Overdispersion test for binomial and poisson data

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.

References

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

Author

Luca Scrucca

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)
#>                    
#> Overdispersion test Obs.Var/Theor.Var Statistic p-value
#>       binomial data         0.7644566  22.16924 0.81311

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)
#>                    
#> Overdispersion test Obs.Var/Theor.Var Statistic  p-value
#>        poisson data          1.472203  42.69388 0.048579