This program comes from(or was inspired by, rather) the chi-square test described within The Art Of Computer Programming, Vol. 2, Seminumerical Algorithms(TAOCP, hereafter). The test is important for random number generators (for testing them, anyway), so I figured I'd make a program to calculate the chi-square test. The only thing that needs to be done by the users of this (beside giving the function some parameters) is to fill in the table and table look-up methods for the test. I left this out for several reasons: (a)it is rather long, and I thought it may distract from the main purpose of the code, (b)there are a variety of tables that could be chosen; what is presented in TAOCP is hardly complete, or even close. Therefore, I leave it open so that it can easily accomodate any data source that you provide. The code is here, and documents itself with comments: 

sub chi_sqr {
    # We take n *independant* observations, each of which 
    #fall into one of k
    # categories; $p[$s] is the probability that each 
    #observation falls into
    # category s, and $y[$s] is the number of observations 
    #that actually *do*
    # fall into category s
    $params = shift;
    $n      = $params->{n};
    $k      = $params->{k};
    $p      = $params->{p};
    $y      = $params->{y};
    for $s(0..$k-1) { $V += ($y->[$s] ** 2 / $p->[$s]) - $n }
    $V = 1/$n * $V;     ## Eq. (8), pp 43. Vol. 2. TAOCP.
    $v = $k - 1; ## We have $v degrees of freedom
    return get_val( $v, $V, $p );
}

sub get_val {
    # Returns likelihood that $V is less than or equal to 
    #the value in row
    # $v with the value $V
    ($v,$V) = @_;
    $p = -- 0..6 --> 1%, 5%, 25%, ... 
                  (from Table 1, as below) --
    @x = qw(-2.33 -1.64 -.674 0.00 0.674 1.64 2.33); 
                   ## ^ From table 1, pp 44.
                   ##   Vol. 2. TAOCP
    $chsqr = sub { $v+sqrt(2*$v)*$x[$p]+2/3*
                    $x[$p]**2-2/3+1/sqrt($v) };
                   ## Ditto ^
    @table = ...Insert table here...
 .....perform table look-up; OR, if row $v isn't in table,
 and $v is more than 30, perform $chsqr closure && return 
 the result of whichever method was performed......
}

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In reply to The Chi Square Test by dimmesdale

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