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 Rao and Scott (1993).

1 2 |

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

`response` |
An optional argument: 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 ( |

`pooled` |
Logical indicating if a pooled design effect is estimated over the |

`deff` |
A numerical vector of |

The method is based on the concepts of design effect and effective sample size.

The design effect in each group *i* is estimated by *deff_i = vratio_i / vbin_i*, where *vratio_i* is
the variance of the ratio estimate of the probability in group *i* (Cochran, 1999, p. 32 and p. 66)
and *vbin_i* is the standard binomial variance. A pooled design effect (i.e., over the *I* groups)
is estimated if argument `pooled = TRUE`

(see Rao and Scott, 1993, Eq. 6). Fixed design effects can be specified
with the argument `deff`

.

The *deff_i* are used to compute the effective sample sizes *nadj_i = n_i / deff_i*, the effective numbers
of successes *yadj_i = y_i / deff_i* in each group *i*, and the overall effective proportion
*padj = sum(yadj_i) / sum(deff_i)*.
The test statistic is obtained by substituting these quantities in the usual *chi-squared* statistic,
yielding:

*
X^2 = sum( (yadj_i - nadj_i * padj)^2 / (nadj_i * padj * (1 - padj)) )*

which is compared to a *chi-squared* distribution with *I - 1* degrees of freedom.

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

for details. The slot `tab`

provides the proportion of successes, the variances of the proportion and the design effect for each group.

Matthieu Lesnoff matthieu.lesnoff@cirad.fr, Renaud Lancelot renaud.lancelot@cirad.fr

Cochran, W.G., 1999, 2nd ed. *Sampling techniques*. John Wiley & Sons, New York.

Rao, J.N.K., Scott, A.J., 1992. *A simple method for the analysis of clustered binary data*.
Biometrics 48, 577-585.

`chisq.test`

, `donner`

, `iccbin`

, `drs-class`

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
data(rats)
# deff by group
raoscott(cbind(y, n - y) ~ group, data = rats)
raoscott(y/n ~ group, weights = n, data = rats)
raoscott(response = cbind(y, n - y), group = group, data = rats)
raoscott(response = y/n, weights = n, group = group, data = rats)
# pooled deff
raoscott(cbind(y, n - y) ~ group, data = rats, pooled = TRUE)
# standard test
raoscott(cbind(y, n - y) ~ group, data = rats, deff = c(1, 1))
data(antibio)
raoscott(cbind(y, n - y) ~ treatment, data = antibio)
``` |

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