Okay. This stain. We want to check for independence between ceremonial ranking and poetry types at 0.5 level of significance are Alfa is 0.5 Okay, let's just draw the table. We have the ceremonial ranking, the ceremonial ranking over you. Right. So these are E B and C. We have the column totals. Then we have, uh, then we have pottery types. There are cooking jar and decorated jar shreds. Okay, so these are cooking jar shreds, and then we have decorated jar. Sure. It's okay. Now, let's just fill in the table. These are going to be our observed values. We will need these in our calculations, so we'll just write them down. 92 over here. We have 79. We have 49. We have 53. We have so many five, right? This is 2 57. This is 1 77. And over here, we're going to have the row totals. Right? The road opens. They're going to be 1 35 1 45. And we have 1 54. And this is 430 for these were the row totals. These were the column totals Okay, now we are performing a chi square test off independence. So again, what do we need? The first thing that we need to find is the expected values E. How do we find that it is going to be wrote? Total multiplied by column Total multiple. We call in total upon the grand total. Yeah, upon the grand total. Okay, this we're going to do for all the sales. So now I'm not writing the labels. I'm just going to drop the table without them because the labels will be the same. Okay, So if I look at the first cell that is for A and C. J s for A and C. J s, this is going to be 1 35 in two 2 57 divided by 4. 34. This is 79.9, 79 0.9 four. All right, for the next value, we have 1 35 in two 2 57. Sorry, this is not to 57. This is 1 77 divided by for 34. This 55.5 55.0 Fife. All right, then we have 1 45 inches. 2 to 57 divided by for 34 with 85.86 85.86 Then we have 1 45 inches to 1. 77 divided by 4. 34 is 59.13 59 point 13 59.13 Okay, then we have 1. 54 in two, 2 57 to 57 divided by 4. 34. This is 91.1991 point 19 Then we have 1. 54 in 21 77. Divided by for the default, the 62 point eight. Or have we made a mistake somewhere? Just a moment. This is 1 54 in 2 to 50 2. 57 divided before 34. Look, this is right. Okay, so this is going to be 1 54 in 21 77. They were before 34 which is 62.8 62.8. All right now. We also have the expected values. These are the expected value. The expected the expected values. Okay, these are the expected values. Now, how do we find the chi square statistic for each of these cells, it is going to be observed minus the expected square Upon expected. We're going to do this for all the cells and then in the end, add them up. And this is going to give us our chi square statistic. That is just come here, make another table. Make this rate in this table. We're just going to write our chi squared values. Okay, so what do we have? This is going to be observed minus, expected or expected minus observed Does not matter, as there is a whole square. So this is going to be 86 minus 79.94 This is a 6.6 I'm squaring it. Divided by 79.9 ft. This values 0.459 or recognizes this 0.46 point 46 Okay, The next one is 55.5 minus 49. I square this 6.5 and I divide this by 55.5 This is 0.6648 Recognizes 0.665 Uh uh, 0.66 fight. Okay, then we have 92 90 to minus 85.86 I square this thing 6.14 okay. And divided by 85.86 85.86 This 0.43 now recognizes this 0.44 point 44 All right, then we have 59.13 minus 53 I squareness and divided by 59.13 which is 0.635 But again, at this 0.64 0.6 four makes sense now. This is 91.19 minus 79. I square this this is 12.19 and I divide this by 91.1 nine. This is 1.629 Or I guess this is 1.63 1.63 Then I have 75 minus 62.8. I square this and divided by 62.8. The weather is by 16, 2.8, which is 2.372 point three. So now these are my chi square values. My guys were values okay for all the cells. Now I'm just going to add these up. This is going to be 0.46 Last point point 665 plus 0.44 plus 0.64 plus 1.63 plus 2.37 the 6.205 So my chi square statistic is 6.205 Now I need the degrees of freedom. Degrees of freedom, that is D F is going to be number off. Rose minus one, multiplied by the number off. Columns minus one. Okay, number of rows is three minus one. Okay, so number of those three minus one and number of columns is too minus one. So this is going to be to my degrees of freedom is to know how do I find the P value? I'm going toe Take the help off an online the value calculator. You can use the chi square table, but you won't get the exact value. Will just get a range from that from a statistical tool or software. You will be able to get the exact even. So this is 6.205 So this my Chrysler that it's 6.205 and my degrees of freedom is too. And my significant level in this question is 0.5 right So this is 0.5 and I hit Calculate and I get my P value at 0.44 My P value is 0.44 What was my Alfa? My Alfa was your 0.5 right? My Alfa was 0.5 I can see that my p value is less than Alfa hands. I reject my age. No. Hence I am going to reject my age, not right. So I can say that these variables that I have these variables what are the videos that I have? I have portrait type and ceremonial ranking. Okay, These two variables are not independent, are not independent. Okay? And this is how we go about doing this question.