The C(alpha) test is a test of the binomial distribution against the alternative of the beta-binomial distribution.

## Arguments

- x
The output of the

`agg_index`

function with`method = "fisher"`

as parameter.- ...
Not yet implemented.

## Value

Same kind of object as the one returns by the stats
`chisq.test`

function for example.

## Details

It is based on calculation of a test statistic, z, that has an asymptotic standard normal distribution under the null hypothesis. It is one-sided (in the way that the alternative is aggregation, not just "non-randomness"), thus with a confidence level of 95 1.64. When all the sampling units contain the same total number of individuals, n, the test statistic is calculated from:

z = (n(N - 1)I - Nn)/(2Nn(n - 1))^(1/2)

where N is the number of sampling units, and I, Fisher's index of aggregation for incidence data.

## References

Neyman J. 1959. Optimal asymptotic tests of composite statistical hypotheses. In: Probability and Statistics, 213-234. Wiley, New York.

Tarone RE. 1979. Testing the goodness of fit of the binomial distribution. Biometrika, 66(3): 585-590.