The two car models: A thought experiment on raw numbers and proportion to the population

Imagine a car company that is doing an internal audit on their cars. This company makes two different car models. Let’s call these Model A and Model B. The company makes 100 of Model A every year and 1000 of Model B every year. The internal audit has found that there are an average of 30 manufacturing faults reported per year. Of the 30 manufacturing faults reported, 10 are related to Model A and 20 are related to Model B.

Which Model is experiencing the more serious issues? When looking at raw numbers, it would be Model B. This is because there are twice as many faults reported for Model B than for Model A. However, when we take into consideration that the company produces ten times as many of Model B than for Model A, then this tells us a different story. What this tells us is that the company has 10% of Model A having a fault reported, whilst only 2% of Model B having a fault reported.

This is why looking only at raw numbers can be misleading when reading statistics. The recent protests against police brutality in the US have brought up arguments concerning the number of African Americans killed by law enforcement. Such arguments against the claim that there is an issue of police violence against African Americans is that more white people are killed by police than African Americans. And this is true. According to The Guardian, the total number of white deaths from police in 2015 was 577 whilst the total number of black deaths was 300. However, when adjusted for population white deaths from police are at a rate of 2.91% whilst blacks deaths from police are at rate of 7.13%. Therefore, African Americans are twice as likely to be killed by police when adjusted for proportion of the population.

It is beyond the scope of this post to argue why African Americans are killed at a higher rate than whites. The main point of this post is to demonstrate that looking at the raw numbers tells us nothing about where there is a significant issue when proportion to the population has not been accounted for.

If you are interested in political philosophy, I have a book on Identity Politics which is available for purchase called “Contrasting Identities: Navigating Identity Politics Conversations”

Reference

https://www.theguardian.com/us-news/2015/dec/31/the-counted-police-killings-2015-young-black-men

Published by

Andrew Tulloch

I have a Bachelor of Arts majoring in Philosophy and Sociology, with a Political Science minor. I am currently completing my honours degree in Philosophy.

5 thoughts on “The two car models: A thought experiment on raw numbers and proportion to the population”

    1. Thank you Saurab,

      That’s great to hear. Indeed, statistics is something I think needs to be understood by everyone. The ability to deceive by how the data is expressed brings about the phrase “there are lies, damned lies, and there are statistics”. However, the phrase always annoyed me, since we need statistics to make sense of the data we observe.

      Thanks again,

      Andrew.

      Liked by 1 person

      1. Haha yes, statistics can easily manipulate the untrained eye.

        But statistics are actually really valuable; most of what we understand the world is because of statistical tests.

        Liked by 1 person

  1. Excellent point that I have often tried to get across to folks who believe statistics without understanding them. Will Rogers once said there are 3 kinds of lies. Lies, Damn Lies, and Statistics. To further illustrate your point, you compare your violence numbers with the total population. If you compare it with the more logical (I believe) population of criminals you get a rather different result. In 2018 3011 white people were convicted of murder while 3177 black people were convicted. I submit that the population of criminals (those people far more likely to be encountered by police) is approximately equally distributed across racial lines which makes your conclusion above somewhat doubtful wouldn’t you say? https://ucr.fbi.gov/crime-in-the-u.s/2018/crime-in-the-u.s.-2018/tables/expanded-homicide-data-table-6.xls

    Liked by 1 person

    1. Thanks Gerald,

      I think it depends on what you are trying to argue. The raw numbers vs proportion to the population was in relation to police violence. Police violence can occur whether or not someone is convicted of a crime. So, if we only allow into the data someone with a criminal conviction, this would be incomplete data since anyone without a criminal conviction that was a victim of police violence would be absent. If you are comparing social issues with one another, saying this is the more pressing social issue, then this would be a stronger argument. However, this risks the fallacy of ‘whataboutism’ or ‘whataboutery’. We can consistently recognise different social issues at the same time. And as I mentioned in my original post, the focus was merely on raw numbers vs proportion to the population. If I were to use that data to conclude that the best explanation is racism by police, this would be too early to make such a conclusion. My knowledge of the data in relation to African Americans is limited, but I have better knowledge in respect to Indigenous Australians. So this is why I limited my argument to raw numbers vs proportion to the population and did not attempt to argue any further.

      Thanks again,

      Andrew.

      Like

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