20.5.4  Testing a distribution with the χ² distribution

The chisquaret command will use the χ² test to compare sample data to a specified distribution.

• chisquaret takes one mandatory argument and a sequence of optional arguments:
  • L, a list of sample data.
  • Optionally, distr. This can be one of
    • The name of a distribution (see Section 20.3.4 for a list of distributions and their parameters).
    • Another list of sample data.
    By default this will be the uniform distribution.
  • params, the parameters of the distribution distr or the symbol classes and optionally c_min and c_dim, the minimum size and default size of a statistics class (by default, class_min and class_size, which themselves default to 0 and 1; see Section 2.5.8).
• chisquaret(L ⟨,distr ⟩) returns the result of the χ² test between sample data and the named distribution or two sample data lists.

Examples

Guessing data is the list of number of elements in each class, adequation to uniform distribution
Sample adequation to a finite discrete probability distribution
Chi2 test result 0.0810810810811,
reject adequation if superior to chisquare_icdf(1,0.95)=3.84145882069 or chisquare_icdf(1,1-alpha) if alpha!=5%

Sample adequation to a finite discrete probability distribution
Chi2 test result 0.742424242424,
reject adequation if superior to chisquare_icdf(1,0.95)=3.84145882069 or chisquare_icdf(1,1-alpha) if alpha!=5%

Binomial: estimating n and p from data 10 0.5055
Sample adequation to binomial(10,0.5055,.), Chi2 test result 7.77825189838,
reject adequation if superior to chisquare_icdf(7,0.95)=14.0671404493 or chisquare_icdf(7,1-alpha) if alpha!=5%

Sample adequation to binomial(11,0.5,.), Chi2 test result 125.617374161,
reject adequation if superior to chisquare_icdf(10,0.95)=18.3070380533 or chisquare_icdf(10,1-alpha) if alpha!=5%

As an example using class_min and class_size:

or (setting class_min to −2 and class_size to −0.25 in the graphical configuration):

Normal density, estimating mean and stddev from data -0.00345919752912 0.201708100832
Sample adequation to normald_cdf(-0.00345919752912,0.201708100832,.), Chi2 test result 2.11405080381,
reject adequation if superior to chisquare_icdf(4,0.95)=9.48772903678 or chisquare_icdf(4,1-alpha) if alpha!=5%

In this last case, you are given the value of d² of the statistic D²=∑_j=1^k (n_j−e_j)/e_j, where k is the number of sample classes for classes(L,-2,0.25) (or classes(L)), n_j is the size of the jth class, and e_j= n p_j where n is the size of L and p_j is the probability of the jth class interval assuming a normal distribution with the mean and population standard deviation of L.