## ← Formalize Within-Group Variability - Intro to Inferential Statistics

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Showing Revision 5 created 05/24/2016 by Udacity Robot.

1. We need to formalize how we will precisely measure each type of variability. We
2. already decided that we're going to use the grand mean, and use the same idea
3. as standard deviation to measure the spread of the sample means. We'll find
4. each square deviation from the mean. And in this case we're going to multiply
5. each square deviation by the sample size. Each square deviation is equivalent
6. to the area of each of these squares. And then we'll mulitiply this area by
7. their respective sample size. Here K represents the number of samples. That
8. means we'll have K sample means. And then we'll add them all up. In this lesson
9. though, we're assuming that all samples have the same size. So, we can get rid
10. of the K. n is just a constant across all samples. That means that we can write
11. the numerator between group variability like this. And then we divide by the
12. degrees of freedom. When we say formal way of measuring something, that means
13. we get one number. If we add up each squared deviation of each sample mean from
14. the grand mean, multiply this by the sample size and then divide by the degrees
15. of freedom. We get one number that describes between group variability. We need
16. to do the same for within group variability. And we'll do something similar to
17. the way we measured between group variability. We'll take the sum of squares
18. for each individual sample from the mean of each sample, and then we'll divide
19. by the degrees of freedom. What do you think the degrees of freedom is in this
20. case? Let's say that we have three samples. More than one option may be
21. correct.