Hypergeometric probability distribution

The UNODC guidelines for sampling are based upon the statistical method known as hypergeometric distribution. Hypergeometric distribution is used to determine the probability of the number of positive samples likely to be found in a certain population. This is based on the following equation ... 

If the probabilities do not remain constant over the trials and if there are k (rather than two) possible outcomes of each trial, the hypergeometric distribution applies. For a sample of size N of a population of size T, where... 

Nature In an experiment in which one samples from a relatively small group of items, each of which is classified in one of two categories, A or >, the hypergeometric distribution can be defined. One example is the probability of drawing two red and two black cards from a deck of cards. The hypergeometric distribution is the analog of the binomial distribution when successive trials are not independent, i.e., when the total group of items is not infinite. This happens when the drawn items are not replaced. 

Therefore, exact tests are considered that can be performed using two different approaches conditional and unconditional. In the first case, the total number of tumors r is regarded as fixed. As a result the null distribution of the test statistic is independent of the common probability p. The exact conditional null distribution is a multivariate hypergeometric distribution. 

The hypergeometric distribution can be generalized to a multivariable form, the multivariate hypergeometric distribution, which can be used to extend Fisher s Exact Test to contingency tables larger than 2 by 2 and to multidimensional contingency tables. There is statistical software available to perform these calculations however, due to the complexity of the calculations and the large number of trial tables whose probability of occurrence must be calculated, this extension has received limited use. 

Table 10.7, the probability of the distribution of responses in the 2x2 table is calculated from the hypergeometric distribution as ... 

Microsoft Excel has a built-in hypergeometric distribution function, HYPERGEOMDIST, that calculates probability. 

Use the Excel function for the hypergeometric distribution to calculate the probability of selecting five seimples that wfll be positive for cocaine if a seizure contains 1000 baggies and past laboratory data suggest that 50% of such recent seizures are cocaine and the rest are not. Study the results and explain how the hypergeometric distribution is similar to a simple binomial distribution. 

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