Intelligent Design

Misuse of Statistics to Draw an Unwarranted Conclusion, Part 2,386

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Here is a story from US News about German’s COVID-19 death rate that demonstrates how one should hesitate to draw conclusions from the face of a statistic. 

First, some basic math.  The death rate for COVID-19 (indeed any rate) is based on a fraction.  We all learned in grammar school that fractions have two parts:  a numerator (the number on top), which is divided by the denominator (the number on bottom).  The fraction for the death rate is [total deaths]/[total cases].

Now, it should be obvious that there are two ways for the rate to go down.  (1) hold the line on total deaths in proportion to total cases  OR  (2)  pump the number of total cases in proportion to deaths.   It should also be obvious that only way (1) is a measure of the efficacy of a country’s health care efforts.  Here is an example.  Assume two countries with equal populations:  Country, X and Country Y.  Let’s assume that both countries have the exact same number of deaths at a given time, say 400.  So the numerator for both cases is the same.

Now let’s assume that the total number of identified cases for County X is 20,000 and 40,000 for Country Y.  So the death rate for County X is 2%.  And the death rate for Country Y is 1%.  It is obvious that Country Y’s healthcare system is twice as good as Country X’s.  After all the death rate in Country X is double the death rate in Country Y. 

Not so fast.  Note the key word is “identified.”  If we assume that identified cases track with actual cases, then the conclusion that Country Y’s healthcare system is better may be warranted.  But what if Country Y has instituted a massive testing program with the goal of testing every single person in the country.  And at the same time, County X tests only those presenting for treatment?  If that were the case, the difference in rates would probably be attributable in part (almost certainly very large part) to the fact that Country Y has included a huge number of asymptomatic people in its total cases number and Country X has not.  In other words, the difference in death rates would have little to do with the relative efficacy of each country’s healthcare system, and almost everything to do with the difference in testing.

Now let’s go to the story.  The reporter notes that Germany’s death rate is low compared to other countries and concludes this “suggests that Germany is doing something right that the others aren’t.”  To his credit the reporter demonstrates that he understands the basic math we just went through:

The most important factor contributing to the low death rate is that Germany appears to be that it is testing far more people than any other European country.  Scientists agree that a large number – probably a big majority – of all coronavirus cases never make it into the official figures because they are not severe enough for hospital treatment.  The more widely a country tests, the more of these milder cases it will find.  Since the most severe cases are almost always tested, the number of coronavirus deaths will likely stay the same.  The net effect is that more testing leads to a lower-looking death rate.

So what is the big deal about Germany?  It is lowering its death rate by identifying a lot of asymptomatic cases.  That says practically nothing about the efficacy of its healthcare system in lowering the rate by reducing deaths through superior treatment.  Yet, the reporter goes on to praise Germany’s universal healthcare system, suggesting that system has something to do with the lower rate.  Maybe it does.  But the reporter does not know that and his musings are nothing but pure speculation.  And he should know this, because he has already shown earlier in the story that Germany’s low death rate is certainly almost entirely an artifact of higher testing rates.

Yet another lesson from the “lies, damn lies and statistics” category.

10 Replies to “Misuse of Statistics to Draw an Unwarranted Conclusion, Part 2,386

  1. 1
    jawa says:

    “Here is a story from US News about German’s COVID-19 dearth rate that demonstrates how one should hesitate to draw conclusions from the face of a statistic. ”
    “death”?

    Barry replies: Thank you Jawa. That sentence had a dearth of good spelling.

  2. 2
    jawa says:

    “Assume two countries with equal populations: Country, X and Country Y. Let’s assume that both countries have the exact same number of deaths at a given time, say 400. So the numerator for both cases is the same.”

    “Now let’s assume that the total number of identified cases for County X is 20,000 and 40,000 for Country Y. So the death rate for County X is 2%. And the death rate for Country Y is 1%. ”

    Country Cases Deaths DR
    X 20K 400 2%
    Y 40K 400 1%

    “It is obvious that Country X’s healthcare system is twice as good as Country Y’s. After all the death rate in Country Y is double the death rate in Country X.”

    Isn’t it the other way around?

    Barry replies: Thanks again Jawa. I need to do better at editing.

  3. 3
    Ed George says:

    A very informative video about how best to view COVID-19 growth rates. It is not prone to the level of testing but it will be affected by changes in the extent of testing g within any country. In spite of that, it is clear that most countries are still in the logarithmic growth phase. This doesn’t mean that the lockdown most of us are experiencing is not effective as there will be a lag time before any effects are seen.

    https://youtu.be/54XLXg4fYsc

  4. 4
    Bob O'H says:

    Jawa @ 1 – I don’t know. It is a dearth if identified cases. 🙂

  5. 5
    Ed George says:

    Another interesting article comparing different US cities during Spanish flu.

    https://apple.news/AVcfT9tVgRhGzBWifOL4PJg

  6. 6
    jawa says:

    “lies, damn lies and statistics” category.

    🙂

  7. 7
    BobRyan says:

    Beyond the unknowns of 2 countries with same population totals having an unknown for infected, since most people don’t show symptoms, you would have to take into account ages. A younger population will have fewer deaths than an older one.

  8. 8
    john_a_designer says:

    The bottom line is that there has been a dearth of the right kind of data. What the CDC in the U.S. needs to do is commission a randomized survey (or surveys) of the American population in different geographical areas the same way polling companies conduct personal opinion polls etc. That will give us a better idea of what’s happening than doing blind “guesstimating.” However, that will probably have to wait till they approve and make available an easier to take or some kind of self-administered test. Until then we’re pretty much all in the dark and that includes the so-called experts.

  9. 9
    Ed George says:

    Dr. Fauci is now saying that the US could see as many as 100,000 deaths.

    Trump fires Fauci in 5, 4, 3,…

  10. 10
    ET says:

    Yes, Eddie, if we keep on as we are doing. However if we follow the guidelines then we won’t hit 100,000. That just means that we will easily reach it

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