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Degrees of Freedom

Degrees of Freedom. Addendum to Chapter 14 Tue, Dec 6, 2005. Goodness-of-Fit Degrees of Freedom. In the goodness-of-fit test for a fair die, we had the following data: Given that the total is 60, how many cells could we fill in arbitrarily and still make the total 60?.

JasminFlorian
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Degrees of Freedom

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  1. Degrees of Freedom Addendum to Chapter 14 Tue, Dec 6, 2005

  2. Goodness-of-Fit Degrees of Freedom • In the goodness-of-fit test for a fair die, we had the following data: • Given that the total is 60, how many cells could we fill in arbitrarily and still make the total 60?

  3. Goodness-of-Fit Degrees of Freedom • Use the spreadsheet DegreesOfFreedom1.xls. • We could fill in all but one of the cells, i.e., n – 1 cells. • That would force the value in the last cell to make the total equal to 60. • Therefore, we have n – 1 degrees of freedom.

  4. Independence Degrees of Freedom • In the test of independence, we use the data • Given the row and column totals, how many cells could we fill arbitrarily and still make the row and column totals the same as before?

  5. Independence Degrees of Freedom

  6. Independence Degrees of Freedom • Use the spreadsheet DegreesOfFreedom2.xls. • Thus, we can fill in all but one value in each row for all but one row. • That is, we can fill in (cols – 1) values in each row for (rows – 1) rows. • So we have (cols – 1)  (rows – 1) degrees of freedom.

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