journalists need to consider their audience when presenting data. It's not the average person's fault for not understanding logarithmic scales. It's the presenter's fault for not understanding how to effectively communicate to the lay populace.
    • It's not the average person's fault for not understanding logarithmic scales.

      In a country with free public education that pushes universal literacy, and covers the relevant math for 3-6 years in a row?
      Sounds like a set of individual choices.

    • It's not the average person's fault for not understanding logarithmic scales. It's the presenter's fault for not understanding how to effectively communicate to the lay populace.

      It's both. No one would ever brag about being illiterate yet being mathematically so is a point of pride for many. If you have such an attitude it is 100% your fault.

  • Another misleading way of describing a statistic is to call the pandemic a 1 in 100 year event. This is misleading as statistics used to describe unpredictable events are average return intervals, or similar measures. An event with an average return interval of 1 in 100 years is a figure derived from historical observations and refers to the likelihood of the event occurring in any one year. The average return interval of a particular event is not necessarily recalculated at regular intervals. This seems re
  • by JoeDuncan ( 874519 ) on Thursday May 21, 2020 @10:31AM (#60086518)

    ... *always* a sure bet.

    That's how casinos work.

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