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Calculate Population-Representative Averages

Source: R/w_mean.R
w_mean.Rd

w_mean() calculates averages that accurately represent your population by using survey weights. This ensures that groups who were over- or under-sampled contribute appropriately to the final average.

Usage

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

Arguments

data

Your survey data (a data frame or tibble)

...

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

weights

Survey weights to make the average representative of your population. Without weights, you get the simple sample average. 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 average(s) with sample size information

Details

When to Use This

Use w_mean() when your survey uses sampling weights and you need population-representative averages. Weights correct for:

  • Oversampling of certain groups (weights < 1)

  • Undersampling of other groups (weights > 1)

  • Non-response patterns

  • Complex survey designs

Understanding the Results

  • Weighted Mean: The population-representative average

  • 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().

Formula

\(\bar{x}_w = \frac{\sum w_i \cdot x_i}{\sum w_i}\)

The effective sample size is: \(n_{eff} = (\sum w_i)^2 / \sum w_i^2\)

References

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

See also

weighted.mean for the base R weighted mean function.

w_sd for weighted standard deviation.

w_median for weighted median.

describe for comprehensive descriptive statistics.

Other weighted_statistics: w_iqr(), w_kurtosis(), w_median(), 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 usage
survey_data %>% w_mean(age, weights = sampling_weight)
#> 
#> Weighted Mean Statistics
#> ------------------------
#> Weights: sampling_weight
#> 
#>   -------------------------------
#>   Variable    Mean     N  Missing
#>   -------------------------------
#>   age       50.514  2516        0
#>   -------------------------------

# Multiple variables
survey_data %>% w_mean(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
#>   ------------------------------------------

# Grouped data
survey_data %>% group_by(region) %>% w_mean(age, weights = sampling_weight)
#> 
#> Weighted Mean Statistics
#> ------------------------
#> Weights: sampling_weight
#> 
#> Group: region = East
#> --------------------
#> 
#>   ------------------------------
#>   Variable    Mean    N  Missing
#>   ------------------------------
#>   age       52.278  509        0
#>   ------------------------------
#> 
#> Group: region = West
#> --------------------
#> 
#>   -------------------------------
#>   Variable    Mean     N  Missing
#>   -------------------------------
#>   age       50.067  2007        0
#>   -------------------------------

# In summarise context
survey_data %>% summarise(mean_age = w_mean(age, weights = sampling_weight))
#> # A tibble: 1 × 1
#>   mean_age
#>      <dbl>
#> 1     50.5

# Unweighted (for comparison)
survey_data %>% w_mean(age)
#> 
#> Mean Statistics
#> ---------------
#> 
#>   -------------------------------
#>   Variable    Mean     N  Missing
#>   -------------------------------
#>   age       50.550  2500        0
#>   -------------------------------