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

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

x | The output of the |
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... | Not yet implemented. |

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.

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.

# For incidence data: my_incidence <- incidence(tobacco_viruses) my_fisher <- agg_index(my_incidence, method = "fisher") calpha.test(my_fisher)#> #> C(alpha) test #> #> data: my_fisher #> z = 13.036, p-value < 2.2e-16 #>