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Test sign

hello youtube today we're gonna be talking about the sign test and statistics this is a nonparametric test I mean this kind of test is mostly used for quick data analysis if you want just check real quick is there a difference between the two things studied in this data so I'm just going to provide a quick example so you have number of I guess cases um in which there's a driver and a passenger and say they're in a car accident and you want to say is there a correlation between the driver injury and the passenger or is there like is there a difference or are they the same I'm going to try to test if the I guess significance of this of the injury is related based on fear of the driver of the passenger so we just want to know the difference not whether not the magnitude of it so this is the key distinction I want to highlight that I'll say it again you want to know that there you just want to test if there's a difference it's a yes-or-no answer but you don't want to know by how much this test will not show you that but if you want to find out quickly this is one way to do it and this is how we're going to do it actually you're going to simply compare the data here and you say okay literally is there a difference well a mathematics difference means comparing two numbers which generally means subtraction so you want to see ok what's 20 or what's 42 minus 35 well that would be a positive number what's 42 minus 35 again a positive number what's 34 minus 45 that's a negative number and you're going to go all the way down do that so 34 minus 45 is also negative number but here's one thing to know if you get the same number oops if you get 45 minus 45 which is 0 that is we pretend like that data point never happened so you can kind of like squiggle it out and then that means your sample size will decrease we'll get to that later but we'll keep going and comparing the rest of the data you can skip forward if you can do the math on your own but I'll do it anyway 40 minus 42 is a negative number this will also be a negative number a negative number positive number negative number negative number positive negative number negative number negative number negative number negative number negative number and again if you guys are still with me we got zero here because again these are the same and we pretend like it never happened again I'm highlighting this is a quick test and you can see that by how fast it just kind of did it right there so now pretty much let's count how many positive tests we got and the negative test so the number of positives were just one two and three one two three so three of them and the number of negative tests we got was 13 because we are not including the zeros so again another note pretend the zeros do not exist that those data points were never acquired so that means your sample size was we have 18 but now it's going to be reduced to 16 because we are excluding those 2 here so this part and this part is not or that sample is not in the data we're just going to pretend like that never happened so our reduced sample sizes 16 but now this side test has a formula to it let me write it down real quick so this is something called a B statistic and pretty much you can get that from a table but the way to you would figure that out is you would simply take the maximum value of either the number of positives or negative values so you look at this data here and you say which numbers bigger 3 or 13 obviously 13 is bigger so that means the maximum number here so our BS statistic is 13 now you want to look that up in a table but the way you you need to look it up first is you need to declare what your alpha is so your alpha let's say is point 0 5 so that would be you 95% confidence kind of interval we can think of so we'll take a look at that in this table here now it is kind of blurry I think but try to make it clear here's a table where you would look it up your I also have highlighted at the top we wanted it be 0.05 and our n on the left is shown there and remember we're not using 18 we're using 16 and we go to 13 as our B statistics and we get this number right here which is point zero to one if it's difficult to read so I'll write that number here so then we get a value of zero point zero to one now what is this what does this really mean well let's compare it to our alpha and notice how it is less than our alpha which is point zero five and we could say technically with finding a p-value as well you would determine that you have to reject the null hypothesis because P is greater or excuse me P would be less than alpha in this case and there actually is a difference between the drivers and the passengers so that's pretty much the sign test here you did figure out say look there's a difference because look you can even look at it even if you didn't use statistics and P values and alphas and all that if you just looked and said okay I got way more negatives and I did positives there probably is a difference and that's kind of the quickest way to look at it in terms of that but you can still prove it statistically as well but hope this helped in terms of checking out a quick sign test if you just want to look at some data real quick and see if you pick up on a few inferences and I determine if there is correlation just based off of time around real quick but what if you wanted to make this test stronger if say these passing driver and passengers were in the same accident like these were in the same cars that would be what's known as a paired sample and then you would do a different test for that and then it's actually using that other test would produce a more reason I guess your data is stronger SIF knowing that your data is paired but that's something else don't worry about that unless you're interested but again sign test is just a quick test for nonparametric these samples are not paired and you're just testing is there a difference is there not not the magnitude in a sense but just saying yes or no is there a difference or not we said yes there is there seems to be a big difference in the passenger seems to be more affected alright so again hope this helped and happy studying