# Testing a distribution with the χ2 distribution: chisquaret

### 8.5.4 Testing a distribution with the χ2 distribution: chisquaret

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

- chisquaret takes one mandatory argument and an unspecified number of optional arguments:
  - L, a list of sample data.
  - Optionally, distr. This can be one of
    - The name of a distribution (see Section 8.3.14 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 keyword classes and optionally cmin and cdim, 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 the sample data and the named distribution or the two sample data.

#### Examples.

- Input:
  chisquaret([57,54])
  Output:

  `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%`
  `0.0810810810811`

- Input:
  chisquaret([1,1,1,1,1,0,0,1,0,1,1],[.4,.6])
  Output:

  `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%`
  `0.742424242424`

- Input:
  chisquaret(ranv(1000,binomial,10,.5),binomial)
  Output:

  `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%`
  `7.77825189838`

- Input:
  chisquaret(ranv(1000,binomial,10,.5),binomial,11,.5)
  Output:

  `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%`
  `125.617374161`

- As an example using class_min and class_size:
  Input:

  L:= ranv(1000,normald,0,.2)
  chisquaret(L,normald,classes,-2,.25)

  or (setting class_min to −2 and class_size to −0.25 in the graphical configuration):
  chisquaret(L,normald,classes)
  Output:

  `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%`
  `2.11405080381`

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