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• Hi, I'm Adriene Hill, and welcome back to Crash Course Statistics.

• Lies. Damn lies. And statistics

• Stats gets a bad rap.

• And sometimes it makes sense why.

• We've talked a lot about how p-values let us know something significant in our data--but

• those p-values and the data behind them can be manipulated.

• Hacked.

• P hacked.

• P-hacking is manipulating data or analyses to artificially get significant p-values.

• Today we're going to take a break from learning new statistical models, and instead look at

• some statistics gone wrong.

• And maybe also some props gone wrong.

• INTRO

• To recap to calculate a p-value, we look at the Null Hypothesis--which is the idea that

• there's no effect.

• This can be no effect of shoe color on the number of steps you walked today, or no effect

• of grams of fat in your diet on energy levels.

• Whatever it is, we set this hypothesis up just so that we can try to shoot it down.

• In the NHST framework we either reject, or fail to reject the null.

• This binary decision process leads us to 4 possible scenarios:

• The null is true and we correctly fail to reject it

• The null is true but we incorrectly reject it.

• The null is false and we correctly reject it.

• The null is false and we incorrectly fail to reject it.

• Out of these four options, scientists who expect to see a relationship are usually hoping

• for this one.

• In NHST, failing to reject the null is a lack of any evidence, not evidence that nothing

• happened.

• So scientists and researchers are incentivised to find something significant.

• Academic journals don't want to publish a result saying: “We don't have convincing

• evidence that chocolate cures cancer but also we don't have convincing evidence that it doesn't".

• Popular websites don't want that either.

• That's like anti-clickbait.

• In science, being able to publish your results is your ticket to job stability, a higher

• salary, and prestige.

• In this quest to achieve positive results, sometimes things can go wrong.

• P-hacking is when analyses are being chosen based on what makes the p-value significant,

• not what's the best analysis plan.

• Statistical tests that look normal on the surface may have been p-hacked.

• And we should be careful when consuming or doing research so that we're not misled

• by p-hacked analyses.

• “P-hackingisn't always malicious.

• It could come from a gap in a researcher's statistical knowledge, a well-intentioned

• belief in a specific scientific theory, or just an honest mistake.

• Regardless of what's behind p-hacking, it's a problem.

• Much of scientific theory is based on p-values.

• Ideally, we should choose which analyses we're going to do before we see the data.

• And even then, we accept that sometimes we'll get a significant result even if there's

• no real effect, just by chance.

• It's a risk we take when we use Null Hypothesis Significance Testing.

• But we don't want researchers to intentionally create effects that look significant, even

• when they're not.

• When scientists p-hack, they're often putting out research results that just aren't real.

• And the ramifications of these incorrect studies can be small--like convincing people that

• eating chocolate will cause weight loss--to very, very serious--like contributing to a

• study that convinced many people to stop vaccinating their kids.

• Analyses can be complicated.

• For example, x-k-c-d had a comic associating jelly beans and acne.

• So you grab a box of jelly beans and get experimenting.

• It turns out that you get a p-value that's greater than 0.05.

• Since your alpha cutoff is 0.05, you fail to reject the null that jelly beans are not

• associated with breakouts.

• But the comic goes on there are different COLORS of jelly beans.

• Maybe it's only one color that's linked with acne!

• So you go off to the lab to test the twenty different colors.

• And the green ones produce a significant p-value!

• But before you run off to the newspapers to tell everyone to stop eating green jelly beans,

• let's think about what happened.

• We know that there's a 5% chance of getting a p-value less than 0.05, even if no color

• of jelly bean is actually linked to acne.

• That's a 1 in 20 chance.

• And we just did 20 separate tests.

• So what's the likelihood here that we'd incorrectly reject the null?

• Turns out with 20 tests--it's way higher than 5%.

• If jelly beans are not linked with acne, then each individual test has a 5% chance of being

• significant, and a 95% chance of not being significant.

• So the probability of having NONE of our 20 tests come up significant is 0.95 to the twentieth

• That means that about 64% of the time, 1 or more of these test will be significant, just

• by chance, even though jelly beans have no effect on acne.

• And 64% is a lot higher than the 5% chance you may have been expecting.

• This inflated Type I error rate is called the Family Wise Error rate.

• When doing multiple related tests, or even multiple follow up comparisons on a significant

• ANOVA test, Family Wise Error rates can go up quite a lot.

• Which means that if the null is true, we're going to get a LOT more significant results

• than our prescribed Type I error rate of 5% implies.

• If you're a researcher who put a lot of heart, time, and effort into doing a study

• similar to our jelly bean one, and you found a non-significant overall effect, that's

• pretty rough. Dissapointing.

• No one is likely to publish your non-results.

• But we don't want to just keep running tests until we find something significant.

• A Cornell food science lab was studying the effects of the price of a buffet on the amount

• people ate at that buffet.

• They set up a buffet and charged half the people full price, and gave the other half

• a 50% discount.

• The experiment tracked what people ate, how much they ate, and who they ate it with, and

• had them fill out a long questionnaire.

• The original hypothesis was that there is an effect of buffet price on the amount that

• people eat.

• But after running their planned analysis, it turned out that there wasn't a statistically

• significant difference.

• member to do some digging and look at all sorts of smaller groups.

• males, females, lunch goers, dinner goers, people sitting alone, people eating in groups

• of 2, people eating in groups of 2+, people who order alcohol, people who order soft drinks,

• people who sit close to buffet, people who sit far away…”

• According to those same emails, they also tested these groups on several different variables

• like “[number of] pieces of pizza, [number of] trips, fill level of plate, did they get

• dessert, did they order a drink...”

• Results from this study were eventually published in 4 different papers.

• And got media attention.

• But one was later retracted and 3 of the papers had corrections issued because of accusations

• of p-hacking and other unethical data practices.

• The fact that there were a few, out of many, statistical tests conducted by this team that

• were statistically significant is no surprise.

• Many researchers have criticized these results.

• Just like in our fake jelly bean experiment, they created a huge number of possible tests.

• And even if buffet price had no effect on the eating habits of buffet goers, we know

• that some, if not many, of these tests were likely to be significant just by chance.

• And the more analyses that were conducted, the more likely finding those fluke results becomes.

• By the time you do 14 separate tests, it's more likely than not that you'll get at

• LEAST one statistically significant result, even if there's nothing there.

• The main problem arises when those few significant results are reported without the context of

• all the non-significant ones.

• Let's pretend that you make firecrackers.

• And you're new to making fire crackers. You're not great at it. And sometimes make mistakes that cause

• the crackers to fizzle when they should goBOOM”.

• You make one batch of 100 firecrackers and only 5 of them work.

• You take those 5 exploded firecrackers (with video proof that they really went off) to

• a business meeting to try to convince some Venture Capitalists to give you some money

• Conveniently, they don't ask whether you made any other failed firecrackers.

• They think you're showing them everything you made.

• And you start to feel a little bad about taking their million dollars.

• Instead, you do the right thing, and tell them that you actually made 100 firecrackers

• and these are just the ones that turned out okay.

• Once they know that 95 of the firecrackers that you made failed, they're not

• going to give you money.

• Multiple statistical tests on the same data are similar.

• Significant results usually indicate to us that something interesting could be happening.

• That's why we use significance tests.

• But if you see only 5 out of 100 tests are significant you're probably going to be

• a bit more suspicious that those significant results are false positives.

• Those 5 good firecrackers may have just been good luck.

• When researchers conduct many statistical tests, but only report the significant ones,

• Depending on how transparent they are, it can even seem like they only ran 5 tests,

• of which 5 were significant.

• There is a way to account for Family Wise Errors.

• The world is complex, and sometimes so are the experiments that we use to explore it.

• While it's important for people doing research to define the hypotheses they're going to

• test before they look at any data, it's understandable that during the course of the

• experiment they may get new ideas.

• One simple way around this is to correct for the inflation in your Family Wise Error rate.

• If you want the overall Type I error rate for all your tests to be 5%, then you can

• One very simple way to do this is to apply a Bonferroni correction.

• Instead of setting a usual threshold--like 0.05--to decide when a p-value is significant

• or non-significant, you take the usual threshold and divide it by the number of tests you're doing.

• If we wanted to test the effect of 5 different health measures on risk of stroke, we would

• take our original threshold--0.05--and divide by 5.

• That leaves us with a new cutoff of 0.01.

• So in order to determine if the effect of hours of exercise--or any of our other 4 measures--has

• a significant effect on your risk of stroke, you would need to have a p-value of below 0.01

• This may seem like a lot of hoopla over a few extra statistical tests, but making sure

• that we limit the likelihood of putting out false research is really important.

• We always want to put out good research, and as much as possible, we want the results we

• publish to be correct.

• If you don't do research yourself, these problems can seem far removed from your everyday

• life, but they still affect you.

• These results might affect the amount of chemicals that are allowed in your food and water, or

• laws that politicians are writing.

• And spotting questionable science means you not have to avoid those green jelly beans.

• Cause green jelly beans are clearly the best.

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

Hi, I'm Adriene Hill, and welcome back to Crash Course Statistics.

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# P-Hacking: Crash Course Statistics #30

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林宜悉 posted on 2020/03/30
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