What is a P Value? What does it tell us?

what's up guys it's been a long time I'm back here hopefully to help you guys understand this thing called p-value we're looking at this thing what is a p-value I know it's a puzzle what is this thing I have been interpreting it but I don't quite understand you're going to keep interpreting this thing so it's real important you have this thing down okay you're going to be at the end of your report you're going to write something like with a p-value so low I reject the null there's strong evidence that people prefer Parmesan cheese and their meatballs not Romano whatever you do you need to know what this thing is so when you write a conclusion you interpret the p-value you know what you're saying okay so hopefully this quick example will help you understand all right so I got coin here here's my coin okay right and you're going to say all right we generally made a null and alternative hypothesis a ho and a ha that's what I say make a ho and ha ha make your own you know hypothesis is always the nothing weirds going on hypothesis it's like the boring hypothesis the no trickery the nystrom's not a magician hypothesis so we're going to talk about this coin we're gonna say it's a fair coin and my na hypothesis that everything's hunky-dory fair coin okay the alternative hypothesis is that there's some trickery going on there's something weird there's something trickery I don't even know if that's a real word yeah maybe it is so it opposes this this is saying all the coins fair this is say there's some trickery going on nice just being silly it's a trick coin but you're not going to go with the trick coin until you have enough evidence so that's kind of like this whole no alternative thing is you go with this oh it's a fair coin you're sassoon things are okay until you like whoa what what is that and that p-value is the whoa what is that the p-value is like the peculiar f that was peculiar so you think about wow that's really peculiar oh that's like a really low p-value and something's like really weird you weren't expecting it to happen randomly that's the low p-value so we're gonna see what happens we go I flip a coin mm-hmm tails its tails so let's here's our observation and then I'll put a p-value here and what happened I am I observed one tail now here's a question do you think that this is a trick coin is a trick coin is there some trickery going on or do you think it's a fair coin you're probably saying I don't have enough information well you do here's your information every single time I flipped it it landed on tails but what you're going to say is oh if the null were true if that was a fair coin if it were a fair coin that happens half the time Anas but I'm not convinced it to trick coin right now I don't think there's any trickery going on and that's good reasoning but that's what that p-value is it's the likelihood of this thing occurring if this no we're true if it were a fair coin okay I flip it again oh that tails again I can't believe it so tails twice to tails now do you believe that it's a trick coin do you believe something trickery is going on you'll say no man that'll happen like one out of every that this happens about half the time this happens about one out of every four times it flip a coin its way so it's about 0.25 p-value I notice think about this the p-value is the likelihood of what you saw happening if the null were true if it were a fair coin because if this were a trick coin meaning a two-tailed tails on both sides how often would you see two tails in a row all the time okay so the p-value is assuming that it's a fair coin it's assuming the null is true let's see when I do it again you're good catch of tails again can you believe tails again I can't believe this three tails in a row and in my class when I'm doing this I'll say so anybody think this is a trick coin and everyone will be like this so then I'll flip it again this happens about 12 and a half the time um flip it again oh my goodness but it happened to land right on tails again look at this tails again so we see four tails in a row and that happens randomly about six percent of the time and after the fourth tail you'll see heads like you know churning it's great when students are doing that they're actually thinking they're like well is this kind of weird good you're saying that's peculiar that's your p-value okay notice what's happened to the p1 from point fifty point two five it's getting lower notice as that p-value gets low it's not getting more peculiar and this is when I say do you think there's a trick coin do you think of up this up and this is when students you'll see a hand go up I think you're up to something I'll say huh I like it like your reasoning and I'll do it again 5 tails 5 tails and right is about 3% of the time with a fair coin that 5th Dale you start saying coo coo coo coo coo people start saying I think that's weird and then I do it again the six tails which only happens about 1% of one and a half percent of the time whatever uh everyone's going okay that's weird now the deal is yes it's a two tailed coin okay you buy a two tailed coin at a magic shop and it is trickery there's definitely some trickery okay I'm never ever show it I will not show the two-tailed coin because in hypothesis testing you never really know you just have to go with your gut but the importance is notice naturally what kind of happens you start feeling it and everybody that starts when you start seeing something right around this area right around here this is lay my hands up I think it's weird vein and that happens when the p-value falls below 0.05 when the p-value gets below 0.05 that's when you start getting a little a little bit sour feel like looks weird it's little strange I don't get it oh that's natural think about a card trick what what p-value makes you go woah it's like a WOW factor if I give you cards and I'm like hair pick a card and you you pull up a card you like hmm and I say hmm that's a red card you're not gonna be like oh my god oh my god II guess my card that's not a why you're not wild with a red card but if I'm like oh it's a heart that's a little more of a WOW factor but you're probably not gonna hire me as a magician at your cousin's birthday party right so what do you need to see in order for a card trick to be like wow I need to shuffle it around I know shuffling around and let you hand you one and say dude you've got the King of Hearts and that's when you're like wow he guessed the king of hearts now the p-value of that the likelihood of me just guessing that randomly if I didn't there was no trickery is 1 in 52 that's like at point O 2 that's like a 2% chance that's a low p-value so look what happens use the thing starts getting low when the p-value gets low you start guessing whether or not it's a fair coin right because that's what people say I know a magic trick the first thing you think is like a proven show me please because you want it you want the p-value to get lo signa oh he's the magician right this is what's happening think of the logic behind the p-value just think about it notice what happened if this were a fair coin the like that have you seen five tails in a row is so unlikely to happen randomly it was so unlikely that you start saying you start wanting to go with the alternative when the p-value gets low when it's unlikely to have happen randomly if the null were true you start saying that was so unlikely to happen randomly if the know were true that I don't think it did happen randomly I think the null is actually false basically you say if the null were true this is the this is how likely what happened randomly which is wicked on random it's unlikely it's so unlikely to happen randomly you don't think it was random meaning when you say that you say it was so unlikely to happen randomly if this were true I don't think this is true I think you've got a trick corny and I do I think you know a magic trick that some trickery and it is that's how hypothesis testing goes so when you see and you interpret your p-value make sure what you're saying is it's the likelihood of this event occurring just randomly if the null were true so when you say the p-value is low I'm going to reject the null you say I'm working it was so unlikely to have happen randomly if this were true that I don't believe it you're starting to believe it's a trick coin you're starting to raise your hand and clasp me like I think there's something fishy going on okay and then that's when you start thinking man that's weird and it happens all the time all the stuff you know how do they prove on these big companies of causing cancer in the in the water supply it's because it's unlikely that half the population of a small town just randomly going to get some sort of cancer because you look at how it happens random they say that if there were nothing fishy going on there that streams it was like a one-in-a-million chance of happening just randomly that I don't think it was random there's some serious pollution going on and someone's going to pay for it okay so you have to understand that the reason why we study randomness at all and the reason why when you do your hypothesis tests and you're having you have that randomness in there you have to make sure that something done randomly if we study randomness so we know how random this happens so we can say just this that that was so unlikely to have happen randomly that I don't think it was random at all there was something weird going on and I'm rejecting that no and I'm going with the alternative and so should you yeah

Channel: MrNystrom

Views: 573,148

Rating: 4.8608437 out of 5

Keywords: Ap, stats, value, statistics, apstatsguy, nystrom, easy, understand, what, is, p value, one, proportion, hypothesis, test, testing, inference, ap statistics, ap stats, reject, retain, null, alsternative, alternative

Id: -MKT3yLDkqk

Length: 10min 30sec (630 seconds)

Published: Wed Feb 18 2015