5 ms·

P-Values can be pretty unintuitive to people unfamiliar, but can readily be explained I think. I do think that this book did an excellent job of explaining it:

P-Values can be pretty unintuitive to people unfamiliar, but can readily be explained I think. I do think that this book did an excellent job of explaining it: What Is a P-Value Anyway? http://www.pearsonhighered.com/vickers/ http://www.pearsonhighered.com/vickers/ Excerpt (starts at p.57 in the link above): [I]f you do nothing else, please try to remember the following sentence: “the p-value is the probability that the data would be at least as extreme as those observed, if the null hypothesis were true.” Though I’d prefer that you also understood it—about which, teeth brushing. I have three young children. In the evening, before we get to bedtime stories (bedtime stories being a nice way to end the day), we have to persuade them all to bathe, use the toilet, clean their teeth, change into pajamas, get their clothes ready for the next day and then actually get into bed (the persuading part being a nice way to go crazy). My five-year-old can often be found sitting on his bed, fully dressed, claiming to have clean teeth. The give-away is the bone dry toothbrush: he says that he has brushed his teeth, I tell him that he couldn’t have. My reasoning here goes like this: the toothbrush is dry; it is unlikely that the toothbrush would be dry if my son had cleaned his teeth; therefore he hasn’t cleaned his teeth. Or using statistician-speak: here are the data (a dry toothbrush); here is a hypothesis (my son has cleaned his teeth); the data would be unusual if the hypothesis were true, therefore we should reject the hypothesis. [...] So here is what to parrot when we run into each other at a bar and I still haven’t managed to work out any new party tricks: “The p-value is the probability that the data would be at least as extreme as those observed, if the null hypothesis were true.” When I recover from shock, you can explain it to me in terms of a toothbrush (“The probability of the toothbrush being dry if you’ve just cleaned your teeth”).

nonbel 11y ago
>"My reasoning here goes like this: the toothbrush is dry; it is unlikely that the toothbrush would be dry if my son had cleaned his teeth; therefore he hasn’t cleaned his teeth." I don't think this works so well because you are jumping from a qualitative statement (dry or not dry) to a quantitative ("at least as extreme").
sbov 11y ago
This is way too much for the layman and full of mathematical language. What is null hypothesis? What is "at least as extreme as"? What is probability? Nevermind that the null hypothesis forces us to think in double negatives, which isn't the most intuitive. It also isn't clear to me how you would apply your example given how most p-values are used. I read an article that says exercising makes you richer with a 95% confidence. So, as a layman, if I attempt to apply your example, it leads me directly into a common p-value mistake: the probability of me becoming richer if I exercise. 95%, right? Wrong!
- elbigbad 11y ago
  To be fair, this isn't "my" example. I selected it from the book above as a pretty good example from the book targeting p-value, the subject of this thread. It is part of a larger scheme of examples and explanations in the book. The book itself goes through and clears up things like "null hypothesis" and "at least as extreme as" using other examples. That one quote wasn't really meant to take the layman from zero to "p-value master" in a handful of sentences.
- ewzimm 11y ago
  I'm having a hard time understanding why p-values are so hard to explain without resorting to jargon... it seems very intuitive to me, and none of these examples really put it in context. I'd explain it like this: It's easy to lie with statistics if you take them out of context. Maybe I have an idea that drinking flouridated water causes cancer, so I take a survey and find that 40% of people who drink flouridated water develop cancer. That number is meaningless without knowing how likely it is for people who don't drink it to develop cancer, which is about 40%, so the numbers match up 1:1, completely normal. In this case, 1 is the p-value, and it gives you a starting point for developing an experiment.
  - nonbel 11y ago
    >"That number is meaningless without knowing how likely it is for people who don't drink it to develop cancer, which is about 40%. That's the p-value, and it gives you a starting point for developing an experiment." That is the frequency of cancer given not drinking fluoridated water. That is not a p-value.

nonbel 11y ago

>"My reasoning here goes like this: the toothbrush is dry; it is unlikely that the toothbrush would be dry if my son had cleaned his teeth; therefore he hasn’t cleaned his teeth." I don't think this works so well because you are jumping from a qualitative statement (dry or not dry) to a quantitative ("at least as extreme").

sbov 11y ago

This is way too much for the layman and full of mathematical language. What is null hypothesis? What is "at least as extreme as"? What is probability? Nevermind that the null hypothesis forces us to think in double negatives, which isn't the most intuitive. It also isn't clear to me how you would apply your example given how most p-values are used. I read an article that says exercising makes you richer with a 95% confidence. So, as a layman, if I attempt to apply your example, it leads me directly into a common p-value mistake: the probability of me becoming richer if I exercise. 95%, right? Wrong!

elbigbad 11y ago
To be fair, this isn't "my" example. I selected it from the book above as a pretty good example from the book targeting p-value, the subject of this thread. It is part of a larger scheme of examples and explanations in the book. The book itself goes through and clears up things like "null hypothesis" and "at least as extreme as" using other examples. That one quote wasn't really meant to take the layman from zero to "p-value master" in a handful of sentences.
ewzimm 11y ago
I'm having a hard time understanding why p-values are so hard to explain without resorting to jargon... it seems very intuitive to me, and none of these examples really put it in context. I'd explain it like this: It's easy to lie with statistics if you take them out of context. Maybe I have an idea that drinking flouridated water causes cancer, so I take a survey and find that 40% of people who drink flouridated water develop cancer. That number is meaningless without knowing how likely it is for people who don't drink it to develop cancer, which is about 40%, so the numbers match up 1:1, completely normal. In this case, 1 is the p-value, and it gives you a starting point for developing an experiment.
- nonbel 11y ago
  >"That number is meaningless without knowing how likely it is for people who don't drink it to develop cancer, which is about 40%. That's the p-value, and it gives you a starting point for developing an experiment." That is the frequency of cancer given not drinking fluoridated water. That is not a p-value.