Working with Survey Weights

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
#> ------------------------
#> Weights: sampling_weight
#> 
#>   ---------------------------------
#>   Variable      Mean     N  Missing
#>   ---------------------------------
#>   income    3743.099  2201      315
#>   ---------------------------------

# Weighted median
w_median(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Median Statistics
#> --------------------------
#> Weights: sampling_weight
#> 
#>   ---------------------------------
#>   Variable    Median     N  Missing
#>   ---------------------------------
#>   income    3500.000  2201      315
#>   ---------------------------------

# Weighted mode
w_modus(survey_data, education, weights = sampling_weight)
#> 
#> Weighted Mode Statistics
#> ------------------------
#> Weights: sampling_weight
#> 
#>   -----------------------------------------
#>   Variable   Mode                N  Missing
#>   -----------------------------------------
#>   education  Basic Secondary  2516        0
#>   -----------------------------------------

Dispersion

# Weighted standard deviation
w_sd(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Standard Deviation Statistics
#> --------------------------------------
#> Weights: sampling_weight
#> 
#>   ---------------------------------
#>   Variable        SD     N  Missing
#>   ---------------------------------
#>   income    1423.966  2201      315
#>   ---------------------------------

# Weighted variance
w_var(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Variance Statistics
#> ----------------------------
#> Weights: sampling_weight
#> 
#>   ------------------------------------
#>   Variable     Variance     N  Missing
#>   ------------------------------------
#>   income    2027677.966  2201      315
#>   ------------------------------------

# Weighted interquartile range
w_iqr(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Interquartile Range Statistics
#> ---------------------------------------
#> Weights: sampling_weight
#> 
#>   ---------------------------------
#>   Variable       IQR     N  Missing
#>   ---------------------------------
#>   income    1900.000  2201      315
#>   ---------------------------------

Distribution Shape

# Weighted skewness
w_skew(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Skewness Statistics
#> ----------------------------
#> Weights: sampling_weight
#> 
#>   ---------------------------------
#>   Variable  Skewness     N  Missing
#>   ---------------------------------
#>   income       0.725  2201      315
#>   ---------------------------------

# Weighted kurtosis
w_kurtosis(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Excess Kurtosis Statistics
#> -----------------------------------
#> Weights: sampling_weight
#> 
#>   ---------------------------------
#>   Variable  Kurtosis     N  Missing
#>   ---------------------------------
#>   income       0.388  2201      315
#>   ---------------------------------

Precision and Range

# Weighted standard error
w_se(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Standard Error Statistics
#> ----------------------------------
#> Weights: sampling_weight
#> 
#>   -------------------------------
#>   Variable      SE     N  Missing
#>   -------------------------------
#>   income    30.353  2201      315
#>   -------------------------------

# Weighted quantiles
w_quantile(survey_data, income,
           probs = c(0.25, 0.5, 0.75),
           weights = sampling_weight)
#> 
#> Weighted Quantile Statistics
#> ----------------------------
#> Weights: sampling_weight
#> 
#>   -----------------------------------------------------
#>   Variable       25%       50%       75%     N  Missing
#>   -----------------------------------------------------
#>   income    2700.000  3500.000  4600.000  2201      315
#>   -----------------------------------------------------

# Weighted range
w_range(survey_data, income, weights = sampling_weight)
#> 
#> Weighted Range Statistics
#> -------------------------
#> Weights: sampling_weight
#> 
#>   ---------------------------------
#>   Variable     Range     N  Missing
#>   ---------------------------------
#>   income    7200.000  2201      315
#>   ---------------------------------

Multiple Variables

All w_* functions accept multiple variables:

w_mean(survey_data, age, income, life_satisfaction,
       weights = sampling_weight)
#> 
#> Weighted Mean Statistics
#> ------------------------
#> Weights: sampling_weight
#> 
#>   ------------------------------------------
#>   Variable               Mean     N  Missing
#>   ------------------------------------------
#>   age                  50.514  2516        0
#>   income             3743.099  2201      315
#>   life_satisfaction     3.625  2437       79
#>   ------------------------------------------

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     N  Missing
#>   --------------------------------------------------------------------------------------------
#>   income             3743.099  3500.000  1423.966  7200.000  1900.000     0.725  2201      315
#>   life_satisfaction     3.625     4.000     1.152     4.000     2.000    -0.499  2437       79
#>   --------------------------------------------------------------------------------------------

# Frequency tables
survey_data %>%
  frequency(education, weights = sampling_weight)
#> 
#> Weighted Frequency Analysis Results
#> -----------------------------------
#> 
#> education (Highest educational attainment)
#> # total N=2516 valid N=2516
#> 
#> +------------------------+------+--------+---------+--------+
#> | Value                  |    N |  Raw % | Valid % | Cum. % |
#> +------------------------+------+--------+---------+--------+
#> | Basic Secondary        |  848 |  33.71 |   33.71 |  33.71 |
#> | Intermediate Secondary |  641 |  25.47 |   25.47 |  59.18 |
#> | Academic Secondary     |  642 |  25.51 |   25.51 |  84.69 |
#> | 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(2178.7) = 0.751, p = 0.453, g = 0.032 (negligible), N = 2201
#> Use summary() for detailed output.

# ANOVA
survey_data %>%
  oneway_anova(life_satisfaction, group = education,
               weights = sampling_weight)
#> One-Way ANOVA: life_satisfaction by education [Weighted]
#>   F(3, 2432) = 65.333, p < 0.001 ***, eta2 = 0.075 (medium), N = 2437
#> Use summary() for detailed output.

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

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

# 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) = 270.42, p < 0.001 ***, N = 2130
#> Use summary() for detailed output.

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    N  Missing
#>   -------------------------------------------------------------------------------------------
#>   age                  52.278    53.000    17.595    77.000    24.000     0.098  509        0
#>   income             3760.687  3600.000  1388.321  7200.000  1700.000     0.721  449       60
#>   life_satisfaction     3.623     4.000     1.203     4.000     2.000    -0.558  488       21
#>   -------------------------------------------------------------------------------------------
#> 
#> Group: region = West
#> --------------------
#> 
#>   --------------------------------------------------------------------------------------------
#>   Variable               Mean    Median        SD     Range       IQR  Skewness     N  Missing
#>   --------------------------------------------------------------------------------------------
#>   age                  50.067    49.000    16.927    77.000    24.000     0.170  2007        0
#>   income             3738.586  3500.000  1433.325  7200.000  1900.000     0.727  1751      256
#>   life_satisfaction     3.625     4.000     1.139     4.000     2.000    -0.481  1949       58
#>   --------------------------------------------------------------------------------------------

survey_data %>%
  group_by(region) %>%
  t_test(income, group = gender, weights = sampling_weight)
#> [region = East]
#> t-Test: income by gender [Weighted]
#>   t(431.2) = 1.674, p = 0.095, g = 0.158 (negligible), N = 450
#> [region = West]
#> t-Test: income by gender [Weighted]
#>   t(1740.2) = 0.009, p = 0.993, g = 0.000 (negligible), N = 1751
#> Use summary() for detailed output.

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    N  Missing
#>   ----------------------------------------------------------------------------------
#>   income    3760.687  3600.000  1388.321  7200.000  1700.000     0.721  449       60
#>   ----------------------------------------------------------------------------------
#> 
#> Group: region = West
#> --------------------
#> 
#>   -----------------------------------------------------------------------------------
#>   Variable      Mean    Median        SD     Range       IQR  Skewness     N  Missing
#>   -----------------------------------------------------------------------------------
#>   income    3738.586  3500.000  1433.325  7200.000  1900.000     0.727  1751      256
#>   -----------------------------------------------------------------------------------

# 4. Weighted hypothesis test
survey_data %>%
  t_test(income, group = gender, weights = sampling_weight)
#> t-Test: income by gender [Weighted]
#>   t(2178.7) = 0.751, p = 0.453, g = 0.032 (negligible), N = 2201
#> Use summary() for detailed output.

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")