 ## Genetics

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3. Extensions to Mendelian Inheritance

# Chi Square Analysis

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concept

## Chi Square Analysis 2m
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Hi in this video, we're gonna be talking about the chi square analysis. So chi square is going to be a statistical test. So we're about to get into a lot of math. I'm really sorry, but it's genetics. It hasn't happen. It. Um So the chi square test statistical test and what it is testing for is whether the expected result that you get is um very similar to the the observed results. So the expected is what you expected to get and the observe is what you actually see. So the reason we have to have this test is because in genetics it's never perfect. Right? You I mean, if you may organisms together and you get, you know, 2000 offspring, for instance, for flies or something, you're not going to get a perfect 3 to 1 ratio. You're just not because there's, you know, there's 2000 offspring. It may be very close, but it's not going to be perfect. I mean, it's just life has never works that way. You also won't get the perfect 9 to 3 to 3 to 1 ratio. Either life isn't perfect, genetics isn't perfect. And so if we are doing this experiment today, we have a bunch of flies, we have 6000 flies and we counted them all. We have these nice ratios and it's like really it's like 2.96 to 1, you know, is that actually close enough 3 to 1 to say, okay, this is our normal, this is so close to expected, this is dandelion inheritance. So that's what the chi square test is for. So it's used to check if your numbers that you got from your experiment are close enough to be expected to say that, to say that, you know, it's dandelion inheritance. So the important numbers that you have to know to do a high square analysis is the observed numbers. These are the numbers you actually get in your own experiment and the expected numbers. And these are the numbers that you are expected to get, the perfect ratio, the 3 to 1, the perfect punnett square, that is the expected. And so of course because we're doing math, there's going to be a formula and it looks like this, realize it's kind of confusing. Here's your chi square, that's what it looks like. Uh, that's the notation for it. You don't remember from math. This means some and then you have these os and ease. So what do they stand for? Well, oh, very clearly means observed numbers. So these are the numbers you get and the expected numbers use green. Are the numbers that the perfect ratio numbers. So that's an overview. Um, let's now move on to the actual practice question and practice using chi square. Um in an actual question that you might get. So let's move on.
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example

## Chi Square Analysis 18m
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example

## Step 1 3m
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Okay. So this question it says that you have done some type of mono hybrid cross. And you observed these F two phenotype in the in the cross. So it looked like you were crossing some type of flowers probably red or white. And the F two generation ended up with around 900 average around 900 red and around 300 white. And it says the question says which of the following null hypotheses is best for using the chi square test. So the chi square test is used to determine whether your expected values are equal to your are the same as your observed value. So in this cross you got these offspring and it's there there's about 900 red, 300 white. So it's saying which of these ratios did you expect for this cross? Like which one of these do you want to test and see if the genetics are working in that fashion? So a 9 to 3 ratio is what we're gonna do this and write it in a ratio. And it was to be a ratio that you're used to seeing one of these ratios here is this most like a 3 to 1 ratio. A 2 to 2 ratio. A 9 to 3 to 3 to 1 ratio or a 3 to 2 ratio. So if you have no idea, I think there should be an obvious one. But if you're still confused, you're not sure. I think there's some that we can easily cancel out. We can easily cancel out 9 to 3 to 3 to 1 because there aren't four phenotype, right? So each one of these would have to be a different phenotype but we only have two phenotype. So we have red or white. So this one obviously can't be it. Um the second one that we can mark out is this to to to because that means that they would be equal. So either both would be 900 or both would be 300. But that's not the case that we're seeing. We're seeing a 900-300 ratio. Therefore this one they're not equal. So be can't be it. So the last two ones that are the options are 3 to 1 or 3 to 2. Now the best way to do this is just to do regular math. So if you are divide 302 900 how many times would it go in? Right? It would be three. Right. So 300 times three is going to be 900 therefore this will be one. Now, if it were a 3-2 ratio, what you would see is a 900-600 ratio, which is not what we saw. And you can do this through just regular division, you can do it by dividing 300-900 and realizing you get three and therefore you have and then you can do 300 times three equals what it's going to equal 900 and therefore that is a 3-1 ratio. Um And so Yeah, so with that the answer here is a so if you got this prototype, the null hypothesis that you would want to test, and you want to see if your values that you got here are equal to the expected values of a 3-1 ratio. So with that let's not move on.
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example

## Step 2 57s
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Okay, so um using the same exact data from before this question is asking you which of the following here represents the degrees of freedom for this problem? So how many degrees of freedom are in this experiment if you were to do a chi square analysis? So we are answers are 123 and four. So which one do you think it is? Write the answer here is actually one. And the reason that it's one is because we have two phenotype, right? That's red and white. That says white, in case you can't read my horrible handwriting. But remember, the formula for degrees of freedom is the number of phenotype which we have 2 -1. So the degrees of freedom for this experiment would be a which is one, so that let's not move on.
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example

## Step 3 2m
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Okay so in this question we are going to actually be calculating the chi square value for this data. So remember the chi square value is given this um interesting symbol here, remember the formula for this is going to be observed. So these values are observed minus expected Squared, so expected would be what? It was a 92 or 3-1 ratio. The expected values will be these an exact 3-1 ratio over expected. And remember this is the sum. So if the sum for the whole thing, so for each one of these we have to do a calculations, let me disappear. And so um first we'll do red. So there we have we have 8 92 minus 900 squared over the expected value of 900 plus the white which the observed 2 94 minus the expected which is 300 squared over 300. Now I'm gonna give you a second, you can pause it if you want, you can do whatever. Um Go ahead, put this in your calculator and what do you get? What is this equals, this equals the high squared value which is one of these values here. So go ahead, put it in your calculator and see what you get. Give you a second. You know it takes a little bit of time. Um So I'll just pause for a second and give you time to punch that into your calculator. And so hopefully you have enough time. If not go ahead and pause it while you finish because I'm about to give the answer. So the answer here is b. This is 0.191, and that is your chi square value. So with that let's not move on.
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example

## Step 4 3m
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alright, So now now that we've calculated the chi square value, we know it's 0.191 and we have our degrees of freedom, which we know is a single one. So that's one, it's a the next step is to determine the range of p value. So what's our p values for this experiment now, in order to do this, you're going to have to have a high square distribution table. You feel free to use the one in the handout which you probably already have up. If you don't go ahead, take your phone computer or whatever, open a new tab, just google high square distribution table. There's a ton of them um wherever they are now to read this table, the first thing you do is you look at your degrees of freedom, there should be a line called degrees of freedom and everything down here, it's going to be listed with different numbers. The one you're interested in is this line here because it's the degrees of freedom of one Now above here, you're gonna have in here, you're gonna have a bunch of different numbers and what you're looking for is the numbers through which .191 sits in the middle. So eventually you're going to get to a table and now it may not be perfect if you're using the table from handout I'll have the exact numbers. If you're using a table from google may be different numbers, but essentially it's going to be the same thing and the problem, it won't mess up the no matter what chi square distribution table you use, it's not going to mess up um the how you solve a chi square problem. So if you're using the table um that I provided we're gonna match perfectly. If you're not it's okay, you're still gonna be correct. But it may, the numbers I'm about to say may not match perfectly, but they'll be close enough. So on the table and the pds that I provided, you're gonna come across numbers 0.15 and I believe 0.46. And if we were to put 0.191, it would fit right in between these numbers. And this is fantastic. So what you do now now that you have these two kind of circle them if you want and you go all the way to the bottom where the p value sits And here what it's going to say is going to give you a bunch of different numbers, but you're interested in the one that's lined up in the same column as these two numbers and that's going to be .70 and 0.50. So the answer to this question is a now remember if you're not using the same table as me, it may not be exactly this, it may be .752.55 or maybe slightly off, but essentially um pick the closest one which for this problem is going to be 10.70 and 0.50. Now when you're doing this in a classroom setting or on a quiz or a test, they're going to provide you with the exact same table as everyone else. So there won't be these weird confusions. But for this, I want to give you a chance to practice looking at different high square distribution table so you can figure out how to look at ones, different ones differently. But for this question, a the answer is 4.70,. So let's figure out what that means in the next question.
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example

## Step 5 53s
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Okay, so this is kind of the next step of this problem. If a chi squared value has led you to receive a p value range 0.70 point 50. Also, uh 70 to 50%. You will you accept or reject the null hypothesis? And so um Do you first do you remember there's certain cases where the P values have to be above or below a certain amount, certain threshold where you determine whether you accept right? That threshold is 5% or 0.05. Now we obviously got much higher than that. And so if it's larger than that, then what does that mean? That means we accept the null hypothesis. And so we're gonna talk about what accepting the null hypothesis means for this question. Um Next. So with that let's move on.
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example

## Step 6 3m
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