7.6 Chi-Square Tables
- Key Idea 1: It turns out that the number of degrees of freedom completely determines which chi-square density we use to compute chi-square probabilities with...
Discussion
- If a chi-square problem puts data into 10 categories (that is, the null hypothesis is a 10-sided die), we need to use a chi-square density having 10 - 1 = 9 degrees of freedom.
- In Figure 7.6 we display chi-square densities having 3, 5, and 9 degrees of freedom, corresponding to the chi-square testing of a 4-sided, a 6-sided, and a 10-sided fair die.
- The argument above that helped convince us that the chi-square density with five degrees of freedom works well for testing the hypothesis of a six-sided fair die could just as easily be made for a die of any number of sides.
- Further, the null hypothesis can be one that specifies a loaded die—that is, we can also use chi-square density areas when the die is hypothesized to be loaded in a specified way.
- Key Idea 2: We now have a way to find the probability of a chi-square as large as or larger than a given value that is more accurate than using experimental probabilities obtained from the six-step method...
Discussion
- We find the approximate area under a chi-square density.
- Tables have been produced that provide theoretical probabilities determined from areas under the theoretical chi-square densities.
Example
- Key Idea 3: For many purposes this crudely estimated probability is adequate. However, for a better approximation, use the following rule, called Linear Interpolation...
Discussion Appendix D has further discussion and formulas regarding linear interpolation.