Statistics 101: Introduction to Hypothesis Formulation

hello thank you for watching and welcome to the next video in my series on basic statistics now a few things before we get started number one if you're watching this video because you're struggling in a class right now I want you to stay positive and keep your head up if you're watching this it means you've accomplished quite a bit already you're very smart and talented and you may have just hit a temporary rough patch now I know with the right amount of hard work practice and patience you can get through it I have faith in you many other people around you have faith in you so so should you number two please feel free to follow me here on YouTube on Twitter or on LinkedIn that way when I upload a new video you know about it and it's always nice to connect with people you'll watch these videos wherever in the world you may be number three on the topic of the video if you'd like it please give it a thumbs up share it with classmates or colleagues or put it on a playlist that does encourage me to keep making them for you on the flipside if you think there's something I can do better please leave a constructive comment below the video and they will try to take those ideas into account when I make new ones for you and finally just keep in mind that these videos are meant for individuals who are relatively new to stats so I'm just going over the basic concepts and I will be doing so in a very slow deliberate manner not only do I want you to understand what's going on but also why so all that being said let's go ahead and get started so this video is the first in a new topic and that topic is hypothesis testing so hypothesis testing is a gigantic part of introductory level stats so we're going to spend many many videos on the topic now this video is just an introduction to try to get your mind in the right framework to begin thinking about hypotheses are form how we ask questions and then how we set up statistical tests to find answers or solutions to those questions so this video is really about trying to get your mind wrapped around the idea of what hypothesis is in the terms of statistics now if you grew up in the u.s. at least sort of when I was in school a hypothesis was always described as an educated guess now for grade school that'll work but in statistics we have a much more formal definition of what a hypothesis is so this is going to be the first video and our efforts to understand exactly what we're doing when we talk about hypothesis tests and stats so all that being said let's go ahead and dive right in so as usual I like to begin my videos with an example and then we'll talk more formally about the topic towards the end so here is our first example a bottled water manufacturers most popular product is a 12 fluid ounce bottle of water which you can see over here on the right now for this problem and due to its inherent superiority which I do agree it is we're going to use the metric system instead so instead of 12 fluid ounces we're going to say 355 milliliters now here's the important bit since this info is actually on the label so if this bottle had its label on it it would say 12 fluid ounces or 355 milliliters because it's on the label we assumed it to be true and that's only important things about hypothesis formulation if we have some bit information like on this water bottle or maybe on a can of soup or on the sticker on a new car that says whatever it's miles per gallon is if it's stated on the product or maybe it's a statistic about the population or something we assume that that is true but the question is is it now as a customer we are concerned that there is at least 355 milliliters in this bottle if there's a little bit more than that that's okay because we're getting a bit more for our money so if there is 360 milliliters in this bottle assuming it would fit we're okay with that because we're at least getting the 355 that is on the label now if we're the manufacturer however we want the volume to be exactly 355 milliliters but why is that well we don't want upset customers if we under fill it so if we're consistently making bottles with 350 milliliters and our customers sort of find out somehow they are not going to be happy because they are paying for less than we say that we are giving them but we also do not want to higher costs or production or overfilling so if we're putting 360 milliliters in each bottle times tens of thousands of bottles that's a lot more water in the bottles than we are actually think we're selling so we're actually putting more water into current bottles instead of that water going into future bottles see what I mean so for the customer we want to know if there's at least 355 milliliters if we're the manufacturer we want it to be exactly 355 if we underfill we're cheating the customer if we overfill we're cheating ourselves because we're creating higher costs or production so as the customer we are assuming there's at least 355 milliliters so we can write that as a little expression so the quantity of water has to be greater than or equal to 355 milliliters for us to be happy again if it's 356 357 that's great guys we're happy we're getting a bit more than we believe we're paying for now for the manufacturer we're assuming exactly 355 milliliters so the quantity of water will be equal to 355 milliliters so you can kind of see what we're doing here we're kind of building the problem outward from the actual text of the problem and then we're starting to slowly put it into sort of a mathematical expression as you can see in this slide and in this case it's about the assumption and again the assumption is an assumption in this case because it's on the label now what about some questions so the customer is saying well is there on average at least 355 milliliters of water in each bottle so that's actually what a customer might say so again the quantity of water greater than or equal to 355 milliliters now what's the manufacturer asking is there on average exactly 355 milliliters of water in each bottle and of course that's our quantity of water equals 355 milliliters so now we're going from the question to sort of a basic mathematical expression to an actual question that we can begin to answer using our statistical techniques and that's one of the important things about hypothesis formulation going from the problem to looking at what the assumptions might be or will talk about claims or assertions later then developing an actual question like this of how we might proceed to answer it so we'll sort of experiment what we set up so we collect 50 bottles from all over the country or the world to randomize the sample in terms of location time manufacturing plant etc we then measure the volume of each bottle in the sample and find the mean volume for those 50 bottles so using those sample means we can test the assumption of 355 milliliters or what we call the status quo so in this case we're using our sample measurements to test the assumption that is stated on the bottle or what we call the status quo so we're sort of using the statistics to back up or test an assumption that's already out there in the world so later when we talk about the null and alternative hypothesis this comes into play so what we're doing here is testing an assumption that's already on the bottle let us take another example and that's an example using the hybrid car engine so an auto manufacturer has developed a new hybrid engine technology it claims reduces fuel consumption while driving in the city the claim is that the new technology improves full fuel efficiency making it better than the old engine that produces 30 miles per gallon so the company will run controlled tests to look for statistical evidence to support the claim that the new engine offers better efficiency than the old model so notice in there I was always stressing the word claim and we're going to talk about the difference between a claim and an assumption because those are two different things and it goes into how we formulate our hypotheses so let's think about what the company is actually claiming here so the company is claiming that the fuel efficiency in the new engine is greater than 30 miles per gallon so it could be 35 miles per gallon it could be 40 miles per gallon it could be 25 miles per gallon that is the claim that we're testing now compare that to the water bottle in the water bottle we knew the status quo we were given an assumption that we were testing here the company is just claiming well this new engine is greater than 30 miles per gallon so the manufacturer is making a claim it was just to test it's not testing an assumption or a status quo that already exists you see the difference so when we're testing this claim we don't know what the answer really is as compared to the previous water bottle example when we were given the assumption we were given the status quo we were given the state of the world and then we were testing that this is much different and when we get into null and alternative hypothesis this is where this idea comes into play so how do we think about hypotheses in general when trying to formulate a statistical hypothesis I want you to ask yourself the following question am i testing an assumption or the status quo that already exists so in this case it was the water bottle the assumption was already stamped on the label of the water bottle or am i testing a claim or an assertion beyond what I already know or can know in this case the hybrid engine so our claim or our assertion with the hybrid engine was that it's fuel consumption was less than the current model or what we consider the old the old model but it's not really out there in the world yet we're making a claim or an assertion that may be true now for the water bottle the ounces or milliliters on the bottle we are assuming is true and that's the difference the assumption of the status quo is assumed to be true the gas mileage on the engine we cannot assume to be true because we're testing if it's different than the current model now if we wanted to test the gas mileage listed on a current car sticker so you go to the car dealership that says this car gets 32 miles per gallon on the interstate that's an assumption that we could then test it's not some assertion or claim that may be true if it's on the sticker we assume that it's the case so then we could go out and test it like we do the water bottle so in your mind just keep these things separate so you can sort of get the distinction between the two am i testing an assumption or the status quo that already exists or am i testing a claim or an assertion about the world beyond what I already know or can know and that's important when we're talking about null hypothesis and the alternative hypothesis which we'll just get into towards the end of this video so here are some basic null and alternative frustrations now I know we haven't really formally defined what these two things are but I would imagine if you're watching this you've at least probably heard of these in your stats class or in a previous class or something like that but again the next video the next series of videos will really pick these apart about what they are but I want to give you some you know some basic reasons why these are in fact so frustrating so formulating hypotheses can be very frustrating a real pain in the to be honest and the reason is is that the null and alternative hypothesis are two opposing roads that lead to the same place you'll sort of see what we mean by that as we go but that's why they can seem so confusing because they are two opposing things that end up leading to the same place now by definition the null and alternative hypothesis are opposites they are mutually exclusive so they both cannot be true so we'll talk about rejecting the null and all that kind of stuff later but just keep in mind that they are opposites they are mutually exclusive the null is either rejected or it's not now only if the null is rejected can we then proceed to the alternative hypothesis and again we'll talk about this in the next video and that's sort of setting up the frustration of what can happen you know when you try to try set them up now researchers can start with either the null or the alternative and then form the other as a compliment to the first so again it just depends on the question we're trying to ask and the question we're trying to you know obviously solve or answer in the end but you can start it either place you can start with a null hypothesis and then form the alternative based on that or you can start with the alternative hypothesis and then form the null based on that so you can start at either place now which to start with largely depends on the point of view of the researcher the context of the problem we're asking and what can or cannot be assumed to be known upfront so what I'm telling you here is that there is no trick there is no easy answer there is no sort of golden key that unlocks null and alternative hypothesis you just have to think you just have to analyze you just have to pick it apart and figure out where you're starting from and of course we're going to do lots of those in upcoming videos so just stay cool stay calm if this is confusing to you because again we're going to do more as we go I'm just trying to set the stage here for what's coming up so what about the null and alternative word salad and here I'm going to sort of put everything on one slide so you can see them as opposed to each other and what they're different so let's think of the null so in the null hypothesis we talked about what we can assume we talked about what the status quo is or what we're given so think of the water-bottle we can assume there is 355 milliliters in it because it's on the label we assume that that's the status quo that that's the way every bottle is and of course we're given that on the actual label physically itself so think of this as this is accepted as true let's test it now what about the alternative so in the alternative hypothesis we might have something that is unknown to us we're making some assertion about the world that we really don't know we're making a claim about something that we really do not know so it's about something that we're unsure of we can not assume to be true or something along those lines so think of this as this might be true let's test it if not the truth is something else so over here on the null side we're saying whatever our null hypothesis is stating we're saying that this is accepted as true let's test it on the alternative hypothesis side we're saying this might be true we're not quite sure let's test it and if not the truth is something else so you might want to look at these two slides we'll let it sink in and then later when we actually talk about forming hypothesis based on the wording and a question you'll see exactly how this works so again I just want to set up the stage sort of prepare you for organ of what we're going to be doing but nuts and bolts of hypothesis formulation and testing in upcoming videos okay so that wraps up our introduction to hypothesis formulation so remember it just in your mind for right now just to keep separate we're talking about null hypothesis and alternative hypothesis the null is all about the things that we assumed to be true or that we are given or that are stated for us and then on the alternative side we're talking about things we're making a claim about something that might be true we're making an assertion about something that might be true so get on the water bottle we have the actual volume stamped on the bottle so we assumed that to be true in the hybrid engine all we're doing is testing whether or not it's fuel consumption is less than the current model or the previous model we don't know what it is we don't even know if it's less or not so we're sort of making some assertion or a claim we're going to test that which may or may not be true okay so just a few reminders if you're watching this video because you were struggling in a class right now I want you stay positive and keep your head up your smart and talented and you may just hit a temporary rough patch please feel free to follow me here on YouTube on Twitter or LinkedIn that way when uploading a video you do know about it and it's always nice for me to connect with people who do watch these videos wherever you may be in the world and finally I just want you to keep in mind that the fact that you're on here trying to learn try to improve yourself trying to better yourself that's what really matters in learning I firmly believe that if you have the right learning process in place the results will take care of themselves so thank you very much for watching I wish you the best of luck in your studies and in your work I look forward to seeing you again next time

Channel: Brandon Foltz

Views: 203,749

Rating: 4.9643354 out of 5

Keywords: formulation of hypothesis, hypothesis testing brandon foltz, hypothesis formulation, brandon foltz hypothesis testing, statistics 101 hypothesis testing, brandon foltz statistics 101, statistics 101 brandon foltz, brandon c foltz, brandon c. foltz, brandon foltz, hypothesis testing, hypothesis, brandon foltz statistics, statistics hypothesis testing, hypothesis testing statistics, hypothesis test, alternative hypothesis, statistics, statistics 101, null hypothesis

Id: JV2-WHzreFo

Length: 21min 9sec (1269 seconds)

Published: Wed Feb 20 2013