Counting degrees of freedom

Topic: Chi-squared tests · more questions on this topic
‹ A two-by-two table is a two-proportion test

Give the degrees of freedom of the Pearson statistic in each case. (a) A 4\times5 contingency table tested for independence. (b) Counts in 8 classes compared with a binomial distribution \operatorname{Bin}(7,p), with p estimated. (c) Counts in 10 classes compared with a normal distribution whose mean and variance are both estimated. (d) The same, with the mean and variance known.

  1. (4-1)(5-1)=12.

  2. 8-1-1=6: eight classes, one estimated parameter.

  3. 10-1-2=7.

  4. 10-1=9: nothing is estimated.