Statistical Thinking in Science: Crash Course Scientific Thinking #2

0:00 I am going to die eventually, which is pretty important to me personally.

0:04 So, I'd like to know roughly at what age I am most likely to die.

0:08 You might guess something like 70,

0:10 which based on a national data set was the average age of death

0:14 [music] in the US for men who died between 2018 and 2023.

0:19 But it might be that 79 is the more accurate answer, which is an extra 9 years.

0:25 So, how can I make sure I'm using the best number to answer my question?

0:29 Can stats really tell me when I might die?

0:32 And is there a way to look at these numbers and not have an existential crisis?

0:36 Hi, I'm Hank Green and this is Crash Course Scientific Thinking.

0:44 Do not worry, I'm not going to teach you how to do statistics today.

0:48 We have a whole other course about that.

0:50 What we're talking about here is how to make

0:52 sense of the stats you encounter in your everyday life.

0:55 Statistics are vital for so much of what goes on around us,

0:59 from designing video games to creating impactful government health policies.

1:03 But statistics can be misleading.

1:05 It's not because the numbers are lying.

1:07 It's that if we don't understand how the numbers are being used,

1:11 we might get the wrong impression about their meaning.

1:13 Scientists use statistics to understand data,

1:16 but when they're looking at those numbers,

1:18 they have all of the context that goes along with them.

1:20 By the time these stats are reported on in the news,

1:23 they often lose some of that context, which can have big impacts on the ways

1:28 that we see the world as consumers of science news.

1:33 [snorts] Scientists rely on numbers to build knowledge.

1:38 But since they can't measure every person, they use samples,

1:42 smaller groups they can measure to better understand a larger group,

1:45 which means there's always some uncertainty.

1:48 So, while stats could never tell me, Hank Green, exactly when I will die,

1:52 they can tell me when a person like me is most likely to die.

1:56 So, what is the typical age of death for an American man?

1:59 Well, when it comes to statistics,

2:01 there's a few different ways of determining what's typical.

2:04 One of the most common is to find the mean or average,

2:07 the sum of all the numbers in a sample

2:10 divided by how many numbers are in that sample.

2:12 That's where we get the first number from.

2:14 Based on a large sample of residents who died between 2018 and 2023,

2:19 the average or mean age of death of a man in the US is 70.

2:24 But that mean is dragged down by people who died way younger than 70,

2:29 even though there are fewer of them.

2:31 So maybe I don't actually want the average.

2:33 Maybe instead I want to know the most common age of death or the mode.

2:38 That answer is actually way different from the mean.

2:41 The mode is the number that shows up the most in the data,

2:44 which is where we get 79 from.

2:46 But actually, most of the numbers in the sample are to the left of the mode.

2:50 So, it's actually more likely that I'd land on one of the numbers

2:54 under 79 than that I'd land squarely on or after 79.

2:58 So, say then I want to find an age somewhat

3:01 close to the average age when someone like me would die.

3:04 I can look at the numbers in the graph and find the standard deviation,

3:08 which tells me how spread out the other points in the sample are from the mean,

3:13 which in turn can help me figure out how typical that number really is.

3:17 If the standard deviation is small,

3:19 that tells me most people in this sample are

3:22 dying at ages pretty close to the average age.

3:25 Another number that might be helpful is

3:27 the median or the point right in the middle

3:29 of the group where an equal number of US men died before and after.

3:33 And that would be 73.

3:35 Still relatively close to 70 and 79,

3:38 but different enough to matter because the median is always

3:42 the number directly in the middle of the data set.

3:44 It is less likely to be skewed one way or the other the way a mean might be.

3:49 So, it might tell me way more about when American men tend to die.

3:52 though of course it still cannot tell me when I'll die.

3:56 The point is averages like mean, median,

3:58 and mode are different ways of telling you what might be typical.

4:01 But they're way more useful when

4:03 you understand how each one operates differently.

4:06 And they're even more useful when combined with the standard deviation,

4:10 which tells us how typical typical really is.

4:14 There's always a degree of uncertainty when it comes to statistics.

4:18 So, another useful question is, okay, but how certain are we of these stats?

4:23 For a stat to really mean anything,

4:25 I need to know how much confidence to have in it.

4:28 How likely is it that if I ran the numbers again, I'd get those same results?

4:32 For that, I'd need to calculate a confidence interval,

4:35 or a range of numbers that I can expect

4:37 a result to fall within a certain percentage of the time.

4:40 A 95% confidence interval means that if scientists

4:44 repeated the study a 100 times with new samples,

4:46 the statistic they're measuring would fall in that range about 95 times.

4:51 It shows how much that number might vary and how much trust can be put into it.

4:56 A stat with a high confidence interval is quite predictive,

4:59 but it is not perfect.

5:00 So when encountering statistics in the real world,

5:03 it's good to remember that every stat actually has two pieces.

5:07 first the number and second how precisely scientists know that number

5:12 and it is way better to be roughly right than precisely wrong.

5:16 Hold on for a moment.

5:17 I'm being told that we have a special guest on the way.

5:19 It sounds like it's time for some sage advice.

5:31 [music] Hi Hank.

5:32 Did you know that women also die?

5:35 Yes, I did sadly know that.

5:36 You just talk about dudes a lot.

5:38 For example, consider this updated birth control pill.

5:40 According to the news,

5:41 it raised the risk of developing deadly blood clots by 100%.

5:46 That's definitely a big statistic.

5:48 It sounds like it, right?

5:49 With the old pill, 1 in 7,000 people were at risk of developing blood clots.

5:54 With the new pill, the risk doubled.

5:58 Do you know what it became?

5:59 Yeah.

5:59 If it doubled, I'd guess it went from one to two.

6:02 What a great guess.

6:03 It sounds like a lot when someone says risk has increased by 100%.

6:08 But that's just what scientists call the relative risk or how much

6:12 the likelihood of something happening gets

6:14 bigger or smaller relative to something else,

6:17 which can be helpful to know, but it doesn't tell us the whole story.

6:20 For that, we need the absolute risk or the number of people

6:23 actually experiencing an event in relation to the population at risk.

6:27 The absolute risk stayed relatively low, right?

6:30 It increased to 2 in7,000.

6:33 Still important, but people need that context

6:36 you talked about earlier to make informed decisions.

6:38 At the time though, a lot of people only

6:41 learned about this risk in relative terms through the news.

6:45 So, people switched to less effective pregnancy prevention methods.

6:48 And you know what poses a higher risk

6:49 of life-threatening blood clots than the birth control pill?

6:52 Pregnancy.

6:53 So, the more we understand numbers in context,

6:56 the better we'll be at making informed decisions for our lives.

6:59 And that's been today's Sage advice.

7:03 Thanks, Sage.

7:04 Sage is correct.

7:05 Understanding the difference between absolute risk

7:08 and relative risk can help us make

7:10 sense of so many of the stats we encounter in our daily lives.

7:14 Like, how great is my risk of developing cancer if

7:17 I go to the beach every day and don't wear sunscreen?

7:20 Which actually brings me to my next point.

7:22 Scientists often analyze relationships in data like

7:25 the relationship between sunscreen and skin cancer.

7:28 These are known as correlations.

7:30 A correlation is a relationship between two or more variables

7:34 which are basically anything that can be measured or counted.

7:37 A correlation between two variables can be loose or it

7:40 can be tight which we quantify with their R value.

7:43 It's a number fromgative -1 to one

7:45 that shows how tightly two things move together.

7:49 One means a perfect match.

7:51 Negative one means perfect opposite and zero means no connection.

7:55 The simplest kind of correlation is linear between just two variables.

7:59 A correlation can be negative meaning one

8:01 variable gets smaller as the other gets bigger.

8:04 Like for example how higher rates of wearing sunscreen

8:07 correlate to lower rates of skin cancer or it

8:10 can be positive like if say higher rates of ice

8:13 cream sales correlate to higher rates of shark attacks.

8:16 You might have heard the saying correlation doesn't equal causation.

8:19 But there's actually more to it than that.

8:21 Like in the case of sunscreen, there's a lot of good evidence that wearing

8:23 it really does lower the risk of cancer.

8:26 There is a causal link in the correlation.

8:28 But in the case of shark attacks,

8:30 it's safe to say that the ice cream isn't causing them.

8:32 Warm weather is indirectly leading to both.

8:35 In this case, weather is a confounding variable or a factor

8:39 that influences the outcome of a study without being controlled for.

8:42 These can blur what's actually going on in the data

8:45 if scientists don't measure and account for them.

8:47 For example, some studies have shown a positive

8:50 correlation between personal health and visits to the beach.

8:53 But it's hard to know if beaches make people healthier,

8:56 if healthy people are more likely to go to the beach,

8:59 or if there's some third confounding variable like the level

9:02 of wealth that results in both better health and more beach visits.

9:06 And even if scientists do a good job of controlling for all of these variables,

9:10 they still have to ask, is it possible this result was just a fluke in our data?

9:15 In other words, was it statistically significant?

9:17 Statistical significance means the result is strong enough

9:20 that it would be surprising to get by random chance.

9:23 But don't let this phrasing mislead you either.

9:25 In science, significant doesn't mean important.

9:28 Like how I say Doritos are a significant part of my life.

9:31 That means they're important to me.

9:32 But that's different from statistical significance.

9:35 Statistical significance doesn't even necessarily

9:37 mean meaningful in the real world.

9:39 It's more like it would be surprising to get this result at random,

9:44 so we should dig deeper.

9:45 And digging deeper is something we can all do when it comes to statistics.

9:49 And that begins by understanding that there will always be some uncertainty.

9:54 Scientists can't possibly measure every version

9:57 of everything they want to study.

9:59 But stats can help them measure the [music] uncertainty.

10:02 And understanding what numbers can and can't

10:05 tell us about ourselves, each other,

10:07 and the world can help us not only better understand the way that science works,

10:12 but also help us make more informed judgments about [music] our own lives.

10:18 In our next episode, we're going to look at how rare it actually is

10:21 for a single experiment to change our understanding of science.

10:25 I'll see you then.

10:26 This episode of Crash Course Scientific Thinking

10:28 was produced in partnership with HHMI Bio Interactive,

10:31 bringing real science stories to thousands of high

10:34 school and undergrad life [music] science classrooms.

10:36 If you're a teacher, visit their website for resources that explore

10:39 the topics we discussed in this video today.

10:42 Thanks for watching this episode of Crash Course Scientific Thinking,

10:44 which was filmed in Missoula,

10:45 Montana, and was made with the help of all these nice people.

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