qccOverdispersionTest: Overdispersion test for binomial and poisson data

In luca-scr/qcc: Quality Control Charts

Overdispersion test for binomial and poisson data

Description

This function allows to test for overdispersed data in the binomial and poisson case.

Usage

qccOverdispersionTest(x, size, 
  type = ifelse(missing(size), "poisson", "binomial"))

Arguments

x	a vector of observed data values
size	for binomial data, a vector of sample sizes
type	a character string specifying the distribution for testing, either "poisson" or "binomial". By default, if size is provided a binomial distribution is assumed, otherwise a poisson distribution.

Details

This very simple test amounts to compute the test statistic

D = s^2 / \sigma^2 \times (n - 1)

where s^2 is the observed variance, \sigma^2 is the theoretical variance, and n is the number of observations. The test statistic is the compared to the critical value of a Chi-square distribution with n-1 degrees of freedom.

Value

The function returns a matrix of results.

Author(s)

Luca Scrucca

References

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control, New York, Chapman and Hall, pp. 216–218

Examples

# data from Wetherill and Brown (1991) pp. 212--213, 216--218:
x  = c(12,11,18,11,10,16,9,11,14,15,11,9,10,13,12,
       8,12,13,10,12,13,16,12,18,16,10,16,10,12,14)
size  = rep(50, length(x))
qccOverdispersionTest(x, size)

x  = c(11,8,13,11,13,17,25,23,11,16,9,15,10,16,12,
       8,9,15,4,12,12,12,15,17,14,17,12,12,7,16)
qccOverdispersionTest(x)

luca-scr/qcc documentation built on June 14, 2025, 9:55 p.m.