00:01
Now in this question we have been given a table what they're asking they're saying that the table describes the data that was presented in the court to show the locations of recently rendered apartments and do we think that there is evidence of racial steering? okay so let us try to look at the table in the table there is section a section b then white black and total.
00:43
White black okay what are the values 87 83 834 87 83 834 all right then we are going to have the totals this is going to be 170 this is going to be 42 this is going to be 95 this is going to be 117 and the addition of these is 212.
01:39
This is the grand token.
01:42
All right.
01:43
Now what we are trying to see here is independence, right? homogeneity or independence, sometimes i just feel like both of them are the same, but actually they're not.
01:56
So we want to see test if there is independence or not.
02:04
Okay.
02:05
So what do we need? we first need to find the expected values for each and every block.
02:11
How do we get the expected value? the expected value for every block is going to be the observed value.
02:17
That is this value, right? this is, oh, just a moment.
02:27
Forget about the observed value.
02:29
This is going to be, the expected value is going to be the row total, multiplied by the column total multiplied by the column total upon the grand total upon the grand total all right so if i draw this table again i'm not going to write the labels the labels are going to be the same right but let me just write these values so for example if i want an expected value for this for white people living in section b it is going to be 117 into 170 by 212 right 117 into 170 by 212 so if i use a calculator for this 117 into 170 divided by 212 this is 93 .82 this is 93 .82 93 .82.
03:42
Similarly for the first value for the first value we are going for 87 we are going to have 95 into 170 by 212 95 into 170 by 212.
03:54
95 into 170 by 212.
03:57
All right so 95 into 170 divided by 212 this is 76 .179.
04:10
Let me write this as 76 .18, 76 .18.
04:22
And i have calculated these values.
04:26
The rest of the values are going to be 18 .82 and 23 .18 .18 .82 and 23 .18 .82 and 23 .18.
04:41
Now what exactly is the kai square statistic what is going to be the kai square value the kai square is going to be summation of observed minus expected whole square upon expected okay and this is in the root right oh no this is not in the root just a moment not an entire thing.
05:18
This is in the root.
05:23
So let us try to find the values for one of them.
05:27
Let's say this is 76 .18.
05:31
This is the expected.
05:32
What is the observed? observed is 87.
05:34
So this is going to be 87 minus 76 .18...