The cell entries are estimated population counts, so Pearson's statistic computed on them is wrong twice: it is on the population scale, and it ignores the variance the weights inflate. Rao and Scott's first-order correction evaluates Pearson's statistic on the weighted proportions and multiplies by the effective sample size neff = (sum w)^2 / sum w^2 in place of n. With equal weights neff = n and the statistic is exactly the uncorrected chisq.test statistic.
Value
List with estimate, statistic_naive, df,
p_value, counts (row-major), prop, rows,
cols, nrow, ncol, neff, deff,
n, method.
Details
Formula: X2 = neff sum_ij (p_ij - p_i. p_.j)^2 / (p_i. p_.j), referred to chi-square on (r-1)(c-1) degrees of freedom.
References
Rao, J. N. K. and Scott, A. J. (1984). On chi-squared tests for multiway contingency tables with cell proportions estimated from survey data. The Annals of Statistics 12(1):46-60. doi:10.1214/aos/1176346391
Examples
Svytbl(c(0, 0, 0, 0, 1, 1, 1, 1), c(0, 0, 1, 1, 0, 1, 1, 1))
#> $estimate
#> [1] 0.5333333
#>
#> $statistic_naive
#> [1] 0.5333333
#>
#> $df
#> [1] 1
#>
#> $p_value
#> [1] 0.4652088
#>
#> $counts
#> [1] 2 2 1 3
#>
#> $prop
#> [1] 0.250 0.250 0.125 0.375
#>
#> $rows
#> [1] "0" "1"
#>
#> $cols
#> [1] "0" "1"
#>
#> $nrow
#> [1] 2
#>
#> $ncol
#> [1] 2
#>
#> $neff
#> [1] 8
#>
#> $deff
#> [1] 1
#>
#> $n
#> [1] 8
#>
#> $method
#> [1] "Rao-Scott first-order corrected Pearson chi-square [Rao & Scott 1984]"
#>