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Find the Population-Representative Middle Value

Source: R/w_median.R
w_median.Rd

w_median() finds the median (middle value) of your data using survey weights. The weighted median is the value where half the population falls below and half falls above. Unlike the mean, the median is not pulled by extreme values, making it a robust measure of the "typical" value in your population.

Usage

w_median(data, ..., weights = NULL, na.rm = TRUE)

Arguments

data

Your survey data (a data frame or tibble)

...

The numeric variables you want to analyze. You can list multiple variables or use helpers like starts_with("income")

weights

Survey weights to make results representative of your population. Without weights, you get the simple sample median. Give a column name (unquoted or as a string), an expression such as sampling_weight * 2, or a numeric vector with one weight per row.

na.rm

Remove missing values before calculating? (Default: TRUE). With FALSE, the result for a variable that contains missing values is NA (as in base R).

Value

Population-weighted median(s) with sample size information, including the weighted median, effective sample size (effective N), and the number of valid observations used.

Details

Understanding the Results

  • Weighted Median: The value that splits the weighted population in half. 50% of the population (by weight) falls below this value, 50% above.

  • Effective N: How many independent observations your weighted data represents.

  • N / Missing: Valid and missing cases. With weights, both are sums of weights (displayed rounded), as SPSS reports them under WEIGHT BY; Kish's effective N is shown by summary().

Comparing the weighted median to the weighted mean is informative:

  • If they are similar, the distribution is roughly symmetric.

  • If the mean is much larger than the median, the distribution is right-skewed (a few very high values pull the mean up, e.g., income).

When to Use This

Use w_median() when:

  • Your data has outliers or is skewed (e.g., income, housing prices)

  • You want a robust "typical value" not influenced by extremes

  • You need the weighted 50th percentile

  • You need SPSS-compatible weighted median values

Formula

The weighted median is the weighted 50th percentile, computed with the SPSS HAVERAGE (quantile Type 6) position h = 0.5 * (W + 1) on the cumulative weights, with linear interpolation between bracketing observations. It is identical to w_quantile(x, probs = 0.5) by construction. Unweighted and weighted values reproduce SPSS FREQUENCIES (with and without WEIGHT BY).

References

IBM Corp. (2023). IBM SPSS Statistics 29 Algorithms. IBM Corporation.

See also

median for the base R median function.

w_mean for weighted means.

w_quantile for arbitrary weighted percentiles.

describe for comprehensive descriptive statistics including the median.

Other weighted_statistics: w_iqr(), w_kurtosis(), w_mean(), w_modus(), w_quantile(), w_range(), w_sd(), w_se(), w_skew(), w_var()

Examples

# Load required packages and data
library(dplyr)
data(survey_data)

# Basic weighted median
survey_data %>% w_median(age, weights = sampling_weight)
#> 
#> Weighted Median Statistics
#> --------------------------
#> Weights: sampling_weight
#> 
#>   -------------------------------
#>   Variable  Median     N  Missing
#>   -------------------------------
#>   age       50.000  2516        0
#>   -------------------------------

# Multiple variables
survey_data %>% w_median(age, income, weights = sampling_weight)
#> 
#> Weighted Median Statistics
#> --------------------------
#> Weights: sampling_weight
#> 
#>   ---------------------------------
#>   Variable    Median     N  Missing
#>   ---------------------------------
#>   age         50.000  2516        0
#>   income    3500.000  2201      315
#>   ---------------------------------

# Grouped data
survey_data %>% group_by(region) %>% w_median(age, weights = sampling_weight)
#> 
#> Weighted Median Statistics
#> --------------------------
#> Weights: sampling_weight
#> 
#> Group: region = East
#> --------------------
#> 
#>   ------------------------------
#>   Variable  Median    N  Missing
#>   ------------------------------
#>   age       53.000  509        0
#>   ------------------------------
#> 
#> Group: region = West
#> --------------------
#> 
#>   -------------------------------
#>   Variable  Median     N  Missing
#>   -------------------------------
#>   age       49.000  2007        0
#>   -------------------------------

# In summarise context
survey_data %>% summarise(med_age = w_median(age, weights = sampling_weight))
#> # A tibble: 1 × 1
#>   med_age
#>     <dbl>
#> 1      50

# Unweighted (for comparison)
survey_data %>% w_median(age)
#> 
#> Median Statistics
#> -----------------
#> 
#>   -------------------------------
#>   Variable  Median     N  Missing
#>   -------------------------------
#>   age       50.000  2500        0
#>   -------------------------------