Hank Green: I am going to die eventually, which is pretty important to me personally. So, I'd like to know roughly at what age I am most likely to die. 

You might guess something like 70, which based on a national data set, was the average age of death in the US for men who died between 2018 and 2023. It might be that 79 is the more accurate answer, which is an extra 9 years. 

So, how can I make sure I'm using the best number to answer my question? Can stats really tell me when I might die? And is there a way to look at these numbers and not have an existential crisis?

Hi, I'm Hank Green, and this is Crash Course: Scientific Thinking. 

[Theme music]

Do not worry, I'm not going to teach you how to do statistics today. We have a whole other course about that. What we're talking about here is how to make sense of the stats you encounter in your everyday life. 

Statistics are vital for so much of what goes on around us, from designing video games to creating impactful government health policies. 

But statistics can be misleading. It's not because the numbers are lying. It's that if we don't understand how the numbers are being used, we might get the wrong impression about their meaning. 

Scientists use statistics to understand data, but when they're looking at those numbers, they have all of the context that goes along with them.

By the time these stats are reported on in the news, they often lose some of that context, which can have big impacts on the ways that we see the world as consumers of science news.

[Drinks contents of test tube; sign warns "do not consume science experiments"]

Scientists rely on numbers to build knowledge. But since they can't measure every person, they use samples, smaller groups they can measure to better understand a larger group, which means there's always some uncertainty. 

So, while stats could never tell me, Hank Green, exactly when I will die, they can tell me when a person like me is most likely to die. 

So, what is the typical age of death for an American man?

Well, when it comes to statistics, there's a few different ways of determining what's typical. 

One of the most common is to find the meaning or average, the sum of all the numbers in a sample divided by how many numbers are in that sample. 

That's where we get the first number from. 

Based on a large sample of residents who died between 2018 and 2023, the average or mean age of death of a man in the US is 70.

But that mean is dragged down by people who died way younger than 70, even though there are fewer of them.

So maybe I don't actually want the average. Maybe instead I want to know the most common age of death, or the mode. That answer is actually way different from the mean. 

The mode is the number that shows up the most in the data, which is where we get 79 from. 

But actually, most of the numbers in the sample are to the left of the mode. So, it's actually more likely that I'd land on one of numbers under 79 than that I'd land squarely on or after 79. 

So, say then I want to find an age somewhat close to the average age when someone like me would die.

I can look at the numbers in the graph and find the standard deviation, which tells me how spread out the other points in the sample are from the mean, which in turn can help me figure out how typical that number really is. 

If the standard deviation is small, that tells me most people in this sample are dying at ages pretty close to the average age. 

Another number that might be helpful is the median, or the point right in the middle of the group where an equal number of US men died before and after.

And that would be 73. Still relatively close to 70 and 79, but different different enough to matter, because the median is always the number directly in the middle of the data set. It is less likely to be skewed one way or the other, the way a mean might be. 

So, it might tell me way more about when American men tend to die. Though of course it still cannot tell me when I'll die. 

The point is, averages like mean, median and more are different ways of telling you what might be typical. 

But they're way more useful when you understand how each one operates differently. And they're even more useful when combined with the standard deviation, which tells us how typical typical really is.

There's always a degree of uncertainty when it comes to statistics. 

So, another useful question is, "okay, but how certain are we of these stats?"

For a stat to really mean anything, I need to know how much confidence to have in it. How likely is it that if I ran the numbers again, I'd get those same results?

For that, I'd need to calculate a confidence interval, or a range of numbers that I can expect a result to fall within a certain percentage of the time. 

A 95% confidence interval means that if scientists repeated the study 100 times with new samples, the statistic they're measuring would fall in that range about 95 times. It shows how much that number might vary and how much trust can be put into it. 

A stat with a high confidence interval is quite predictable, it is not perfect.

So when encountering statistics in the real world, it's good to remember that every stat actually has two pieces. First, the number and second, how precisely scientists know that number. And it’s way better to be roughly right than precisely wrong. 

Hold on for a moment. I'm being told rhat we have a special guest on the way. It sounds like it's time for some sage advice. 

[Title card: "Sage Advice"]

Sage: Hi, Hank. Did you know that women also die?

Hank: Yes, I did sadly know that. 

Sage: You just talk about dudes a lot. 

For example, consider this updated birth control pill. According to the news, it raised the risk of developing deadly blood clots by 100%.

Hank: That's definitely a big statistic. 

Sage: It sounds like it, right? With the old pill, 1 in 7000 people were at risk of developing blood clots. With the new pill, the risk doubled. Do you know what it became?

Hank: Yeah. If it doubled, I guess it went from one to two. 

Sage: What a great guess.

It sounds like a lot when someone says risk has increased by 100%. But that's just what scientists call the relative risk, or how much the likelihood of something happening gets bigger or smaller relative to something else.

Which can be helpful to know, but it doesn't tell us the whole story. For that, we need the absolute risk, or the number of people actually experiencing an event in relation to the population at risk. 

Hank: The absolute risk stayed relatively low, right? 

Sage: It increased to 2 in 7000. Still important, but people need that context you talked about earlier to make informed decisions. 

At the time though, a lot of people only learned about this risk in relative terms through the news. So people switched to less effective pregnancy prevention methods. 

And you know what poses a higher risk of life-threatening blood clots than the birth control pill? Pregnancy. 

So, the more we understand numbers in context, the better we'll be at making informed decisions for our lives. And that's been today's Sage advice. 

[Title card]

Hsnk: Thanks, Sage. 

Sage is correct. Understanding the difference between absolute risk and relative risk can help us make sense of so many of the stats we encounter in our daily lives. 

Like, how great is my risk of developing cancer if I go to the beach every day and don't wear sunscreen? 

Which actually brings me to my next point. Scientists often analyse relationships in data, like the relationship between sunscreen and skin cancer. These are known as correlation. 

A correlation is a relationship between two or more variables, which are basically anything that can be measured or counted.

A correlation between two variables can be loose or it can be tight, which we qualify with their R-value. It's a number from -1 to 1, that shows how tightly two things move together. 1 means a perfect match. -1 means perfect opposite. 0 means no connection. 

The simplest kind of correlation is linear between just two variables.

A correlation can be negative, meaning one variable gets smaller as the other gets bigger. Like for example how higher rates of wearing sunscreen correlate to lower rates of skin cancer. 

Or, it can be positive, like if say higher rates of ice cream sales correlate to higher rates of shark attacks.

You might have heard the saying, "correlation doesn't equal causation". But there's actually more to it than that. 

Like in the case of sunscreen, there's a lot of good evidence that wearing it really does lower the risk of causal link in the correlation. 

But in the case of shark attacks, it's safe to say that the ice cream isn't causing them. Warm weather is indirectly leading to both.

In this case, weather is a confounding variable, or a factor that influences the outcome of a study without being controlled for. 

These can blur what's actually going on in the data if scientists don't measure and account for them. 

For example, some studies have shown a positive correlation between personal health and visits to the beach.

But it's hard to know if beaches make people healthier, if healthy people are more likely to go to the beach, or if there's some third confounding variable, like the level of wealth that results in both better health and more beach visits. 

And even if scientists do a good job of controlling for all of these variables, they still have to ask, is it possible this result was just a fluke in our data? 

In other words, was it statistically significant?

Statistical significance means the result is strong enough that it would not be surprising to get by random chance. 

But don't let this phrasing mislead you, either. In science, significant doesn’t mean important, like how I say Dorito's are a significant part of my life, that means they're important to me. But that's different from statistical significance. 

Statistical significance doesn’t even necessarily mean in the real world. It's more like it would be surprising to get this result at random, so we should dig deeper.

And digging deeper is something we can all do when it comes to statistics. And that begins by understanding that there will always be some uncertainty. 

Scientists can't possibly measure every version they want to study. But stats can help them measure uncertainty. 

And understanding what numbers can and can't tell us about ourselves, each other, and the world can help us not only better understand the way that science works, but also help us make more informed judgements about our own lives. 

In our next episode, we're going to look at how rare it actually is for a single experiment to change our understanding of science. I'll see you then. 

This episode of Crash Course: Scientific Thinking was produced in partnership with HHMI BioInteractive, bringing science stories to thousands of high school and undergrad life science classrooms. If you're a teacher, visit their website for resources that explore the topics we discussed in this video today. 

Thanks for watching this episode of Crash Course: Scientific Thinking, which was filmed in Missoula, Montana, and was made with the help of all these nice people. If you want to help keep Crash Course free for everyone forever, you can join our community on Patreon.