Description Usage Arguments Details Value Author(s) References See Also Examples

Tests the homogeneity of proportions between *I* groups (H0: *p_1 = p_2 = ... = p_I* ) from clustered
binomial data *(n, y)* using the adjusted *chi-squared* statistic proposed by Donner (1989).

1 2 |

`formula` |
An optional formula where the left-hand side is either a matrix of the form |

`response` |
An optional argument indicating either a matrix of the form |

`weights` |
An optional argument used when the left-hand side of |

`group` |
An optional argument only used when |

`data` |
A data frame containing the response ( |

`C` |
If not NULL, a numerical vector of |

The *chi-squared* statistic is adjusted with the correction factor *C_i*
computed in each group *i*. The test statistic is given by:

*
X^2 = sum( (y_i - n_i * p)^2 / (C_i * n_i * p * (1 - p)) )*

where *C_i = 1 + (nA_i - 1) * ρ*, *nA_i* is a scalar depending on the cluster sizes,
and *rho* is the ANOVA estimate of the intra-cluster correlation, assumed common
across groups (see Donner, 1989 or Donner et al., 1994). The statistic is compared to a *chi-squared*
distribution with *I - 1* degrees of freedom. Fixed correction factors can be specified
with the argument `C`

.

An object of formal class “drs”: see `drs-class`

for details. The slot `tab`

provides the proportion of successes and the correction factor for each group.

Matthieu Lesnoff [email protected], Renaud Lancelot [email protected]

Donner, A., 1989. *Statistical methods in ophthalmology: an adjusted chi-squared approach*. Biometrics 45, 605-611.

Donner, A., 1993. *The comparison of proportions in the presence of litter effects*. Prev. Vet. Med. 18, 17-26.

Donner, A., Eliasziw, M., Klar, N., 1994. *A comparison of methods for testing homogeneity of proportions in
teratologic studies*. Stat. Med. 13, 1253-1264.

`chisq.test`

, `raoscott`

, `drs-class`

1 2 3 4 5 6 7 8 9 10 | ```
data(rats)
donner(formula = cbind(y, n - y) ~ group, data = rats)
donner(formula = y/n ~ group, weights = n, data = rats)
donner(response = cbind(y, n - y), group = group, data = rats)
donner(response = y/n, weights = n, group = group, data = rats)
# standard test
donner(cbind(y, n - y) ~ group, data = rats, C = c(1, 1))
data(antibio)
donner(cbind(y, n - y) ~ treatment, data = antibio)
``` |

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