This course aims to help you to draw better statistical inferences from empirical research. First, we will discuss how to correctly interpret p-values, effect sizes, confidence intervals, Bayes Factors, and likelihood ratios, and how these statistics answer different questions you might be interested in. Then, you will learn how to design experiments where the false positive rate is controlled, and how to decide upon the sample size for your study, for example in order to achieve high statistical power. Subsequently, you will learn how to interpret evidence in the scientific literature given widespread publication bias, for example by learning about p-curve analysis. Finally, we will talk about how to do philosophy of science, theory construction, and cumulative science, including how to perform replication studies, why and how to pre-register your experiment, and how to share your results following Open Science principles. In practical, hands on assignments, you will learn how to simulate t-tests to learn which p-values you can expect, calculate likelihood ratio's and get an introduction the binomial Bayesian statistics, and learn about the positive predictive value which expresses the probability published research findings are true. We will experience the problems with optional stopping and learn how to prevent these problems by using sequential analyses. You will calculate effect sizes, see how confidence intervals work through simulations, and practice doing a-priori power analyses. Finally, you will learn how to examine whether the null hypothesis is true using equivalence testing and Bayesian statistics, and how to pre-register a study, and share your data on the Open Science Framework. All videos now have Chinese subtitles. More than 10.000 learners have enrolled so far!
The Null is Always False
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From the course by Eindhoven University of Technology
Improving your statistical inferences
351 ratings
Meet the Instructors
Daniel LakensAssociate Professor
Department of Human-Technology Interaction
[MUSIC]
In this lecture we'll talk about which hypothesis you might want to test.
In science, we often rely on null hypothesis significance testing, but
there are also some people who say that testing the null is very boring,
because the null is always false.
Is this criticism valid, and if so, which hypothesis might we want to test instead?
Let's take a look.
In science, we very often use a null-hypothesis significance test.
Is the data we have observed surprising, assuming that the null-hypothesis is true?
This practice is also often criticized.
One of the critics of this is Cohen who says, the null hypothesis,
taken literally, is always false in the real world.
So if the null is always false, what's the big deal about rejecting it?
So is this really true?
Is the null hypothesis always false?
Well, not really, sometimes with very large sample sizes,
some effects are pretty darn close to zero.
We can take a look in the many labs data set.
Many labs project was a big replication study where 36 different
laboratories all replicated the same set of studies.
So here every line is a different study.
And if we look at the bottom, we see that at least two of these studies with more
than 5,000 participants yield an effect size that is indistinguishable from 0.
Now the question is whether if we would continue to an infinite
number of observations there will be a statistically significant effect.
We don't really know, but
it seems unlikely that this really matters in practice most of the time.
It's important to distinguish between one situation
where the null is a very reasonable hypothesis and
a situation where the null is not a very reasonable hypothesis.
If we use random assignment to conditions and we successfully accomplish this,
then there's no reason to assume that there is a difference between two groups,
unless the manipulation that we use in our experiment actually has an effect.
And if it's possible that the manipulation has no effect and
this is a question you're interested in, then we can test the null.
However, we also sometimes test for measured variables.
An example of a measured variable is gender.
People often enter the lab with a specific gender.
They have the same gender throughout their lives,
so it's not something that you can easily change.
If you want to look at differences between men and women, for
example, then you cannot directly manipulate this.
You can only measure this variable and look at the differences.
Now let's see why this matters.
We can compare the effect of random assignment and
measured variables in the many labs data set.
Let's take a look at one manipulated condition.
In this case, we look at the anchoring condition people are randomly assigned.
Now in anchoring, people receive either a high or a low number as a manipulation.
Then after that,
they all mak the same estimate about something they're uncertain about.
And what the literature shows is that this estimate is influenced by the height
of the anchor.
If they first get a very high number,
their judgment under uncertainty is increased a little bit.
And if they get a very low number, then their estimate is slightly lower.
Now, we can take a look at whether being assigned to the high
anchoring condition or the low anchoring condition
has an effect on any of the other tests that participants did.
So they did a lot of tests.
I'll look at ten different outcomes and see whether the random assignment to
the anchoring condition has an effect on any of these other dependent variables.
We can also take a look at whether there are gender effects.
If we do this, we see that the anchoring condition only has an effect on one
specific dependent variable, the anchoring effect that it's intended to influence.
However, if we look at gender effects in this dataset,
we see that 7 out of the 10 dependent variables here all show a gender effect.
That's a very high number.
So why is this the case?
We don't know.
There are probably things that vary with gender
that also influence the other dependent variables that we're measuring.
Now in all these studies there are also manipulations, and
these were the main interests in the test.
But we see that gender effects are always present or very often present.
So whenever we have a measured variable,
it might be less interesting to test the null.
Very often the null is not true.
It's not a very interesting thing to see.
So why is this the case?
There is systematic noise in your data.
Lykken and Meehl call this the crud factor.
As long as you measure enough observations, these systematic differences
that are present in your data will always yield a statistically significant result.
Now remember that in the many labs projects there were
more than 5,000 participants.
So this is a very large data set.
And these tiny,
systematic noises will lead to differences on your dependent variable.
So these things are not completely interesting.
They might be, but it's very difficult to pinpoint the origin of these effects.
It might be just some sort of noise you're not interested in.
So whenever we can manipulate the factor, the null might be more interesting, but in
these cases of measured variables, there's always the crud factor to keep in mind.
So we can conclude that in principle, all models are wrong, but
some models are useful.
This is a statement by George Box.
What he means is that you can have a model that can be a useful test.
After randomization it's possible, so when you can randomly assign people to
conditions, the null can be a useful and a true hypothesis that you're interested in.
But without randomization, the alternative,
saying that there is an effect is not a very bold prediction.
There very often is an effect.
If the null is rarely true,
then refuting the null says very little about the truth of a theory.
You have to make a better prediction.
You have to do something more than just testing the null hypothesis.
The null hypothesis itself is what we know as a very weak hypothesis.
Let's give an example.
If I predict that it will rain next year in April,
then that's not a very strong hypothesis.
It's very easy to say that this is true.
This is going to happen.
And you won't be impressed if I make this prediction and it turns out to be true.
You can also make a strong prediction, have a strong hypothesis.
If I say that it will rain 7 millimeters on April 2nd next year and
it turns out that this prediction is true,
now that will get me a job as a very good weatherman.
So null hypothesis significance testing rejects the null compared to
any alternative, any other prediction goals.
And that's not very exciting in some situations.
In these situations,
just as with the weather, you want to make a point prediction.
You want to say, this is what I predict.
I just don't predict an effect, but I can predict with my theory,
which is pretty good, an effect of a specific size.
And if you can accomplish this, that's much more impressive.
So confirming strong hypotheses gives a theory greater verisimilitude,
and that's a very difficult word for something that's akin to truth likeness.
It gets you money in the bank.
This is a finding that will increase your confidence in the theory,
and that's what you want.
Now let's play a small game.
I'll ask you what the rule is underlying the numbers that are presented
on the screen.
You see the numbers 2, 4, and 6.
You can test the rule by naming any other number that you think will follow
the rule.
Come up with any number you want, and I will say, yes,
it follows the rule or no, it will not the follow the rule.
Take a moment to think of any number you want.
Which number would you like to test?
Let's say that you come up with the number 8.
This makes sense, right?
You see 2 and you add 2, you get 4, you add 2, you get 6, so
maybe this is the rule, just adding 2.
So if you would test 8, I can say yes, that's a valid number.
It follows the rule.
You might have a different theory.
You might say, well, maybe it's 4 plus the number that comes before it.
So then we have 4 and 2 and 6, and then the next number might be 10.
So, if you want to test the number 10, perfectly fine.
Yes, it also follows the same rule.
But you have not learned a lot.
Is this really the underlying rule?
What would happen if you would say 7?
Now, that's a very interesting question, because in this case,
you're not trying to confirm the rule that you have in your mind.
You're trying to disconfirm, falsify your prediction.
If I say 7, or if you say 7, then I'd say yes, that's also following
the same rule because in this case, the rule might be increasing numbers.
As long as the next number is an increasing number,
it follows the rule that I have.
And you would never discover this if you just tried to confirm the idea that you
have in your head.
So whenever we do a study and we try to confirm our predictions,
then this confirmation bias can be a systematic error in inductive reasoning.
You cannot learn whether your theory is actually true if you
only set out to confirm your predictions.
Instead, you should try to have stronger
theoretical predictions where one of your predictions can be falsified.
One way to do this is to set out test two competing predictions.
Either the one hypothesis is true or the other, but they can't both be true.
So when I find some data, I can say this is at least in line with the one theory
but is not in line with the other theory.
So this is already a more interesting comparison to make.
This is known as strong inference,
crucial experiments that can exclude one alternative hypothesis.
And this is a very good way to have scientific progress.
According to Platt, who talks about strong inference,
you should always ask yourself the question when you design a study.
But what experiment could disprove your hypothesis?
That's the main thing you should set out to do.
Of course you might not feel like disproving all the nice ideas that you
have, but for science this is a very good thing to set out to do.
So we've seen that people sometimes criticize null hypothesis significance
testing because it's a very weak prediction.
Anything goes as long as the null is not true.
And when you don't have random assignment,
even this idea of the null being true is not a very interesting hypothesis to make.
So you should try to set out to make strong predictions,
test competing hypotheses whenever this is possible.
[MUSIC]
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