MultinomialTest Class

In statistics, the multinomial test is the test of the null hypothesis that the parameters of a multinomial distribution equal specified values. The test can be approximated using a chi-square distribution.

References:

• Wikipedia, The Free Encyclopedia. Multinomial Test. Available on: http://en.wikipedia.org/wiki/Multinomial_test

The following example is based on the example available on About.com Statistics, An Example of Chi-Square Test for a Multinomial Experiment By Courtney Taylor.

In this example, we would like to test if a die is fair. For this, we will be rolling the die 600 times, annotating the result every time the die falls. In the end, we got a one 106 times, a two 90 times, a three 98 times, a four 102 times, a five 100 times and a six 104 times:

int[] sample = { 106, 90, 98, 102, 100, 104 };

// If the die was fair, we should note that we would be expecting the
// probabilities to be all equal to 1 / 6:

double[] hypothesizedProportion = 
{ 
   //   1        2           3          4          5         6
   1 / 6.0,   1 / 6.0,   1 / 6.0,   1 / 6.0,   1 / 6.0,   1 / 6.0, 
};

// Now, we create our test using the samples and the expected proportion
MultinomialTest test = new MultinomialTest(sample, hypothesizedProportion);

double chiSquare = test.Statistic; // 1.6
bool significant = test.Significant; // false

Since the test didn't come up significant, it means that we don't have enough evidence to to reject the null hypothesis that the die is fair.

Reference