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The author is just as wrong as the people he criticizes. A much better measure of “the economy” is median income because that is a more accurate reflection

The author is just as wrong as the people he criticizes. A much better measure of “the economy” is median income because that is a more accurate reflection of the economic well being of most people. This is a problem in many fields including engineering. A median or average has a measurement error (and just because one bar is higher than another it doesn't really mean it is actually higher). The distribution is what is interesting and important. Which gives, start publishing numbers as (x1,x2,x3,x4,x5) at 10,30,50,70,90th percentile or whatever. And give up pretending complex system are simple.

pastacacioepepe 4y ago
> Which gives, start publishing numbers as (x1,x2,x3,x4,x5) at 10,30,50,70,90th percentile or whatever. And give up pretending complex system are simple. How are then the institutions going to sell us the narrative that all is well and growth is always good, once we realize poor people stay poor and rich people get richer?
deleted 4y ago
[deleted]
dwater 4y ago
This is stats 101. Mean and median are measured of central tendency, and the median is generally better for skewed distributions. The 5 number summary (or your 5 percentiles) gives slightly more information, but ultimately you are summarizing a complex distribution with a few simple stats. There are upsides (it’s fast) and downsides (it’s incomplete) to doing so. The real problem is how few people understand stats 101, which makes them easy to mislead.
- sitkack 4y ago
  Maybe we should teach stats 101 starting from kindergarten?
  - quickthrower2 4y ago
    And have the news outlets talk intelligently about what the numbers mean. The BBC website does something nice where they often have an "Analysis" section under the news. A sentence or two about how to interpret the number would be useful. If they think we need analysis to understand what is happening in Ukraine, I think we probably need it for interpreting economics numbers. "We" being ... most people. And it wont always bet stats 101.
- hammock 4y ago
  Mean and median are both typically taught around and better suited for use with normal distributions. Income distribution is not that complex, but it’s also not normal - it’s a power law (zipfs law). A combination of Total GDP (or income) and something like the Gini coefficient is more useful. And commonly used, as well
pfisherman 4y ago
I mean if we want to go down that road, then why not just publish the first four moments of the distribution?
superb-owl 4y ago
You're technically correct--the distribution carries a lot more information than the average or median alone. The problem is that many of these decisions are being made democratically, or by democratically elected representatives. They need to be able to explain the impact of their decisions to the average voter. Having a single number that goes up or down makes communication and coordination a lot easier, and I think it's worth discussing what the best single number might be.
- coldtea 4y ago
  Or those "elected represenatives" could help educate the people - to e.g. understand distributions. But instead they educate them in BS, both in schools, and through their government communication. It's more convenient to emphasize BS in curriculums than proper life/political skills...
- scarmig 4y ago
  Choosing a single number necessarily removes information about the distribution, though, and which information is being discarded is inherently a political decision. The Rawlsian veil of ignorance (at least a naive version) would have us choose p0 as the meaningful number; a utilitarian with certain beliefs about the marginal utility of money would prefer the distribution mean. Even the choice to use a normalize GDP per capita is taking a strong stance on the repugnant conclusion.
- JackFr 4y ago
  > They need to be able to explain the impact of their decisions to the average voter. No, not the “average” voter - messaging should be aimed at the marginal voter.
  - quickthrower2 4y ago
    Well a distribution across all voters. Some voters are more swing-able than others. Some voters are in more marginal seats than others. But all voters can swing given enough "force". If the force is negative force for who they normally vote for.
  - 4y ago
AstralStorm 4y ago
It so happens that the most useful number is usually the dominant (also known as mode or most common value), which is not visible on the histogram, especially for flat heavy tailed distributions such as income these days.
- thaumasiotes 4y ago
  > the most useful number is usually the dominant (also known as mode or most common value), which is not visible on the histogram Are you kidding? It's the highest point on the histogram; a histogram places very heavy visual emphasis on the mode while obscuring the mean and median.
  - AstralStorm 4y ago
    Sometimes true, but it is the only value that can be estimated without error in some cases. Neither median nor average is useful for a central tendency in a weird distribution - and income tends to be one. Histograms typically bucket data potentially hiding the true value of mode or adding error to it. It really should be given directly, with a count of occurences. Mode is not the same as modal class - which is what you would get from a histogram.
    - thaumasiotes 4y ago
      > Histograms typically bucket data potentially hiding the true value of mode or adding error to it. It really should be given directly I can't agree with that. It is true that histograms bucket data. But the width of the buckets is chosen to make sense in context. It just isn't relevant if people making $20,176 slightly outnumber people making $20,359. So we put them in the "$15,000 - $24,999" bucket, which preserves most of the information of interest while omitting the information that is of absolutely no interest. In other contexts, you see other bucket widths. Chinese university entrance exam scores are published with a bucket width of one point. (Some things may be obscured. When I was looking into this, I found that it was very common for the top scores to be bucketed with each other, presumably for some kind of privacy reasons. Beijing was notable in putting low scores into buckets of width ten even in what was technically labeled an 一分一段表 (literally: "one point -- one section" table). Fujian was notable the other way, for preserving the bucket width of one point even for the highest scores; I have trouble believing it's a coincidence that Fujian is one of the academically highest-performing regions of China.) > Mode is not the same as modal class - which is what you would get from a histogram. For almost all purposes, modal class is more interesting, more useful, and more statistically valid than raw mode is.
mihaic 4y ago
Fully agree. Most people use life expectancy at birth to believe that everyone died in their 30s in ancient times, even though these numbers are skewed because of huge infant mortality. Introducing something like life-expectancy at birth, 5, 10, 20, 40 years would paint a much better picture, but it takes hard work and a belief that your audience is not stupid.
- blackoil 4y ago
  It is even more complicated. eg. to understand state of healthcare using life-expectancy at 20 or 40 may provide wrong info. Because it ignores fact that most of the sick and weak individuals have already died by then.
  - mihaic 4y ago
    Yeah, you get more information the more data point you explicitly define. The challenge is reaching a compromise between "easy to explain" and "captures a lot of information". Depending on your audience, you probably want to expose more granular data, but for the laymen I think multiple points all on the same function is they best compromise, since you just need to explain one simple function and 4-5 well picked values for that function.
bfung 4y ago
https://medianism.org/medianism/about_the_medianist/ https://medianism.org/medianism/about_the_medianist/ Who Is This Medianist? Jonathan Andreas is an Associate Professor at Bluffton University who received his Ph.D. in Economics from the University of Illinois at Chicago. Ok, cool, not some armchair tech bro that spent 5 minutes writing up some blog.
drewcoo 4y ago
Mean, mode, and median are all averages. They have meanings. They don't have "measurement errors," but the people using them may have "usage errors." https://www.dummies.com/article/academics-the-arts/math/pre-algebra/the-three-types-of-average-median-mode-and-mean-168773/ https://www.dummies.com/article/academics-the-arts/math/pre-... Distributions give us richer data. But even distribution of incomes (in the article) or spending (GDP) aren't terribly rich. They don't answer why. So we can add dimensions to what we measure or fall back to just so stories. And that's why most people don't trust economists - oversimplified models and just so stories.
- rightbyte 4y ago
  > They don't have "measurement errors" Sure. I am not arguing that a median is not a median. By measurement error I really meant noise and disturbance, as defined in control theory. E.g. it is perfectly possible to have a value "average tax in county" with zero noise as in perfect value to the cent, but year to year variance due to disturbances.
benreesman 4y ago
There are many mappings from the English word “average” to maths: arithmetic mean, median, geometric and harmonic means. We could be here all day. But “median is better than arithmetic mean for knowing if a lot of people are struggling” should be uncontroversial. We’ve rigged up a system that is a race to the bottom on wealth inequality. People have tried to run systems like this before and it always ends in tears. The interesting question isn’t how to parse the maths, or even if we have a bad, bad problem. The question is, can we and/or will we do something about it soon enough that Western civilization lasts for climate change or whatever to even matter. Because we’re on pace to get into tennis courts and guillotines before much if any of Manhattan is below the water line.

pastacacioepepe 4y ago

> Which gives, start publishing numbers as (x1,x2,x3,x4,x5) at 10,30,50,70,90th percentile or whatever. And give up pretending complex system are simple. How are then the institutions going to sell us the narrative that all is well and growth is always good, once we realize poor people stay poor and rich people get richer?

deleted 4y ago

[deleted]

dwater 4y ago

This is stats 101. Mean and median are measured of central tendency, and the median is generally better for skewed distributions. The 5 number summary (or your 5 percentiles) gives slightly more information, but ultimately you are summarizing a complex distribution with a few simple stats. There are upsides (it’s fast) and downsides (it’s incomplete) to doing so. The real problem is how few people understand stats 101, which makes them easy to mislead.

sitkack 4y ago
Maybe we should teach stats 101 starting from kindergarten?
- quickthrower2 4y ago
  And have the news outlets talk intelligently about what the numbers mean. The BBC website does something nice where they often have an "Analysis" section under the news. A sentence or two about how to interpret the number would be useful. If they think we need analysis to understand what is happening in Ukraine, I think we probably need it for interpreting economics numbers. "We" being ... most people. And it wont always bet stats 101.
hammock 4y ago
Mean and median are both typically taught around and better suited for use with normal distributions. Income distribution is not that complex, but it’s also not normal - it’s a power law (zipfs law). A combination of Total GDP (or income) and something like the Gini coefficient is more useful. And commonly used, as well

pfisherman 4y ago

I mean if we want to go down that road, then why not just publish the first four moments of the distribution?

superb-owl 4y ago

You're technically correct--the distribution carries a lot more information than the average or median alone. The problem is that many of these decisions are being made democratically, or by democratically elected representatives. They need to be able to explain the impact of their decisions to the average voter. Having a single number that goes up or down makes communication and coordination a lot easier, and I think it's worth discussing what the best single number might be.

coldtea 4y ago
Or those "elected represenatives" could help educate the people - to e.g. understand distributions. But instead they educate them in BS, both in schools, and through their government communication. It's more convenient to emphasize BS in curriculums than proper life/political skills...
scarmig 4y ago
Choosing a single number necessarily removes information about the distribution, though, and which information is being discarded is inherently a political decision. The Rawlsian veil of ignorance (at least a naive version) would have us choose p0 as the meaningful number; a utilitarian with certain beliefs about the marginal utility of money would prefer the distribution mean. Even the choice to use a normalize GDP per capita is taking a strong stance on the repugnant conclusion.
JackFr 4y ago
> They need to be able to explain the impact of their decisions to the average voter. No, not the “average” voter - messaging should be aimed at the marginal voter.
- quickthrower2 4y ago
  Well a distribution across all voters. Some voters are more swing-able than others. Some voters are in more marginal seats than others. But all voters can swing given enough "force". If the force is negative force for who they normally vote for.
- 4y ago

AstralStorm 4y ago

It so happens that the most useful number is usually the dominant (also known as mode or most common value), which is not visible on the histogram, especially for flat heavy tailed distributions such as income these days.

thaumasiotes 4y ago
> the most useful number is usually the dominant (also known as mode or most common value), which is not visible on the histogram Are you kidding? It's the highest point on the histogram; a histogram places very heavy visual emphasis on the mode while obscuring the mean and median.
- AstralStorm 4y ago
  Sometimes true, but it is the only value that can be estimated without error in some cases. Neither median nor average is useful for a central tendency in a weird distribution - and income tends to be one. Histograms typically bucket data potentially hiding the true value of mode or adding error to it. It really should be given directly, with a count of occurences. Mode is not the same as modal class - which is what you would get from a histogram.
  - thaumasiotes 4y ago
    > Histograms typically bucket data potentially hiding the true value of mode or adding error to it. It really should be given directly I can't agree with that. It is true that histograms bucket data. But the width of the buckets is chosen to make sense in context. It just isn't relevant if people making $20,176 slightly outnumber people making $20,359. So we put them in the "$15,000 - $24,999" bucket, which preserves most of the information of interest while omitting the information that is of absolutely no interest. In other contexts, you see other bucket widths. Chinese university entrance exam scores are published with a bucket width of one point. (Some things may be obscured. When I was looking into this, I found that it was very common for the top scores to be bucketed with each other, presumably for some kind of privacy reasons. Beijing was notable in putting low scores into buckets of width ten even in what was technically labeled an 一分一段表 (literally: "one point -- one section" table). Fujian was notable the other way, for preserving the bucket width of one point even for the highest scores; I have trouble believing it's a coincidence that Fujian is one of the academically highest-performing regions of China.) > Mode is not the same as modal class - which is what you would get from a histogram. For almost all purposes, modal class is more interesting, more useful, and more statistically valid than raw mode is.

mihaic 4y ago

Fully agree. Most people use life expectancy at birth to believe that everyone died in their 30s in ancient times, even though these numbers are skewed because of huge infant mortality. Introducing something like life-expectancy at birth, 5, 10, 20, 40 years would paint a much better picture, but it takes hard work and a belief that your audience is not stupid.

blackoil 4y ago
It is even more complicated. eg. to understand state of healthcare using life-expectancy at 20 or 40 may provide wrong info. Because it ignores fact that most of the sick and weak individuals have already died by then.
- mihaic 4y ago
  Yeah, you get more information the more data point you explicitly define. The challenge is reaching a compromise between "easy to explain" and "captures a lot of information". Depending on your audience, you probably want to expose more granular data, but for the laymen I think multiple points all on the same function is they best compromise, since you just need to explain one simple function and 4-5 well picked values for that function.

bfung 4y ago

https://medianism.org/medianism/about_the_medianist/ https://medianism.org/medianism/about_the_medianist/ Who Is This Medianist? Jonathan Andreas is an Associate Professor at Bluffton University who received his Ph.D. in Economics from the University of Illinois at Chicago. Ok, cool, not some armchair tech bro that spent 5 minutes writing up some blog.

drewcoo 4y ago

Mean, mode, and median are all averages. They have meanings. They don't have "measurement errors," but the people using them may have "usage errors." https://www.dummies.com/article/academics-the-arts/math/pre-algebra/the-three-types-of-average-median-mode-and-mean-168773/ https://www.dummies.com/article/academics-the-arts/math/pre-... Distributions give us richer data. But even distribution of incomes (in the article) or spending (GDP) aren't terribly rich. They don't answer why. So we can add dimensions to what we measure or fall back to just so stories. And that's why most people don't trust economists - oversimplified models and just so stories.

rightbyte 4y ago
> They don't have "measurement errors" Sure. I am not arguing that a median is not a median. By measurement error I really meant noise and disturbance, as defined in control theory. E.g. it is perfectly possible to have a value "average tax in county" with zero noise as in perfect value to the cent, but year to year variance due to disturbances.

benreesman 4y ago

There are many mappings from the English word “average” to maths: arithmetic mean, median, geometric and harmonic means. We could be here all day. But “median is better than arithmetic mean for knowing if a lot of people are struggling” should be uncontroversial. We’ve rigged up a system that is a race to the bottom on wealth inequality. People have tried to run systems like this before and it always ends in tears. The interesting question isn’t how to parse the maths, or even if we have a bad, bad problem. The question is, can we and/or will we do something about it soon enough that Western civilization lasts for climate change or whatever to even matter. Because we’re on pace to get into tennis courts and guillotines before much if any of Manhattan is below the water line.