Multiplicity

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Del curso dictado por Johns Hopkins University

Data Science in Real Life

1319 calificaciones

Johns Hopkins University

Data Science in Real Life

1319 calificaciones

Curso 4 de 5 en SpecializationExecutive Data Science

Have you ever had the perfect data science experience? The data pull went perfectly. There were no merging errors or missing data. Hypotheses were clearly defined prior to analyses. Randomization was performed for the treatment of interest. The analytic plan was outlined prior to analysis and followed exactly. The conclusions were clear and actionable decisions were obvious. Has that every happened to you? Of course not. Data analysis in real life is messy. How does one manage a team facing real data analyses? In this one-week course, we contrast the ideal with what happens in real life. By contrasting the ideal, you will learn key concepts that will help you manage real life analyses. This is a focused course designed to rapidly get you up to speed on doing data science in real life. Our goal was to make this as convenient as possible for you without sacrificing any essential content. We've left the technical information aside so that you can focus on managing your team and moving it forward. After completing this course you will know how to: 1, Describe the “perfect” data science experience 2. Identify strengths and weaknesses in experimental designs 3. Describe possible pitfalls when pulling / assembling data and learn solutions for managing data pulls. 4. Challenge statistical modeling assumptions and drive feedback to data analysts 5. Describe common pitfalls in communicating data analyses 6. Get a glimpse into a day in the life of a data analysis manager. The course will be taught at a conceptual level for active managers of data scientists and statisticians. Some key concepts being discussed include: 1. Experimental design, randomization, A/B testing 2. Causal inference, counterfactuals, 3. Strategies for managing data quality. 4. Bias and confounding 5. Contrasting machine learning versus classical statistical inference Course promo: https://www.youtube.com/watch?v=9BIYmw5wnBI Course cover image by Jonathan Gross. Creative Commons BY-ND https://flic.kr/p/q1vudb

De la lección

Introduction, the perfect data science experience

This course is one module, intended to be taken in one week. Please do the course roughly in the order presented. Each lecture has reading and videos. Except for the introductory lecture, every lecture has a 5 question quiz; get 4 out of 5 or better on the quiz.

Multiplicity6:52

Effect size, significance, & modeling7:31

Comparison with benchmark effects4:09

Negative controls5:27

Conoce a los instructores

Brian Caffo, PhD
Professor, Biostatistics
Bloomberg School of Public Health
Jeff Leek, PhD
Associate Professor, Biostatistics
Bloomberg School of Public Health
Roger D. Peng, PhD
Associate Professor, Biostatistics
Bloomberg School of Public Health

Hi, my name is Brian Caffo, and this is the lecture on multiplicity and

multiple comparisons.

So in this lecture we're gonna go fishing.

And as a homework problem, I'd like you to read this XKCD comic, comic number 882.

And it's really a great description of multiple comparisons and

so I won't rehash it here cuz it's a long one, but go read that.

That's part of your homework.

It's pretty funny.

So what is multiple comparisons?

Multiple comparisons is the idea of repeatedly doing

hypothesis tests until one comes up significant.

Okay?

And this sounds nefarious, but

it can be often done with the best of intentions, right?

And multiple comparisons issues can creep in in unexpected ways.

So to just give you an example of multiple comparisons,

that's sort of famous in the field that I work in, is someone took a dead salmon and

put it in a functional magnetic resonance imaging scanner.

And they ran the pixel by pixel analysis,

actually it's three dimensions so it's often called a voxel instead of a pixel.

They ran a voxel by voxel analysis and checked for

a statistical significance at each voxel of whether or

not brain activation existed, and they found significant things.

And the reason they found significant things is because of a lack of

adjustment for multiple comparisons.

And of course, there was no brain activation because it was a dead salmon.

So multiple comparisons, this basically just arises from applying many tests and

focusing on the significant ones.

That's the negative aspect of multiple comparisons, but

basically the idea of multiple comparisons exists just from doing a lot of tests,

even if all the tests are null,

the fact that you will just get some rejections by chance, just by randomness.

So this can arise from fitting too many models,

this can arise from looking at too many quantities of interest,

like in our fish example they just simply looked at too many voxels, or

not too many they just didn't appropriately control for it.

Or I think the nefarious version of multiple comparisons,

the most nefarious version, is fishing expeditions.

And that's basically testing hypotheses, testing everything without a priori

hypotheses and just trying to focus in on those ones that are just significant.

So that's the most negative version of multiple comparisons.

You have a large dataset, you want to explain an outcome.

You look at every variable you have, every combination of variables

with lots of models, pick out the small subset of significant ones, and

report them as if you hadn't looked at all the others.

And I think everyone can agree that there's some problem

with doing something like that.

But I also want to emphasize, multiple comparisons is not intrinsically,

in looking at lots of hypothesis tests, is not intrinsically a bad thing to do.

The bad thing to do is to do a lot of hypothesis tests and not be up front and

account for the fact that you've done a lot of hypothesis tests, and

that's basically the point of this lecture.

And I want to give you the easiest fix possible.

There is a vast literature on multiple comparisons, but the easiest fix uses

an inequality that's named after the mathematician, Bonferroni.

And because it's named after his inequality,

it's called the Bonferroni correction.

And the easiest way to execute a Bonferroni correction is if you

have a bunch of P-values,

simply multiply your P-values by the number of tests that you're performing.

So, for example, if you perform ten tests and

one of the P-values is 0.01, then that P-value is now 0.10.

Okay, cuz you've multiplied it by ten.

So the Bonferroni correction is highly robust and it works in all circumstances.

The only problem is, is it's quite conservative.

So you can imagine, if you perform a thousand tests, you're multiplying all

your p values by a thousand, it's unlikely you're going to get anything significant.

So the result of the Bonferroni correction is often that it is very conservative,

tends to err on the side of declaring fewer things significant.

But it's the easiest thing and then if you want to get into harder versions of

multiple comparisons, you can look into further reading.

You can read up on things like false discovery rates and

things like, we actually had a relatively well-known multiple comparisons paper come

out of this department from the faculty member named David Duncan, and Duncan's

multiple range test is an example in ANOVA of multiple comparisons corrections.

But I think all of those are much harder than the simple Bonferroni correction so

that's what I would go with now.

One thing I would mention about the Bonferroni correction is that

it doesn't give you any guidance on what number to multiply by.

So if you do a bunch of tests,

and some are related and another set are kind of unrelated, they're two groups.

Should you aggregate all of those tests together, and count, say, if you did ten

tests of this sort, and ten tests of this sort for a totally different hypothesis.

Do you aggregate all of them together, and multiply all your p values by 20?

Or you just say, well this is one separate investigation from this

other separate investigation and so we multiply these by ten and these by ten.

The Bonferroni correction gives no guidance on this problem.

The Bonferroni correction doesn't tell you what is the right number of tests to

multiply by, and that is an inherent problem.

So the best advice I can give on that is to be your own critic.

Be a critic of the results that you have and

include all the tests that you think a critic of yours would want you to include

as penalizing for having looked at the data.

Okay, so again, I would just reiterate there's a vast literature on some other

techniques for handling multiple comparisons, but again,

the Bonferroni correction is the simplest and easiest one.

And if you're managing someone who's done a lot of tests or

looked at a lot of models,

fit a lot of models, the easiest thing to do is when you're looking at the output.

And you discuss the number of models they fit and the number of parameters they

looked at, you can just kind of do a kind of rough calculation,

round it up to the easiest number to multiply by, and use that correction.

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