Working with Survey Weights • mariposa

library(mariposa)
library(dplyr)
data(survey_data)

Overview

Survey weights correct for sampling biases so your results represent the target population, not just your sample. Common reasons for weighting include oversampling of small groups, differential non-response, and post-stratification to known demographics.

In mariposa, adding weights is as simple as weights = sampling_weight in any function call. This guide covers the dedicated w_* functions, the effective sample size concept, and best practices.

The Impact of Weights

# Without weights (describes the sample)
unweighted <- survey_data %>%
  summarise(
    mean_age = mean(age, na.rm = TRUE),
    mean_income = mean(income, na.rm = TRUE)
  )

# With weights (represents the population)
age_w <- w_mean(survey_data, age, weights = sampling_weight)
income_w <- w_mean(survey_data, income, weights = sampling_weight)

comparison <- data.frame(
  Variable = c("Age", "Income"),
  Unweighted = c(unweighted$mean_age, unweighted$mean_income),
  Weighted = c(age_w$results$weighted_mean, income_w$results$weighted_mean)
)
print(comparison)
#>   Variable Unweighted  Weighted
#> 1      Age    50.5496   50.5144
#> 2   Income  3753.9341 3743.0994

The difference between weighted and unweighted results reflects how biased your sample is. Larger differences mean weights are doing more important work.

Weighted Statistics Functions

mariposa provides 11 w_* functions for individual weighted statistics.

Central Tendency

# Weighted mean
w_mean(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Mean Statistics
#> ------------------------
#> 
#> --- income ---
#>  Variable weighted_mean Effective_N
#>    income      3743.099      2158.9

# Weighted median
w_median(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Median Statistics
#> --------------------------
#> 
#> --- income ---
#>  Variable weighted_median Effective_N
#>    income            3500      2158.9

# Weighted mode
w_modus(survey_data, education, weights = sampling_weight)
#> 
#> Weighted Mode Statistics
#> ------------------------
#> # A tibble: 1 × 3
#>   Variable  weighted_mode   effective_n
#>   <chr>     <ord>                 <dbl>
#> 1 education Basic Secondary       2469.

Dispersion

# Weighted standard deviation
w_sd(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Standard Deviation Statistics
#> --------------------------------------
#> 
#> --- income ---
#>  Variable weighted_sd Effective_N
#>    income    1423.966      2158.9

# Weighted variance
w_var(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Variance Statistics
#> ----------------------------
#> 
#> --- income ---
#>  Variable weighted_var Effective_N
#>    income      2027678      2158.9

# Weighted interquartile range
w_iqr(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Interquartile Range Statistics
#> ---------------------------------------
#> 
#> --- income ---
#>  Variable weighted_iqr Effective_N
#>    income         1900      2158.9

Distribution Shape

# Weighted skewness
w_skew(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Skewness Statistics
#> ----------------------------
#> 
#> --- income ---
#>  Variable weighted_skew Effective_N
#>    income         0.725      2158.9

# Weighted kurtosis
w_kurtosis(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Excess Kurtosis Statistics
#> -----------------------------------
#> 
#> --- income ---
#>  Variable weighted_kurtosis Effective_N
#>    income             0.388      2158.9

Precision and Range

# Weighted standard error
w_se(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Standard Error Statistics
#> ----------------------------------
#> 
#> --- income ---
#>  Variable weighted_se Effective_N
#>    income      30.353      2158.9

# Weighted quantiles
w_quantile(survey_data, income,
           probs = c(0.25, 0.5, 0.75),
           weights = sampling_weight)
#> 
#> Weighted Quantile Statistics
#> ----------------------------
#>  Variable Quantile Value    N Effective_N         Weights
#>    income      25%  2700 2186      2158.9 sampling_weight
#>    income      50%  3500 2186      2158.9 sampling_weight
#>    income      75%  4600 2186      2158.9 sampling_weight
#> ----------------------------------------

# Weighted range
w_range(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Range Statistics
#> -------------------------
#> 
#> --- income ---
#>  Variable weighted_range Effective_N
#>    income           7200      2158.9

Multiple Variables

All w_* functions accept multiple variables:

w_mean(survey_data, age, income, life_satisfaction,
       weights = sampling_weight)
#> 
#> Weighted Mean Statistics
#> ------------------------
#> 
#> --- age ---
#>  Variable weighted_mean Effective_N
#>       age        50.514      2468.8
#> 
#> --- income ---
#>  Variable weighted_mean Effective_N
#>    income      3743.099      2158.9
#> 
#> --- life_satisfaction ---
#>           Variable weighted_mean Effective_N
#>  life_satisfaction         3.625      2390.9

Effective Sample Size

Weighting reduces statistical precision. The effective sample size ( $n_{eff}$ ) tells you how much information your weighted sample actually carries:

$n_{eff} = \frac{\left(\sum w_i\right)^2}{\sum w_i^2}$

actual_n <- nrow(survey_data)
age_w <- w_mean(survey_data, age, weights = sampling_weight)
effective_n <- age_w$results$effective_n

cat("Actual sample size:", actual_n, "\n")
#> Actual sample size: 2500
cat("Effective sample size:", round(effective_n), "\n")
#> Effective sample size: 2469
cat("Design effect:", round(actual_n / effective_n, 2), "\n")
#> Design effect: 1.01

A design effect of 1.0 means weights have no impact on precision. Values above 1 mean larger standard errors than an unweighted sample of the same size.

Weights in Analysis Functions

Every analysis function in mariposa supports the weights argument:

# Descriptive statistics
survey_data %>%
  describe(income, life_satisfaction, weights = sampling_weight)
#> 
#> Weighted Descriptive Statistics
#> -------------------------------
#>           Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>             income 3743.099   3500 1423.966  7200 1900    0.724      2158.9
#>  life_satisfaction    3.625      4    1.152     4    2   -0.498      2390.9
#> ----------------------------------------

# Frequency tables
survey_data %>%
  frequency(education, weights = sampling_weight)
#> 
#> Weighted Frequency Analysis Results
#> -----------------------------------
#> 
#> education (Highest educational attainment)
#> # total N=2516 valid N=2516 mean=NA sd=NA skewness=NA
#> 
#> +------------------------+------------------------+--------+--------+--------+--------+
#> |                  Value |                  Label |      N |  Raw % |Valid % | Cum. % |
#> +------------------------+------------------------+--------+--------+--------+--------+
#> |        Basic Secondary |        Basic Secondary |    848 |  33.71 |  33.71 |  33.71 |
#> | Intermediate Secondary | Intermediate Secondary |    641 |  25.47 |  25.47 |  59.18 |
#> |     Academic Secondary |     Academic Secondary |    642 |  25.51 |  25.51 |  84.69 |
#> |             University |             University |    385 |  15.31 |  15.31 | 100.00 |
#> +------------------------+------------------------+--------+--------+--------+--------+
#> |                  Total |                        |   2516 | 100.00 | 100.00 |        |
#> +------------------------+------------------------+--------+--------+--------+--------+

# t-test
survey_data %>%
  t_test(income, group = gender, weights = sampling_weight)
#> t-Test: income by gender [Weighted]
#>   t(2178.9) = 0.751, p = 0.453 , g = 0.032 (negligible), N = 2201

# ANOVA
survey_data %>%
  oneway_anova(life_satisfaction, group = education,
               weights = sampling_weight)
#> One-Way ANOVA: life_satisfaction by education [Weighted]
#>   F(3, 2433) = 65.359, p < 0.001 ***, eta2 = 0.075 (medium), N = 2437

# Chi-square
survey_data %>%
  chi_square(education, employment, weights = sampling_weight)
#> Chi-Squared Test: education × employment [Weighted]
#>   chi2(12) = 130.696, p < 0.001 ***, V = 0.132 (small), N = 2518

# Correlation
survey_data %>%
  pearson_cor(age, income, weights = sampling_weight)
#> Pearson Correlation: age x income [Weighted]
#>   r = -0.005, p = 0.828 , N = 2201

# Regression
survey_data %>%
  linear_regression(life_satisfaction ~ age + income,
                    weights = sampling_weight)
#> Linear Regression: life_satisfaction ~ age + income [Weighted]
#>   R2 = 0.203, adj.R2 = 0.202, F(2, 2127) = 270.45, p < 0.001 ***, N = 2130

Grouped Weighted Analysis

All functions work seamlessly with group_by():

survey_data %>%
  group_by(region) %>%
  describe(age, income, life_satisfaction,
           weights = sampling_weight)
#> 
#> Weighted Descriptive Statistics
#> -------------------------------
#> 
#> Group: region = East
#> --------------------
#> ----------------------------------------
#>           Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>                age   52.278     53   17.595    77   24    0.098       477.0
#>             income 3760.687   3600 1388.321  7200 1700    0.718       421.9
#>  life_satisfaction    3.623      4    1.203     4    2   -0.556       457.4
#> ----------------------------------------
#> 
#> Group: region = West
#> --------------------
#> ----------------------------------------
#>           Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>                age   50.067     49   16.927    77   24    0.170      1993.1
#>             income 3738.586   3500 1433.325  7200 1900    0.726      1738.1
#>  life_satisfaction    3.625      4    1.139     4    2   -0.481      1934.8
#> ----------------------------------------

survey_data %>%
  group_by(region) %>%
  t_test(income, group = gender, weights = sampling_weight)
#> [region = 1]
#> t-Test: income by gender [Weighted]
#>   t(431.6) = 1.676, p = 0.094 , g = 0.158 (negligible), N = 450
#> [region = 2]
#> t-Test: income by gender [Weighted]
#>   t(1739.9) = 0.009, p = 0.993 , g = 0.000 (negligible), N = 1751

Diagnosing Weight Issues

Checking Weight Distribution

weight_stats <- survey_data %>%
  summarise(
    min = min(sampling_weight, na.rm = TRUE),
    max = max(sampling_weight, na.rm = TRUE),
    mean = mean(sampling_weight, na.rm = TRUE),
    sd = sd(sampling_weight, na.rm = TRUE)
  )
print(weight_stats)
#> # A tibble: 1 × 4
#>     min   max  mean    sd
#>   <dbl> <dbl> <dbl> <dbl>
#> 1 0.702  1.40  1.01 0.113

A rule of thumb: weights should range from about 0.2 to 5. Extreme values (below 0.1 or above 10) may indicate problems with the weighting scheme.

Missing Weights

missing <- sum(is.na(survey_data$sampling_weight))
total <- nrow(survey_data)
cat("Missing weights:", missing, "/", total,
    "(", round(missing / total * 100, 1), "%)\n")
#> Missing weights: 0 / 2500 ( 0 %)

Weight Trimming

If weights are extreme, trim them to reduce variance at the cost of a small increase in bias:

trimmed <- survey_data %>%
  mutate(
    weight_trimmed = case_when(
      sampling_weight > 5 ~ 5,
      sampling_weight < 0.2 ~ 0.2,
      TRUE ~ sampling_weight
    )
  )

original <- w_mean(survey_data, income, weights = sampling_weight)
trimmed_result <- w_mean(trimmed, income, weights = weight_trimmed)

cat("Original weighted mean:", round(original$results$weighted_mean, 1), "\n")
#> Original weighted mean: 3743.1
cat("Trimmed weighted mean:", round(trimmed_result$results$weighted_mean, 1), "\n")
#> Trimmed weighted mean: 3743.1

Complete Example

# 1. Inspect weight properties
survey_data %>%
  summarise(
    n = n(),
    mean_weight = mean(sampling_weight, na.rm = TRUE),
    sd_weight = sd(sampling_weight, na.rm = TRUE),
    min_weight = min(sampling_weight, na.rm = TRUE),
    max_weight = max(sampling_weight, na.rm = TRUE)
  )
#> # A tibble: 1 × 5
#>       n mean_weight sd_weight min_weight max_weight
#>   <int>       <dbl>     <dbl>      <dbl>      <dbl>
#> 1  2500        1.01     0.113      0.702       1.40

# 2. Compare weighted vs unweighted
vars <- c("age", "income", "life_satisfaction")
for (var in vars) {
  unw <- mean(survey_data[[var]], na.rm = TRUE)
  w_result <- w_mean(survey_data, !!sym(var), weights = sampling_weight)
  w <- w_result$results$weighted_mean
  cat(sprintf("%s: unweighted = %.2f, weighted = %.2f (diff = %.1f%%)\n",
              var, unw, w, (w - unw) / unw * 100))
}
#> age: unweighted = 50.55, weighted = 50.51 (diff = -0.1%)
#> income: unweighted = 3753.93, weighted = 3743.10 (diff = -0.3%)
#> life_satisfaction: unweighted = 3.63, weighted = 3.62 (diff = -0.1%)

# 3. Weighted group comparison
survey_data %>%
  group_by(region) %>%
  describe(income, weights = sampling_weight)
#> 
#> Weighted Descriptive Statistics
#> -------------------------------
#> 
#> Group: region = East
#> --------------------
#> ----------------------------------------
#>  Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>    income 3760.687   3600 1388.321  7200 1700    0.718       421.9
#> ----------------------------------------
#> 
#> Group: region = West
#> --------------------
#> ----------------------------------------
#>  Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>    income 3738.586   3500 1433.325  7200 1900    0.726      1738.1
#> ----------------------------------------

# 4. Weighted hypothesis test
survey_data %>%
  t_test(income, group = gender, weights = sampling_weight)
#> t-Test: income by gender [Weighted]
#>   t(2178.9) = 0.751, p = 0.453 , g = 0.032 (negligible), N = 2201

Best Practices

Always use weights when they are provided. They correct for sampling biases and make your results generalizable.
Report both weighted and unweighted sample sizes. The actual n tells readers about data collection; the effective n tells them about statistical precision.
Check for extreme weights. Large variation inflates standard errors and reduces statistical power. Consider trimming if necessary.
Document the weight source. Explain how weights were calculated and what they adjust for (e.g., age, gender, region post-stratification).
Report the effective sample size. This tells readers how much precision was lost due to weighting.

Summary

Survey weights make results representative of the population, not just the sample
The 11 w_* functions provide individual weighted statistics
All analysis functions support weights via weights =
The effective sample size measures how much precision weighting costs
Check and document weight distributions, extreme values, and missing weights

Next Steps

Get started with the package — see vignette("introduction")
Explore your data — see vignette("descriptive-statistics")
Test hypotheses — see vignette("hypothesis-testing")
Import weighted data from SPSS — see vignette("data-io")