Design-corrected p-value for a naively computed chi-square statistic

A statistic computed from complex-survey data while pretending the sample was simple and random is inflated by roughly the design effect, and its nominal p-value is correspondingly too small. The first-order correction is a single division; it is what Korn and Graubard recommend when only a summary design effect is available, and it is exactly Rao and Scott's first-order adjustment when the design effect used is the mean generalized design effect.

Usage

Survip(test_stat, DEFF = 1, df = 1)

Arguments

test_stat

Non-negative naive chi-square statistic.

DEFF

Positive design effect; 1 returns the uncorrected p-value.

df

Degrees of freedom, at least 1.

Value

List with estimate (corrected p-value), p_naive, statistic, statistic_naive, deff, df, inflation, method.

Details

Formula: X2_adj = X2 / deff, p = P(chi2_df > X2_adj).

References

Korn, E. L. and Graubard, B. I. (1999). Analysis of Health Surveys. Wiley, chapter 3. doi:10.1002/9781118032619

Examples

Survip(3.841458820694124, 1, 1)
#> $estimate
#> [1] 0.05
#> 
#> $p_naive
#> [1] 0.05
#> 
#> $statistic
#> [1] 3.841459
#> 
#> $statistic_naive
#> [1] 3.841459
#> 
#> $deff
#> [1] 1
#> 
#> $df
#> [1] 1
#> 
#> $inflation
#> [1] 1
#> 
#> $method
#> [1] "first-order design correction X2/deff [Korn & Graubard 1999]"
#>