Survey Package R Exercises: 20 Complex-Survey Practice Problems

Explanation: id = ~1 signals no clustering (single-stage). strata = ~stype tells survey to compute variances within each stratum and pool them, which is what makes stratified estimators more efficient than simple random sampling. weights = ~pw carries the inverse-inclusion-probability weight so totals scale up to the population. Dropping strata would leave point estimates unchanged but inflate standard errors because the stratification gain would be ignored.

Explanation: With cluster sampling, the unit of randomization is the cluster (the district), not the school, so id = ~dnum is critical: every school in the same district shares the same selection event and their outcomes are correlated. Passing id = ~1 here would treat the 183 schools as independent draws and shrink the standard errors well below their true value, which is the most common beginner mistake with clustered data.

Explanation: When you supply fpc, svydesign derives the weights from the inclusion probabilities at each stage, so you do not pass weights. The two-stage id formula ~dnum + snum declares that variability comes first from sampling districts and then from sampling schools inside chosen districts. The fpc columns are the population sizes at each stage: dropping fpc2 would treat the within-district sample as drawn with replacement and overstate the variance for population-total estimators.

Explanation: svymean() ignores the unweighted mean(apistrat$api00) and uses the survey weights, which is essential when the sampling fractions differ by stratum (here, high schools were oversampled). The standard error comes from a Taylor-series linearization that accounts for stratification, so it is smaller than what a naive t.test would produce. The result prints as a one-row matrix with class svystat; pass it to confint() for a Wald confidence interval.

Explanation: svytotal() multiplies each observation by its weight and sums, giving an estimate of the finite-population total. Without survey weights you would underestimate the total dramatically because the sample only contains 200 schools. The standard error here is large in absolute terms but small as a fraction of the estimate (about 3%), reflecting the design's efficiency. Use coef() and SE() to pull out the numeric values for downstream code.

Explanation: svyquantile() inverts the weighted empirical CDF, so the result is the value at which the cumulative weight first crosses the requested probability. Standard errors come from a Woodruff confidence-interval inversion by default, which is more reliable than bootstrap quantiles in small samples. The interquartile range of 191 points here tells a richer story than the mean: the bottom quartile is more than a full standard deviation below the top, signaling persistent inequality across schools.

Explanation: The design effect (DEff) is the ratio of the actual sampling variance to the variance you would have got under simple random sampling of the same size. A DEff below 1 (here, 0.55) means stratification has reduced the variance, roughly halving it: the effective sample size is 200 / 0.55 or about 364. Cluster designs in the same data show a DEff well above 1, since intra-cluster correlation costs precision. Always report DEff alongside SE in survey publications so readers can compare designs.

Explanation: svyby() is the survey-aware analogue of tapply() or dplyr::group_by() + summarise(): it slices the design by the grouping variable and applies the chosen statistic within each slice while preserving the design metadata. The result is a data frame, so it composes well with ggplot2. To produce a covariance matrix between the three subgroup means (needed for contrasts), add covmat = TRUE. Do not subset the data frame manually and call svymean separately: that breaks the strata and inflates SEs.

Explanation: subset() applied to a survey.design object zeros out the weights for excluded rows rather than dropping them, which keeps the stratum count intact so variance estimation is still valid. This is the right way to do domain estimation in survey; calling svydesign() on a pre-filtered data frame is wrong because losing a whole stratum collapses the variance calculation in that cell. The big gap between 560 here and the 662 overall mean illustrates why poverty researchers always demand domain-conditional estimates.

Explanation: Without covmat = TRUE, svyby only retains the per-group SEs and svycontrast() will fall back to assuming independence between groups, which biases the test. Because the three school-type means are estimated from disjoint strata in this design the covariance happens to be zero, but in cluster or multistage designs subgroup estimates are usually correlated and the difference SE can be much smaller (or larger) than sqrt(SE1^2 + SE2^2). Always pass covmat = TRUE when you plan to combine subgroup estimates.

Explanation: svytable() returns a table of weighted counts, not unweighted frequencies, so the cell values sum to an estimate of the population total in each cell. A common pitfall: do not pass this result to chisq.test(), which assumes the entries are independent unweighted counts; use svychisq() (next exercise) for a design-aware test. Pass Ntotal = sum(weights) if you want the table rescaled to the actual population size for a cleaner display in reports.

Explanation: The classical Pearson chi-square statistic does not have a chi-square distribution under complex sampling because the cell counts are not multinomial. svychisq() reports a Rao-Scott corrected statistic, scaled by the average generalized design effect, distributed as F with adjusted degrees of freedom. The decisive p-value here confirms a strong association between school type and meeting the schoolwide growth target: high schools are far less likely than elementary schools to clear the bar.

Explanation: When a proportion is close to 0 or 1, the symmetric Wald interval can spill outside [0,1]; method = "logit" transforms to the log-odds scale, builds a symmetric interval there, then inverts it, guaranteeing a valid interval. The other useful methods are "likelihood" for very small samples and "beta" for the Clopper-Pearson style. For mid-range proportions like 0.59 all methods give nearly identical answers; the choice matters most near the edges.

Explanation: svyglm() differs from a weighted lm() in two ways: it computes design-consistent (sandwich) standard errors that respect strata and clusters, and the residual degrees of freedom default to nrow(design) - 1 - (#strata - 1). Calling lm(api00 ~ ell + meals, weights = pw) would give the same point estimates but wrong SEs because it treats the weights as precision weights, not sampling weights, and ignores the stratification.

Explanation: family = quasibinomial() is preferred over binomial() for survey logistic regression because the latter triggers a "non-integer successes" warning whenever the weights are not integers; quasibinomial uses the same logit link with a free dispersion parameter and otherwise identical estimates. The strong api99 coefficient (prior-year score) tells the obvious story: schools that did well last year tend to keep doing well. Once you control for that, meals adds nothing.

Explanation: svycontrast() takes a named list of linear combinations and returns each combination's estimate and SE using the full coefficient covariance matrix, so the resulting SE is smaller than sqrt((25*SE_ell)^2 + (60*SE_meals)^2) whenever ell and meals are positively correlated in the design (and they are: schools with many ELL students also tend to have many meal-eligible students). Manually adding the variances ignores that covariance and would overstate the uncertainty by 20-40%.

Explanation: Post-stratification adjusts weights so that the sum of weights in each post-stratum equals the known population total, which reduces variance when the post-stratum variable is correlated with the outcome and corrects for non-response or coverage bias. It is not the same as stratified sampling: the strata in the design control variance estimation, while post-strata control the weight adjustment. After post-stratifying, the standard errors of svytotal() for variables related to stype drop noticeably.

Explanation: Raking (iterative proportional fitting) is the right tool when you know the marginal distributions of two or more auxiliary variables but not their joint distribution: it cycles through each margin, adjusting the weights so each marginal sums correctly, and iterates until everything matches simultaneously. Compared with full post-stratification it loses a little efficiency but is the standard approach in election polling and national health surveys where joint totals are simply unavailable.

Explanation: Replicate-weight methods (jackknife, BRR, bootstrap) sidestep linearization by re-computing the estimator under many perturbed weight columns and treating the variability of those replicate estimates as the variance. Bootstrap replicates are robust for medians, quantiles, ratios, and pretty much any non-linear estimator. Many public-use survey files (CPS, ACS, NHANES) ship with replicate weights already attached; load them with svrepdesign() directly rather than svydesign().

Explanation: srvyr is a thin wrapper around survey that exposes a dplyr grammar: group_by for subgroups, summarise with survey_mean, survey_total, survey_quantile, and survey_prop. The numerical results are byte-identical to svyby because the same underlying linearization runs under the hood. Use it when your team is already fluent in dplyr, or when you want survey estimates to flow into a ggplot2 pipeline without intermediate as.data.frame() calls.