Compare survey estimates between domains

Each domain's estimate against a reference domain: the difference, its standard error from the design (the covariance between the two estimates included, which is what a pair of separate intervals leaves out), a confidence interval and a two-sided p-value from the normal approximation. Use it to test whether two regions or groups differ, rather than checking whether their separate intervals overlap: overlapping intervals do not mean no difference, and domains of one survey are not independent.

Usage

survey_compare(
  design,
  data,
  y,
  by,
  stat = c("mean", "total", "proportion", "ratio"),
  denominator = NULL,
  levels = NULL,
  ref = NULL,
  conf_level = 0.95
)

Arguments

design

A survey_design() built on data.

data

The data frame the design was built on.

y

Character scalar, the analysis column: numeric for a mean, total or ratio; any type for a proportion (each distinct value is a category).

by

The domain columns to compare across.

stat

"mean", "total", "proportion" or "ratio" (of y to denominator).

denominator

For a ratio, the denominator column.

levels

For a proportion, the categories to report (default all observed).

ref

The reference domain, as its label (for several by columns, the labels joined with " / "); a number is matched as the label it prints as. Default NULL: the first domain.

conf_level

Numeric scalar in (0, 1), the confidence level; default 0.95.

Value

A data frame of class c("rmbl_svy_compare", "data.frame"), one row per non-reference domain (and category): domain, level (for a proportion only), numeric estimate (the domain's), reference (the reference domain's), difference, se, lower, upper and p_value. Attributes ref, stat, y and conf_level.

Details

The estimates come from survey_estimate() with Wald intervals. For domain \(i\) and reference \(0\) the difference is \(d = \hat\theta_i - \hat\theta_0\) with \(SE(d) = \sqrt{V_{ii} + V_{00} - 2V_{i0}}\) from the design covariance; the interval is \(d \pm z\,SE(d)\) and the p-value \(2\Phi(-|d|/SE(d))\), both on the normal distribution (there is no df argument). For a proportion every category is compared separately. No adjustment for multiple comparisons is made.

Errors: by missing or empty; fewer than two domains; a ref that is not a single domain label present in the data; and every error of survey_estimate().

Examples

set.seed(1)
d <- data.frame(region = rep(c("north", "south", "east"), length.out = 150),
                smoker = rbinom(150, 1, 0.3), w = runif(150, 50, 150))
des <- survey_design(d, weights = "w")
survey_compare(des, d, "smoker", by = "region", stat = "proportion",
               levels = "1", ref = "north")
#> Survey proportion of smoker against north (95% interval)
#>  domain level estimate reference difference      se   lower   upper p_value
#>    east     1   0.2538    0.3701    -0.1164 0.09485 -0.3023 0.06954  0.2199
#>   south     1   0.2352    0.3701    -0.1350 0.09464 -0.3205 0.05052  0.1538

# means, against the default (first) domain, at 90 percent
d$drinks <- rpois(150, 3)
survey_compare(des, d, "drinks", by = "region", conf_level = 0.90)
#> Survey mean of drinks against east (90% interval)
#>  domain estimate reference difference     se   lower  upper p_value
#>   north    3.066     3.361    -0.2952 0.3947 -0.9444 0.3539  0.4544
#>   south    3.083     3.361    -0.2779 0.3811 -0.9048 0.3490  0.4659

# the reference must be one of the domains
try(survey_compare(des, d, "drinks", by = "region", ref = "west"))
#> Error : `ref` is not one of the domains: east, north, south