Video instructions and help with filling out and completing Who Form 8815 Calculators

Instructions and Help about Who Form 8815 Calculators

Hello welcome to this lesson and mastering statistics we're going to continue working with hypothesis testing in this particular case we're going to start to talk about the concept of a p-value so keep in mind that this right for now is in the context of our large sample hypothesis testing of means so we're doing hypothesis testing with means we're doing large samples for right now and so we have sample size is greater than 30 now up until now we've been doing everything in terms of rejection regions all right and that's basically where the level of significance alpha whether it's left tail right tail or to tail you have to set it all up but essentially you create these boundaries and these are rigid boundaries that you can then look at calculate your test statistic from your data see where it falls and depending on where it falls you can tell if you have rejected the null hypothesis or if you fail to reject it all right well every once in a while when I do teaching I get around to a topic that I get really excited about because p-values in this case is something that gives a lot of students a lot of heartburn a lot of you know scratching your head and trying to figure out what it really means well I'm excited because I can explain this to you I think with some concrete examples and especially after we get through this we do a couple more examples hopefully I believe that you will have very very good understanding what p-values are intuitively number one thing before you do any kind of you know diving into this is I want you to keep in the back your mind that's the purpose of a p-value really the process and sort of the reason that we do it is really no different than what we've been doing before essentially we want to figure out Lin which reject that null hypothesis and when we fail to reject it so before we we were using the rejection regions and figuring out where it falls here we're doing something very similar at first it's going to look totally different but then when I start talking about it enough you'll realize it's exactly the same thing so keep that in back your mind we're using it for the same purpose so we just go down my list make sure I say everything rejection regions work perfectly fine and statistics there's nothing wrong with rejection region but p-values are more common to real research so if you read a real research paper in statistics they do a big study they figure out what the hypothesis is and reject a null hypothesis you're going to see p-values running around there their explanation so it's much much more calm and I'll explain why it's more common in real research and so that's why we learn it here and I've already said this once I'll repeat it again p-values are just another trigger to decide when we should reject that null hypothesis and when we should fail to reject it first I need to write down a definition of what you're going to see in a book what a p-value is so let me get that down for you but just keep in mind don't worry too much about the definition as we write it down I mean I'll kind of explain it but as we go through it you'll get a much more intuitive understanding of what a p-value is that will be much more concrete than what I'm going to write down here the following is what you'll typically see in a book it will say p-values and a book will typically define it as follows this is a good definition there's nothing wrong with it it's just I need to show you some pictures for you to really understand it it's basically the probability and by the way that's called a p-value because it's basically P for probability of obtaining of obtaining a sample I'm going to put in quotes here because I need to explain it more extreme then then the ones observed in your data assuming that the null hypothesis is true the crucial part of what we're reading here is that the concept of a p-value is just a probability and you know what probability has been talking about that for ages in the class probability right it's a decimal between 0 and 1 the probability of obtaining a sample more extreme than the ones observed in your data now what do I mean by observed in your data it's because all of these hypothesis tests involve you know you write down your null hypothesis you write down your alternate and then you go get some data because you need to try to you know just prove the null hypothesis or reject it or whatever so you last 23 or 28 or 99 people what they had for breakfast that morning or whatever that's the data so you collect that data that sample data that you have whether it's 50 samples or 60 samples that's your sample data and you have all of those different values they're typically you're looking at a mean in this case we've been talking about hypothesis testing of means so you're looking at the length of pencils on an assembly line volume of water being filled into you know the bottles of water in a factory or something you're talking about numbers and the hypothesis test that we've been doing so far have been all about the mean values of those things so we go and select some to study and sample to try to test that alternate research hypothesis and we get the values back the p-value is the probability of obtaining a sample more extreme than the ones observed in your data so you have a collection of data