What Is Statistics: Crash Course Statistics #1

Summary

In this Crash Course episode on statistics, Adriene Hill introduces the world of probabilities, paradoxes, and data analysis. Through engaging stories, like the tea-tasting experiment and waffle-making salaries, she explains key concepts of statistics, including descriptive and inferential statistics. Viewers learn how statistics help us make sense of data in everyday decisions, from fast food habits to complex policy making. The video emphasizes that while statistics are valuable tools, they require understanding and critical thinking to avoid misleading conclusions.

Takeaways

• 📊 **Statistics Defined**: Statistics is the field of study that involves collecting, analyzing, and making sense of data, as well as the data summaries themselves.
• 🔍 **Purpose of Statistics**: It helps in making informed decisions in uncertain situations, such as predicting consumer behavior or evaluating the effectiveness of a new product.
• 🎩 **Ronald A. Fisher's Contribution**: Fisher's work on experimental design was pivotal in turning statistics into a scientific discipline, providing methods to test hypotheses and make inferences.
• 🧐 **Understanding Data**: Statistics are tools that help us filter and interpret vast amounts of data, allowing us to see patterns and make decisions despite inherent uncertainty.
• 📈 **Descriptive vs. Inferential Statistics**: Descriptive statistics summarize and organize data, while inferential statistics allow us to make predictions and generalizations beyond the data collected.
• 🤔 **Limitations of Surveys**: Surveys can provide insights but may not always reflect true motivations or behaviors due to factors like dishonesty or lack of self-awareness.
• 📉 **Proxy Measurements**: Often, statistics measure a 'proxy' for what we're truly interested in, such as using fast food consumption as a proxy for stress levels.
• 📚 **Educational Use**: The script uses the example of a waffle factory worker using descriptive statistics to negotiate a raise, illustrating how statistics can be applied in real-life scenarios.
• 🎯 **Inferential Applications**: Inferential statistics are crucial for making decisions based on samples, such as estimating the preferences of a population or testing the effectiveness of a new drug.
• ⚖️ **Uncertainty and Decision-Making**: Statistics provide a framework for dealing with uncertainty, but the final decision-making often requires human judgment and context.
• ⚠️ **Caution with Statistics**: Misuse or misunderstanding of statistics can lead to incorrect conclusions, emphasizing the importance of knowing how and when to apply statistical methods.

Q & A

What is the main focus of Crash Course Statistics?

The main focus of Crash Course Statistics is to explore the world of probabilities, paradoxes, and p-values through games, thought experiments, and coin flipping, ultimately teaching viewers how to use statistics and the questions to ask when encountering statistics in everyday life.

How does the course aim to help viewers understand statistics?

The course aims to help viewers understand statistics by explaining their applications in various real-life scenarios, such as predicting TV show preferences, making decisions about education and health services, and interpreting weather forecasts.

What is the historical anecdote mentioned in the script about tea and milk?

The historical anecdote mentioned is about a woman at a 1920s English tea at Cambridge who claimed that tea with milk added last tasted different from tea where the milk was added first. This led to an experiment to test her claim, which was attended by Ronald A. Fisher, a future statistician who contributed significantly to the field of statistics.

What is the significance of Ronald A. Fisher in the field of statistics?

Ronald A. Fisher is significant in the field of statistics because he began work that set the stage for a large portion of statistical theory and practice. His insights into experimental design helped turn statistics into its own scientific discipline.

What are the two meanings of the word 'statistics' as mentioned in the script?

The two meanings of the word 'statistics' are: 1) the field of statistics, which is the study and practice of collecting and analyzing data, and 2) statistics as in facts or summaries of data.

What is the difference between descriptive and inferential statistics?

Descriptive statistics describe and summarize data, such as measures of central tendency and dispersion, while inferential statistics allow us to make conclusions that extend beyond the data we have in hand, such as testing hypotheses and estimating population parameters from samples.

How does the script illustrate the concept of descriptive statistics?

The script illustrates descriptive statistics by using the example of a waffle maker who wants a raise. By calculating the average salary and the spread of salaries at the company, the waffle maker can understand their position relative to others and use this information to negotiate a raise.

What is an example of a question that cannot be directly answered by statistics, as per the script?

An example of a question that cannot be directly answered by statistics is 'Why do people eat fast food?' because it involves understanding the motivations and thoughts of individuals, which cannot be fully captured by survey responses alone.

How does the script explain the concept of using a sample to make inferences about a population?

The script explains the concept by comparing it to grabbing a handful of taffy from a barrel to estimate the proportion of each color, instead of counting every single piece. This is an example of using inferential statistics to make conclusions about the entire population based on a sample.

What is the role of inferential statistics in testing hypotheses?

Inferential statistics play a role in testing hypotheses by allowing us to determine the likelihood that observed differences between groups or the relationship between variables are not due to chance, thus helping us make informed decisions despite uncertainty.

How does the script emphasize the importance of understanding statistics?

The script emphasizes the importance of understanding statistics by comparing them to tools that are only useful when properly used. It highlights that statistics can help us reason but do not eliminate uncertainty, and that misuse can lead to incorrect conclusions.

Outlines

00:00

📊 Introduction to Statistics

Adriene Hill introduces Crash Course Statistics, a journey into the world of probabilities, paradoxes, and p-values. The course aims to explain the use and application of statistics in everyday life, from predicting TV show preferences to deciding on education investments. The importance of understanding statistics is emphasized, as it is omnipresent in decision-making processes. The video uses the historical anecdote of a tea-tasting experiment to illustrate the beginnings of statistical thinking, led by Ronald A. Fisher, who contributed significantly to the field. The distinction between the field of statistics and statistics as data summaries is clarified, setting the stage for exploring what statistics can do, such as answering questions through data analysis and understanding the difference between correlation and causation.

05:00

🔍 Descriptive and Inferential Statistics

This section delves into the two main types of statistics: Descriptive and Inferential. Descriptive statistics are used to summarize and organize data, providing measures of central tendency and dispersion. The example of a waffle factory worker seeking a raise illustrates how descriptive statistics can help understand salary distributions and make informed decisions. Inferential statistics, on the other hand, allow for drawing conclusions and making inferences from samples to entire populations. The concept is exemplified through the candy barrel analogy, where sampling is used to estimate the total population's characteristics. The paragraph also touches on the limitations of statistics in providing definitive answers to certain questions, such as personal motivations, and the importance of understanding statistical tools to make informed decisions despite inherent uncertainties.

10:01

⚖️ The Utility and Limitations of Statistics

The final paragraph discusses the role of statistics as a tool for making sense of information and the importance of knowing both its capabilities and its limitations. Descriptive statistics are likened to filters that make data more digestible, while inferential statistics help in decision-making under uncertainty. The analogy of statistics to chainsaws is used to caution against the misuse of statistical tools, which can lead to incorrect conclusions if not properly understood and applied. Examples of how statistics can aid in various decisions, from personal choices like vacation planning to critical policy decisions, are provided. The paragraph concludes with a reminder that statistics can assist in reasoning but does not replace the need for human judgment, and that statistical literacy is essential to differentiate between what can and cannot be answered through data analysis.

Keywords

💡Statistics

Statistics refers to the field of study that involves the collection, analysis, interpretation, presentation, and organization of data. In the context of the video, statistics are presented as tools that help make sense of data and support decision-making in various aspects of life, from personal choices like what to eat to policy decisions like investing in education. The video emphasizes that statistics are ubiquitous and essential for understanding the world around us.

💡Probability

Probability is the measure of the likelihood that an event will occur. The video mentions probabilities in the context of understanding the likelihood of outcomes, such as guessing the correct order of milk and tea in a cup or being accepted into Harvard. It's a fundamental concept in statistics that helps quantify uncertainty and make informed decisions.

💡P-values

P-values are used in statistical hypothesis testing to determine the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis is true. The video alludes to p-values as part of the statistical jargon that helps in determining the significance of findings, although it does not delve into the specifics of how p-values are calculated or interpreted.

💡Descriptive Statistics

Descriptive statistics summarize and organize data to provide a basic description of the dataset. The video uses the example of a waffle factory to illustrate how descriptive statistics like the average salary can help an employee understand their pay relative to others in the company and the industry. These statistics help in making the data more digestible and understandable.

💡Inferential Statistics

Inferential statistics allow us to make predictions or draw conclusions about a larger group based on a sample. The video explains inferential statistics through the candy barrel analogy, where by sampling a handful of taffy, one can make inferences about the entire barrel's contents. This type of statistics is crucial for making decisions when complete data is not available or feasible to collect.

💡Hypothesis Testing

Hypothesis testing is a process of making inferences about a population by testing a hypothesis. The video touches on this concept when discussing the use of inferential statistics to test ideas, such as whether a new brain vitamin improves IQ. Hypothesis testing is a fundamental part of the scientific method and is used to determine the likelihood of observed results under different assumptions.

💡Central Tendency

Central tendency refers to the center or typical value of a dataset, which can be measured using measures like the mean, median, or mode. The video mentions central tendency in the context of descriptive statistics, explaining how it helps to find the middle of the data, providing a sense of the 'average' value within a dataset.

💡Variability

Variability, or the spread of data, is a measure of how much the data points differ from each other. The video discusses how descriptive statistics can measure how spread out data is, which is crucial for understanding the consistency or diversity within a dataset. Variability is often measured using standard deviation or range.

💡Proxy

A proxy is a variable that is used as a substitute for another variable of interest. In the video, the concept of a proxy is introduced when discussing how people might answer a survey about why they eat fast food. The actual reasons might be complex, and what they report (the proxy) may not fully capture their true motivations, such as convenience or stress.

💡Uncertainty

Uncertainty in statistics refers to the inherent lack of complete knowledge or the unpredictability in the data. The video emphasizes that statistics is a tool for dealing with uncertainty, allowing us to make informed decisions even when we do not have all the information. It's a central theme that statistics helps us navigate the unknown.

💡Data

Data are the raw facts and figures collected through observation and used for analysis. The video discusses how statistics is all about making sense of data, turning it into actionable information. Data is the foundation upon which statistical analysis is built, and the video illustrates various ways in which data is used in everyday life, from personal decisions to policy-making.

Highlights

Introduction to the concept of statistics and its widespread application in daily life, from Harvard admissions to Netflix recommendations.

Explanation of a famous anecdote about Ronald A. Fisher and the tea-tasting experiment, illustrating early experimental design in statistics.

Distinction between two meanings of 'statistics': the field of study and the descriptive summaries of data.

Description of 'proxy' measurements, which are related to the phenomena we want to measure but are not perfect representations.

Explanation of descriptive statistics, including measures of central tendency and data spread, which help summarize large datasets.

Descriptive statistics example with waffle maker salaries, highlighting the importance of central tendency and spread in understanding wage distribution.

Introduction to inferential statistics and how they allow us to draw conclusions beyond the data at hand, using saltwater taffy as an analogy.

Example of using inferential statistics to test hypotheses, such as determining whether a brain vitamin improves IQ.

Clarification of uncertainty in inferential statistics and the role of individuals in making decisions based on statistical evidence.

Statistics as a tool to reason through uncertainty, helping make decisions in various real-world contexts, from healthcare to consumer choices.

Statistics are compared to chainsaws, emphasizing the importance of understanding how to use them correctly to avoid harm or misinterpretation.

Insight into how poor statistical practices can lead to misguided conclusions, akin to chainsaw misuse resulting in injuries.

Discussion on the diverse applications of statistics, from optimizing food aid distribution to evaluating college loan repayment policies.

Acknowledgment of the limitations of statistics, noting that some questions, like personal relationships, are beyond the reach of statistical analysis.

Concluding note about thinking statistically and distinguishing between questions statistics can and cannot answer.

Transcripts

Hi, I’m Adriene Hill, and this is Crash Course Statistics.

Welcome to a world of probabilities, paradoxes and p-values.

There will be games.

And thought experiments.

And coin flipping.

A lot of coin flipping.

Statisticians love to talk about coin flipping.

By the time we finish the course, you’ll know why we use statistics.

And how.

And what questions you ought to be asking when you run across statistics in the world.

Which is ALL THE TIME.

Statistics can help you make a guess whether or not you’re going to be accepted to Harvard.

Marketers use them to sell us gold-lame pants.

Netflix uses stats to predict what show we might want to watch next.

You use statistics when you look at the weather forecast and decide what to wear--dress or jeans.

Policy makers use them to decide whether or not to invest in more early childhood education,

whether or not to spend more on mental health services.

Statistics is all about making sense of data--and figuring out how to put that information to use.

Today, we’re going to answer the question “What IS Statistics?”

INTRO

The legend says that during a late 1920’s English tea at Cambridge, a woman claimed

that a cup of tea with milk added last tasted different than tea where the milk was added first.

The brilliant minds of the day immediately began to think of ways to test her claim.

They organized eight cups of tea in all sorts of patterns to see if she really could tell

the difference between the milk first and tea first cups.

But even after they had seen her guesses, how could they really decide?

Because, she’d get about half the cups right just by randomly guessing either milk or tea.

And even if she really could tell the difference, it’s completely possible that she would

miss a cup or two.

So how could you tell if this woman was actually a tea-savant?

What is the line between lucky tea guesser and tea supertaster?

As fate would have it, future super-statistician and part time potato scientist Ronald A. Fisher

was in attendance.

During his lifetime, Fisher began work that set the stage for a large portion of Statistics

which is the focus of this series.

These statistics can help us make decisions in uncertain situations, tea-taste-tests and beyond.

Fisher’s insights into experimental design helped turn statistics into its own scientific

discipline.

And, although Fisher didn’t publish results of this tea-test...the story has it...the

woman sorted all the tea cups correctly.

Just in case you were curious.

At this point, it’s worth mentioning that there are two related--but separate--meanings

of the word statistics.

We can refer to the field of statistics... which is the study and practice of collecting

and analyzing data.

And we can talk about statistics as in facts about... or summaries... of data.

To answer the question “What is statistics?”, we should first...

...ask the question “What can statistics do?”

Let's say you wake up at your desk after a long evening studying for finals with a cheeseburger

wrapper stuck to your face.

And you wonder... "why do I eat this stuff?

Is fast food controlling my life?"

But then you tell yourself, "No.

It's just super convenient.."

But you're worried, you're thinking about how great it is that McDonald's serves breakfast

all day RIGHT NOW.

But maybe that's normal, finals are this week afterall, so you google the question “Fast

Food consumption” and you find the results of a fast food survey.

The first thing you might do is start asking questions that interest you.

For example, you could ask, Why do people eat fast food?

Do people eat more fast food on the weekend than on weekdays?

Does eating fast food stress me out?

Now that we have some interesting questions, we need to ask ourselves an even more important

one: Can these questions be answered by statistics?

Like I mentioned earlier, statistics are tools for us to use, but they can’t do all the

heavy lifting.

To answer the question about why people eat fast food, you can ask them to fill out a

questionnaire, but you can’t know whether their answers truly represent what they’re

thinking.

Maybe they answer dishonestly because they don’t want to admit that they scarf McDonalds

because they’re too tired to cook dinner, or because they are ashamed to admit they

think Del Taco is delicious, or because none of the given answers represented their reasons,

or they may not really know why they eat fast food.

Armed with the results of the survey, you could tell you that the most common reason

that people reported eating fast food was convenience, or that the average number of

meals they eat out each week is five.

But you’re not truly measuring why people eat so much fast food.

You’re measuring what we call a “proxy”, something that is related to what we want

to measure, but isn’t exactly what we want to measure.

To answer whether people eat more fast food on the weekends, or whether eating it more

than twice a week increases stress, we’d not only need to know how much people are

eating fast food, which our questionnaire asked, but also which days they eat it.

And we’d need an additional measure of “stress”.

You can use statistics to give a good answer about whether you’re going through the drive-thru

more on the weekend, but even the question of whether eating fast food is associated

with higher levels of stress is hard to answer directly.

What is stress and how can we measure it?

And are people eating fast food because they are stressed?

Or does eating all those calories make them stressed?

It’s often the case that some of the most interesting questions are the ones that can’t

be directly answered by statistics--like why people eat fast food.

Instead we find questions that we can answer-- like whether people who eat fast food often

work more than eighty hours a week.

The tools we use to answer these questions are statistics-plural--and there are two main

types: Descriptive and Inferential.

Descriptive statistics, well... they describe what the data show!

Descriptive statistics usually include things like where the middle of the data is--what

statisticians call measures of central tendency--and measures of how spread out the data are.

They take huge amounts of information that may not make much intuitive sense to us, and

compress and summarize them to ...hopefully... give us more useful information.

Let’s go to the the Thought Bubble.

You’ve been working for two years in the local waffle factory.

Day in and day out, you create the golden-browny-iest, tastiest frozen waffles ever created.

The holes are perfectly spaced.

Screaming for syrup.

And now you want a raise.

You deserve a raise.

No one can make a waffle as well as you can.

But how much do you ask for?

An extra thousand dollars?

An extra 5-thousand dollars?

You know you’re valuable, but have no idea what other waffle makers get paid.

So you dig around online and find there’s an entire subreddit devoted to waffle makers.

And someone username “waffleleaks” has posted a spreadsheet of waffle maker salaries.

Now with a quick glance at this huge list of numbers, you can see whether the woman

who works a similar job at the rival frozen waffle company makes more than you.

You can see how much more you are making than the new guy, who’s just now learning to

mix batter.

But you still don’t know much about the paychecks of your waffle company as a whole.

Or the industry.

Cause it turns out there are thousands of waffle makers out there.

And all you see is a list with data points, not patterns that can help you learn more

about how much you might be able to convince the boss to pay you.

Here is where descriptive statistics come in.

You could calculate the average salary at your company as well as how spread out everyone’s

salaries are around that average.

You’d be able to see whether the CEOs’ paychecks are relatively close to the entry-level

batter makers, or incredibly far away.

And how your salary compares to both of their salaries.

You could calculate the average salary of everyone in the industry with your job title.

And see the high and low end of that pay.

And then, armed with those descriptive statistics, you could confidently walk into the waffle

bosses office and demand to be paid for your talents.

Thanks, Thought Bubble.

While descriptive statistics can be great, they only tell us the basics.

Inferential statistics allows us to make….inferences.

(Clever namers, those statisticians.)

Inferential statistics allow us to make conclusions that extend beyond the data we have in hand.

Imagine you have a candy barrel full of salt water taffy.

Some pink, some white, some yellow.

If you wanted to know how many of each color you have, you could count them.

One by one by one.

That’d give you a set of descriptive statistics.

But who has time for all that?

Or, you could grab a giant handful of taffy, and count just those you have pulled out,

which would be using descriptive statics.

If your candy was, in fact, mixed pretty evenly throughout the barrel, and you got a big enough

handful, you could use inferential statistics on that “sample” to estimate the content

of the entire taffy stash.

We ask inferential statistics to do all sorts of much more complicated work for us.

Inferential statistics let us test an idea or a hypothesis.

Like answering whether people in the US under the age of 30 eat more fast food than people

over 30.

We don’t survey EVERY person to answer that question.

Let’s say someone tells you that their new brain vitamin--Smartie-vite--improves your

IQ.

Do you rush out and buy it?

What if they told you that the average IQ increase for Group A-- twenty people who took

Smartie-vite for a month--was two IQ points, and the average IQ increase for Group B--twenty

people who took nothing--was one IQ point.

How about now?

Still not sure?

It is a pretty small difference right]?

Inferential statistics give you the ability to test how likely it is that the two populations

we sampled actually have different IQ increases.

However, it’s up to you, as an individual, to decide whether that’s convincing or not.

And don’t be alarmed if the bar you set isn’t the same in every situation.

It’s entirely okay to have different standards for the questions “does my cat like Fancy

Feast more than Meow Mix?” vs “does this drug cure lung cancer?”.

It might take more evidence to convince you to take a new supposedly cancer curing drug

than to switch cat food brands.

It should take more evidence to convince you to take a new supposedly cancer curing drug

than to switch cat food brands.

With inferential tests, there will always be some degree of uncertainty since it can

only tell you how likely something is or is not.

Your job is is to take that information and use it to make a decision *despite* that uncertainty.

If Statistics were a superhero, it’s batcall would be uncertainty, and it’s tagline would

be “When you don’t know for sure, but doing nothing isn’t an option.”

Statistics are tools.

Statistics help us make sense of the vast amount of information in the world.

Just like our eyes and ears filter out unnecessary stimuli to just give us the best, most useful

stuff, statistics help us filter the loads of data that come at us everyday.

Descriptive statistics make` the data we get more digestible, even though we lose information

about individual data points.

Inferential statistics can help us make decisions about data when there’s uncertainty (like

whether Smartie-vite actually will increase your IQ).

But statistics can’t do all of the work.

They’re here to help us reason, not to reason for us.

They help us see through uncertainty, but they don’t get rid of that uncertainty.

To push our tool analogy a step further.

Statistics, like chainsaws , are pretty useless even dangerous without understanding how they work.

We need to know how to use them and how not to use them.

As we will see in later episodes, statistics done poorly can lead us to some pretty silly

conclusions.

And, chain sawing done poorly leads to about 36-thousand injuries in the US each year.

81% of which are lacerations.

Did you know that almost no one dies because of chainsaw injuries?

Once in a while, but it's very rare.

95% of the people who are hurt by chain saws are male.

This does NOT necessarily tell us that males are significantly worse chain sawers.

Statistics can help us plan a vacation to Bali in December.

They can help us optimize our chances of winning our fantasy football league.

They can help us budget our meal card at college.

Statistics can help us decide whether that additional insurance the guy at Best Buy is

trying to sell us on our new blender is worth it.

Statistics can also help us decide whether or not to go ahead with an invasive heart surgery.

Statistics can help NGOs optimize the amount of food aid they send to refugee camps.

They can help policymakers decide if they should spend more or less money on helping

students pay back their school loans.

And can help you decide how much money you should be comfortable borrowing for college

in the first place.

There is a lot statistics can help us with but some things statistics can’t do.Thinking

statistically means knowing the difference.

So, when your brother says he used statistics to prove that your mom loves him more you

can rest easy knowing the only question he answered is whether she gives him slightly

more ice cream each night.

And you’ve got data suggesting she gives you extra sprinkles.

Thanks for watching. I'll see you next time.