How To Know Which Statistical Test To Use For Hypothesis Testing

[Music] so in most statistics classes students are supposed to learn a dozen or so statistical tests and a really great question I get from my students every semester is how do I know which tests I'm supposed to use and that's a great question considering there's like a dozen of them and if you just learn all of the different statistical tests then you end up leaving a statistics class thinking I mean I know all these tests but I just don't know which one to use and when so this lecture is going to be dedicated to introducing the different types of statistics tests specifically the ones that are typically involved in undergraduate level statistics classes and when to use them so I'm going to first run through all the different tests that we will be covering throughout this course and then I'm going to analyze when to use which one so there are one sample z-test for the mean one sample t-test for the mean one sample z-test for proportions one sample t-test for proportions two sample two independent sample tests for the mean two independent sample tests for proportions matched or paired sample tests chi-squared tests regression tests and one-way anova tests that's a huge list of tests and it could kind of be overwhelming and I understand that it took me a while to be able to understand which one to use and when so in order to do that I'm gonna break down all these different tests explain what they are what their purposes are and that should hopefully clarify when to use which test so let's start with the first category of tests there are two tests in this category this is the one sample z-test for the mean and there is the one sample she tests that's not how you spell test for the mean now these two tests are really similar to each other I'm gonna break down the differences in a second here but let me first address what this does suppose Apple claims that the average age of their user was like 45 now you and I both know that's not correct so suppose we gather like a sample of like a thousand Apple users and we find the average age we have this average I want to clarify that we are calculating a mean here and we're trying to compare that mean to what the scientific community believes in so the scientific community right I guess in this case Apple believes that the average is 45 and we're trying to prove them wrong we're trying to say now you say it's 45 I don't think it's 45 I actually think it's not 45 I think it might be around 20-something right so you gathered a large sample you calculate the average you notice the average is different than 45 and then these tests will allow you to determine if the difference between the averages the average that you calculate with your sample and apples claim which is 45 these two tests will determine whether that those two numbers are different from each other now what's the difference between a Z test and a T test it's a great question pretty much nothing um so let me explain what I mean by that first off Z tests in general are terrible they suck they make the math a little bit easier but no one should ever use a z-test if you ever see z-test in general just avoid them like the plague because they make assumptions that should never be made in the first place typically T tests are way better if I ever read a research paper that involves any statistics test I will never see a Z test and if I do I'm gonna start questioning the authority of what the paper is trying to say so we're gonna talk about this later on but just for now I'll just understand that the one sample T test for the mean is the purpose of that is to determine whether your sample average is statistically significant than what everyone thinks the average is now let's move on to the next category the next category is very similar it's the one one sample Z test for in this case not the mean but the for a proportion now what's the difference between a mean and portion a proportion is meant for rather qualitative variables so for example I'm interested in maybe are you a Republican or are you not a Republican that kind of question is a qualitative question and if I gather a huge sample I can't really compute an average like I would compute a proportion of Republicans so for example if I gather at a thousand people I wouldn't say that the average is like Republican you can't really compute average if the responses are all qualitative you have Republicans and not Republicans same thing with gender if you gather a huge group of people and you want to know you want to know information about the that group of people in terms of their gender you have male and female right and the idea is you can't really calculate the average you can't add up all the numbers and divide by the total number of numbers because the responses aren't numbers they're qualitative responses and so you can make it quantitative by calculating a proportion so you might say okay well fifty percent of the sample was male or fifty-one percent of the sample was male or you might say 70 percent of the of the sample was not Republican and so now you have something to work with and so these type of tests are more for qualitative variables and the same principle applies let's say for example in the 2016 election there are all of these claims that Hillary Clinton was gonna win the election on and let's say people were saying that she was gonna win and people were certain that she was gonna win by like I don't know it was like 50 electoral votes or something like that or that 60 something 65 percent of the people we're gonna vote for Hillary Clinton well that wasn't the case was it those those proportions were incorrect those polls in a sense were incorrect or the way they conducted their polling was poor in a sense it wasn't representative of the actual population and so the idea is if someone comes out and says no I disagree with this this claim about the proportion of people who are gonna vote for Hillary Clinton I have a different proportion I think it's actually 45% now are those two proportions different from each other that's what these tests measure these test measure is your proportion of your sample you're one sample different from what everyone believes the proportion is let me give you one more example 75% of the people claim to be Christian in the u.s. at least in the US on what might be interesting is to say I don't think it's 75% I think it's a different percentage so you can't you gather a group of like 1000 people you calculate what proportion of that sample is Christian you find it's 60% now the next question is is 60% different from 75% or should I say is it different enough to say yeah it's not 75% it's 60% and that's what these tests can do but once again what's the difference between a Z test and a t-test I'll tell you it's us of sloppiness if you use this then you're sloppy I know that sounds crazy but that's actually legit if you use a z-test ever I'm just I'm baffled why you would ever use something like that so um so far we've gone over four different tests and these are all with one sample but let's talk about what you do with multiple samples and this is where things get kind of interesting so first let's talk about the two independent sample tests for the mean so I'm going to write that down the two sample independent test for the mean so this is really useful if you're conducting an experiment whenever you're conducting an experiment you typically will have a control group and a treatment group you will have two samples and you want to know are these samples are the results of these samples statistically significant and so you want to measure the mean of this group mean one and the mean of this group mean two and the question is are these two averages different from each other different enough to suggest that whatever the treatment was it made a difference so for example suppose you found a cure to cancer and you notice that the results of one group all these people are getting cured and the other group not so much on the control group the you know no one's getting cured right you might notice that hey my treatment does something here and it's statistically significant that's the kind of thing that we're dealing with when we talk about two sample tests in general now this is a two sample test for the mean so cancer might only work for proportions like we would say well 50% of the report 50% of the people here were cured and the other 50% we're not you know that's more proportion stuff I might be more interested in let's say how much cholesterol is in at the average cholesterol in each group after giving a certain medication and I notice that the average cholesterol and the treatment group was significantly smaller than the cholesterol and the other group and so you might say this medicine lowers cholesterol because the two samples here these two samples have statistically significant differences and therefore the treatment can be that the the thing that we associate to why there is a difference likewise there is a two-sample independent test for proportions and so you could probably guess what this is going to be in this case instead of measuring sample averages we're measuring proportions we have proportion 1 in proportion to so for example we're measuring whether or not maybe something qualitative are you depressed might be the question and we give one group the control group a placebo and we give the other treat a group the treatment group some antidepressants some things that make people anti depressed and in both groups we gather maybe some people who claim to be depressed or they're considered oppressed and we want to see does this antidepressant act antidepressant actually affects something well at the end of the gun of the study we asked the question are you sad but saying or are you depressed and we notice that the treatment group has a higher proportion of people who say yeah I feel better now I don't I don't feel sad whereas the control group you have just the same amount and you notice those two proportions are now statistically significant and that's how you can associate the treatment to the cause of why the proportion is now different so so far we're over we're pretty much almost done with all the different types of statistics tests let's talk about the paired sample test or sometimes is referred to as the matched or paired sample test now this is very similar to the two sample on tests for the mean or the proportion what we just talked about but in this case the samples are typically the same group of people they're not independent of each other they're not like completely different samples in fact typically it's the same sample but measured twice so for example I might be interested in an average before and an average after and I might be interested in did the average actually change enough was there a change in this in this experiment and that's what this test can measure so in this case the samples are not independent of each other they're actually dependent of each other and typically they're the same sample so for example maybe I have a classroom and I want to know whether or not my lecture improves the the test score of my math test and so what I do is I give a pretest and I get an average before and then I do my lecture and then I give the test again and I calculate the average after and so now the question is are those averages statistically significant from each other and so in this case again the two samples are dependent on each other they are not independent of each other so that's the slight difference here next up we have the chi-squared test now let's talk about the regression test before we go into the chi-square test I'm gonna switch these up a little bit let's talk about the regression test so you've probably heard regression at some point maybe in high school mathematics this is typically taught in high school math or at least it should be according to the Common Core Standards but the idea is we have two variables and they're both quantitative and we want to measure do these two variables have any sort of association with them is there any sort of correlation involved and regression will help you determine how correlated or how associated two variables are so you have variable one X and variable two Y and you want and they're both quantitative and the idea is for every dot here every single dot represents you measuring both x and y simultaneously so for example I might want to calculate your age and your GPA and I would plot that on this graph and I do that with every one I measured their age and their GPA age GPA and I graph all these points and I I'm interested in whether or not age has anything to do with GPA and so that's what regression is now oops I just completely exited out that let me pull that back up this is my this is my control panel for all of you who are interested in that alright let's go back to this very good let's talk about the chi-squared test the chi-squared test is very similar the chi-square test determines if there is a relationship with two variables that are qualitative so for example in this case I'm not going up to you and I'm not going to ask you quantitative questions I'm actually gonna ask you qualitative questions so in this case I might ask you are you let me see if I can get this rate let's do there we go yeah so are you male are you female but I'm gonna ask you two questions I'm gonna ask you what's your gender but I might also ask you let's say are you blonde or not blonde and I wanted to determine is there a relationship between your gender and your hair color now it's really hard to determine that if there's a relationship because those aren't quantitative you can't measure them on a graph you can't draw up plot points because these variables are binary there are only two options and so in this case maybe we notice that there are on you know a hundred male male blondes but only two males that are not blonde and three females that are blonde and 250 females that are not blonde in this example we noticed that if you're male you're probably gonna be a blonde and if you're a female you're probably gonna be not blonde there's sort of a relationship here there's a correlation between these two variables but it's hard to see there because we can't really graph it there's no way to graph this and so the chi-squared test can solve this problem by allowing us to determine whether or not two qualitative variables are different from each other now last but not least have the one-way ANOVA test I'll just do one way ANOVA test now many many statistics classes will not go this far they will stop before we even get here but every once in a while I'll see a statistics class that will talk about the one-way ANOVA test so let me explain what the one-way ANOVA test is the idea is the one the ANOVA test in general is the same thing as I'll even write this down ANOVA is the same thing as the two sample independent test independent there we go test so if you remember the two sample two independent test was you have two samples that are not the same samples maybe like a treatment group in a control group and you want to know whether or not the treatment group makes us it makes some sort of difference and in the results well the ANOVA test is exactly the same thing except instead of two samples typically we would do some like n samples so maybe we have all sorts of different medications we have a control group treatment one treatment two treatment three we want to try all sorts of different things the one-way ANOVA test can help us do that we want to see which of the different treatments is going to affect the results that are quantitative in nature so again it's very it's basically the concept of the two sample independent t-test but instead of a treatment group in a control group we would have control group srimad group one treatment group two treatment group three and we want to know are those groups statistically significant from each other and that's what it'd be ANOVA test is for now in the upcoming lectures we're gonna be talking about the many different all of these statistics tests and we're gonna explain how to conduct them and you know I'm gonna re-emphasize their purposes again so that we get a better understanding of when to use them as well anyways thank you guys so much I'll seen the next lecture

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Keywords: statistics, which statistical test should i use?, statistical test, choosing a statistical test, statistical tests, which statistical test to use?, inferential statistics, statistical hypothesis testing, statistical, statistics (field of study), statistics 101, how to choose a statistical test, which t test to apply, statistical tests psychology, test, tests, selecting a statistical test, design and statistical tests, t-test, anova, chi squared, t test, what is chi square test, chi

Id: ChLO7wwt7h0

Length: 19min 53sec (1193 seconds)

Published: Thu Sep 05 2019