Statistical Thinking in Science: Crash Course Scientific Thinking #2

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 dataset,

was the average age of death in the US for men who died between

2018 and 2023.

But it might be that 79 is the more accurate answer,

which is an extra nine 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.

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 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.

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’s 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 mean, 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 this sample are to the left of

the mode.

So it’s actually more likely

that I’d land on one of the 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 U.S. men die before and after.

That would be 73.

Still relatively close to 70 and 79, but different enough to matter.

Because the median is always the number directly in the middle of a 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 mode 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 “OK, 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 percent 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 predictive…

but 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 is way better to be roughly right than precisely wrong.

Hold on for a moment,

I’m being told that we have a special guest on the way.

It sounds like it’s time for some Sage Advice.

Hi, Hank.

Did you know that women also die?

Yes, I did sadly know that.

Well you were just talking 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 percent.

That’s definitely a big statistic.

It sounds like it, right?

With the old pill,

one in 7,000 people were at risk of developing blood clots.

With the new pill, the risk doubled.

Do you know what it became?

Yeah, if it doubled, I'd guess it went from 1 to 2.

What a great guess!

It sounds like a lot when someone says risk has “increased by 100 percent.”

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.

The absolute risk stayed relatively low.

Right?!

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.

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 analyze relationships in data, like the relationship between sunscreen and skin cancer.

These are known as correlations.

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 quantify 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, and 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 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 cancer.

There is a causal link in the correlation.

But in the case of shark attacks,

it's safe to say 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 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 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 that Doritos 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 “meaningful 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 of everything they want to study.

But stats can help them measure the 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 judgments about our own lives.

In our next episode,

we’re gonna 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 real 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.

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