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← Extended t-Test Numerator - Intro to Inferential Statistics

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

  1. Remember that if we use the maximum distance between any two sample means,
  2. that's pretty much finding the range of all the sample means. And this doesn't
  3. give us a good measure of the variability of sample means. That's because we
  4. could add a bunch of samples to this data set whose means are within this
  5. range. And the variabiltiy then wouldn't change if we use the range as that
  6. measure. We want to account for all samples. You also found before that the
  7. average deviation adds to zero. So this can't work either. If we find the
  8. distance each sample mean is from each of the other sample means, then we might
  9. as well do a bunch of t tests. We'll have to do the same number of these
  10. calculations as t-test anyway. And t-test are a better measure of whether or
  11. not two samples are statistically different. We've reached our answer. Find the
  12. average square deviation of each sample mean from the total mean. Since we're
  13. only concerned with the variability between means. For now we're not concerned
  14. with the variablity between each sample. We're only looking at the mean of each
  15. sample. And rememeber, this is how you calculated the standard deviation. If we
  16. had a data set, and we find the mean. We found each squared deviation from the
  17. mean. And then in the case of a sample standard deviation, we divided by n
  18. minus 1. That's exactly what we're going to do when we find the variabiltiy
  19. between means. The average square deviation of each value in each sample from
  20. the total mean also includes the error caused by individual differences between
  21. subjects in each sample. And we don't want to include this error in our measure
  22. of between subjects variability. This is the total sum of squares. And we'll
  23. reference back to this later. For now, we're only concerned with the square
  24. deviations of each sample mean from the total mean. The mean of all values from
  25. all samples. This total mean is called the grand mean in statistical terms. And
  26. we're going to denote this by x bar sub g.