calpha.test {epiphy}

C(alpha) test.

Description

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

Usage

calpha.test(x, ...)

## S3 method for class 'fisher'
calpha.test(x, ...)

Arguments

x

The output of the agg_index function with method = "fisher" as parameter.

...

Not yet implemented.

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.

Value

Same kind of object as the one returns by the stats chisq.test function for example.

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.

See Also

chisq.test, z.test

Examples

# For incidence data:
my_incidence <- incidence(tobacco_viruses)
my_fisher <- agg_index(my_incidence, method = "fisher")
calpha.test(my_fisher)