## ← DF - Marginal Totals - Intro to Inferential Statistics

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Showing Revision 5 created 05/25/2016 by Udacity Robot.

1. Let's pick any number in here. Let's say 5. Can we choose this number and still
2. have this sum to 9, and still have these columns sum to 9? Yeah. Let's say 3.
3. So together those make 8, and that means this one is forced it has to be 1.
4. Okay, can we pick a value here. Yeah, let's say 8. So those sum to 13, which
5. means that this value is forced. This has to be negative 4, and then can we
6. pick a value here, and have this row and this column still sum to 9? Yeah,
7. let's say 7. Now if this column has to sum to 9, then this entry's forced, it's
8. negative 1. And as you can see, this entry's forced too, this adds to 15, so to
9. add to 9, this should be negative 6. And this entry's forced as well, this has
10. to be 14. Then both this column and this row sum to 9. So in this case there
11. are 4 degrees of freedom. But if we have an n by n table, in this case this is
12. a 3 by 3 table. This is a 4 by 4 table. Then we would be able to chose all of
13. these entries but then these ones would be forced. This number of tiles is n
14. minus 1. And this number of tiles is also n minus 1. So the total number that
15. we can choose is n minus 1 squared. So here in this 3 by 3 table, we were able
16. to choose 2 times 2. In this 4 by 4 table, we were able to choose 3 times 3. So
17. when we have an n by n table, we can choose n minus 1 times n minus 1, or just
18. n minus 1 squared.