Confounded Variables; Statistical Significance

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Mindware: Critical Thinking for the Information Age

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University of Michigan

Mindware: Critical Thinking for the Information Age

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Most professions these days require more than general intelligence. They require in addition the ability to collect, analyze and think about data. Personal life is enriched when these same skills are applied to problems in everyday life involving judgment and choice. This course presents basic concepts from statistics, probability, scientific methodology, cognitive psychology and cost-benefit theory and shows how they can be applied to everything from picking one product over another to critiquing media accounts of scientific research. Concepts are defined briefly and breezily and then applied to many examples drawn from business, the media and everyday life. What kinds of things will you learn? Why it’s usually a mistake to interview people for a job. Why it’s highly unlikely that, if your first meal in a new restaurant is excellent, you will find the next meal to be as good. Why economists regularly walk out of movies and leave restaurant food uneaten. Why getting your picture on the cover of Sports Illustrated usually means your next season is going to be a disappointment. Why you might not have a disease even though you’ve tested positive for it. Why you’re never going to know how coffee affects you unless you conduct an experiment in which you flip a coin to determine whether you will have coffee on a given day. Why it might be a mistake to use an office in a building you own as opposed to having your office in someone else’s building. Why you should never keep a stock that’s going down in hopes that it will go back up and prevent you from losing any of your initial investment. Why it is that a great deal of health information presented in the media is misinformation.

À partir de la leçon

Lesson 3: Correlation

It can be extremely difficult to make an accurate assessment of how two variables are related to one another; prior beliefs can be more important than data in estimating the strength of a given relationship. You will learn simple tools to estimate degree of association. You will learn about the nature of illusory correlations and how to avoid them. You will learn about the concepts of confounded variable and self-selection error.

Correlations3:46

The Draw-a-Person Test4:55

Illusory Correlation6:20

Confounded Variables; Statistical Significance9:55

Rencontrer les enseignants

Richard E. Nisbett
Theodore M. Newcomb Distinguished University Professor
Department of Psychology

So, what if we don't have any theories about the connection between variables?

Are we better at getting the relationship right?

Well, in this next demonstration,

I'd like you to look at the names of people as they appear on the screen.

Try to remember as many names as you can.

Were there more names beginning with A or names beginning with Z?

Was there an association between position

of the first letter of the name in the alphabet and the font size for the name?

In other words, were there bigger fonts for names that came early in the alphabet

or smaller fonts for names that came early in the alphabet?

Think about that for a minute.

What you recall?

There was actually a correlation of 0.65 for names and font size.

That's a very, very large correlation.

Later in the alphabet, the bigger the font, but

you don't have a theory about that association.

So you're not likely to see it and that's true, even when the events are very clear

as they were here, couldn't be clearer than there is the name, there is the font.

When the timing is right between the events at a given occasion, in this case,

simultaneously, you see the name simultaneously with the font.

And even when the timing is right across occasions, so

you don't forget the associations you've seen before.

So if you have no expectation at all,

you're very unlikely to see a correlation even though it's staring you in the face.

Now instead of you indicating what the association is,

I'm going to tell you about a few associations.

There all real associations, I have no more tricks.

Your job is to tell me what accounts for the associations.

So in the 1950s, there was found to be an association between the number of

popsicles sold in a given week and the number of new cases of polio.

Why do you suppose that was the case?

Let's think about that for a bit.

Would it have made sense to ban the sale of popsicles?

Couples who spend more time on wedding preparations are less likely to be

divorced.

Why do you suppose that is?

If you have friends who are going to be married,

should you encourage them to spend a lot of time on wedding preparations?

Pipe smokers live longer than most other people.

Why do you suppose that is?

Should you take up pipe smoking?

There are hugely more fatal accidents per vehicle mile for

Ford F 150 pickups than for Volvo station wagons.

Why do you suppose that is?

Should you advise your friends to stay away from Ford pickups?

So, let's have a brief quiz.

See if you can match the driver with the auto.

So, does this suggest and

idea about why the difference might be there in auto accident rates?

Well, for each of the correlations we've just been talking about,

there's a big problem.

The variables in those examples are confounded with other variables.

A variable which is associated with both variables of interest,

X and Y and which could explain the association between them.

The variable of type of automobile is confounding with the variable

of type of owner.

It could be the type of owner that so

heavily influences the fatality rate of different kinds of autos.

And in fact, there are some very strong associations between auto type and

owner type.

Young males have more accidents than other demographic groups and

they're more likely to be driving sports cars, muscle cars, hot rods and pickups.

Middle-aged women who wear sensible shoes are more likely to be driving Buick

sedans, station wagons and Priuses, but those young guys are dangerous no

matter what they drive and the middle ages women are relatively safe.

So with the other findings I was just talking about,

let's play spot the confound.

So we're looking for a C variable, which could be causing both A and B.

In the 1950s, there was found to be an association between the number of

popsicles sold in a given week and the number of new cases of polio.

Why do you suppose that was?

Can you think of a c variable here?

Well, heat would be a pretty good candidate.

People eat popsicles on the summer and they go to swimming pools in the summer.

In swimming pools is where kids were catching polio in the early 50s.

Couples who spend more time on wedding preparations are less

likely to be divorced.

Why do you supposed that might be?

If you have friends who are about to get married,

should you encourage them to spend lots of time on wedding preparations?

What could the C variable be?

Well, in this case, people who spend lots of time on wedding preparations are in

general, different sorts of people than those who have more hurried arrangements.

They tend to be better off financially.

They tend to be older when they get married and

they tend to have know each other longer, and all of those C variables

are associated with greater longevity of the marriage.

Pipe smokers live longer than most other people.

Why do you suppose that is?

Should you take up a pipe?

Well, C variable here is that very different kinds of people

are smoking pipes and other kinds of things or not smoking at all.

People who smoke pipes tend to be in high status occupations.

They lead relatively relaxed lives and they have better access to healthcare.

So, we've started to talk about causality.

Disentangling correlation and causality is going to be the topic of the next lesson.

How do you prove that some relationship is causal?

But first, I want to talk about the statistical concept that applies to both

correlations and experiments.

If you found a correlation between two variables

of 0.35, should you believe if there's a relationship or not?

Well, that depends on whether the correlation is statistically significant.

Statistical significance is the probability that a result at least

as extreme as the one obtained could have occurred given that there is in fact,

no relationship.

That's expressed as p less than some quantity.

For example, p less than 0.05 which means the probability

that the result obtained or even a stronger one could have been

obtained even if there's no relationship is less than 5 in a 100.

So if I say, I've found a correlation of 0.35 between the amount

of fish people eat and the number of television shows they watch,

is that something you should pay attention to if you're interested

in that particular topic of what people eat and what they watch?

Now if the correlation was based on three subjects, you wouldn't be impressed.

you say, I have a friend Joe and he eats lots of fish and

watches lots of TV and Bill doesn't eat fish really at all and

hardly ever watches TV, you're not going to be impressed.

In fact, you would have to have 30 cases in order to reach

0.05 level of significance.

In the next section, we'll be talking about experiments.

Research of a kind that's usually essential

if you want to do what correlations normally can't.

Namely, show whether one of your variables actually exerts

a causal influence on the other.

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