The Importance of Numbers to Support Arguments

Something happened recently that got me thinking about how numbers are often used to mislead people. I’ll talk more about it in this post.

Table with numbers

At the start of this month, Amazon announced that it was increasing the minimum wage of all its workers to $15 an hour. I read the news and thought “That’s great! I’ve seen a lot of people online complain about the low minimum wage. This means they finally get a well-deserved pay-raise, especially due to the increased costs of living nowadays”.

But not soon after, I noticed a lot of people complaining about it, which confused me. As I dug further, I found out why: Amazon was removing the monthly bonuses and stock awards provided to those workers. And here comes the crux of my argument: When you make an argument about something, do not mislead people by providing them with half the information. I never knew Amazon minimum wage workers received these bonuses or these stock rewards.

Note that I am not saying that their argument is invalid. All I am stating is that intentionally leaving information out for the fear that it might weaken your argument is disingenuous. And this is exactly what happened here.

Getting exact numbers for this was also difficult. From what I could gather, the bonuses were around $150 a month, and could be as high as $200 a month, depending on how well the building performed during that time period. The staff bonus doubles for the holiday season. Additionally, the workers would get somewhere between 2-4 shares per year, depending on the share price.

Again, the amount is not that significant, especially to those that are living on minimum wage. Having a greater guaranteed income is much better than a chance at a nice payoff from the stock. But my point still stands: people who complained about the minimum wage always (intentionally) left out the fact that they were getting other kickbacks from the company. Serves them right.

This is not the first time numbers have been used to mislead people. Numbers hold a lot of power, because they portray precision and confidence. Here’s a really interesting example for you.

Consider a disease exists without symptoms. There exists a test with a 99% accuracy for this disease. Someone gets tested, and their result comes up positive. What is the probability that they have that disease? You’d think the answer would be 99%, but you’d be wrong. This is because it actually depends on how rare the disease is. The more common the disease is, the higher the chance that this test is correct.

The best way to see this is to throw numbers at the scenario. So, consider a population of 1,000,000 people. Assume that this disease affects 1 person in 10,000 people. So, in the population, 100 people will have the disease and the rest not.

Now, it’s time for a little table as we test each one. Remember that the test is 99% accurate. This means that there is a chance for a false positive for Non-infected people and a false-negative for infected people:

Not Infected (999900 total) Infected (100 total)
Test Negative 989901 1
Test Positive 9999 99

Now look at that highlighted row. This is the total percentage of people that get a positive result for having the disease. So, if a test result comes up positive, there is roughly only a 1% chance the person actually has the disease.

And the above demonstrates how important having complete information about any situation is. By omitting the rarity of the disease, you can come to vastly different assumptions about the test result.

The same applies to every day matters too. Always make sure you get as complete of a picture as possible before making a decision or formulating an opinion. In the age of so much misinformation, being aware can potentially save you from life-ruining decisions.

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