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Calculate Population-Representative Variance

Source: R/w_var.R
w_var.Rd

w_var() calculates variance that accurately represents your population by using survey weights. Variance measures how far values spread out from the average – it is the square of the standard deviation. A larger variance means more dispersion in your population's responses.

Without weights, you describe the spread in your sample only. With weights, you estimate how spread out values are in the entire population.

Usage

w_var(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("trust")

weights

Survey weights to make results representative of your population. Without weights, you get the simple sample variance. 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 variance(s) with sample size information, including the weighted variance, effective sample size (effective N), and the number of valid observations used.

Details

Understanding the Results

  • Weighted Variance: The population-representative variance. Because variance is in squared units (e.g., years-squared for age), it is often easier to interpret the standard deviation (w_sd) instead.

  • Effective N: How many independent observations your weighted data represents. Always less than or equal to the actual sample size.

  • 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().

When to Use This

Use w_var() when:

  • You need variance for further calculations (e.g., pooled variance, F-tests)

  • You want to compare variability across groups with proper weighting

  • Your analysis formulas require variance rather than SD

  • You need SPSS-compatible weighted variance values

For reporting purposes, w_sd is usually preferred because the standard deviation is in the same units as the original variable.

Formula

The weighted variance uses the SPSS frequency weights formula:

\(s^2_w = \frac{\sum w_i (x_i - \bar{x}_w)^2}{V_1 - 1}\)

where \(V_1 = \sum w_i\) is the sum of all weights and \(\bar{x}_w = \sum w_i x_i / V_1\) is the weighted mean.

Note: \(s^2_w = (s_w)^2\), i.e., the weighted variance is the square of the weighted standard deviation.

References

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

See also

var for the base R variance function.

w_sd for weighted standard deviation (the square root of variance).

w_mean for weighted means.

describe for comprehensive descriptive statistics including variance.

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

Examples

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

# Basic weighted variance
survey_data %>% w_var(age, weights = sampling_weight)
#> 
#> Weighted Variance Statistics
#> ----------------------------
#> Weights: sampling_weight
#> 
#>   ---------------------------------
#>   Variable  Variance     N  Missing
#>   ---------------------------------
#>   age        291.857  2516        0
#>   ---------------------------------

# Multiple variables
survey_data %>% w_var(age, income, weights = sampling_weight)
#> 
#> Weighted Variance Statistics
#> ----------------------------
#> Weights: sampling_weight
#> 
#>   ------------------------------------
#>   Variable     Variance     N  Missing
#>   ------------------------------------
#>   age           291.857  2516        0
#>   income    2027677.966  2201      315
#>   ------------------------------------

# Grouped data
survey_data %>% group_by(region) %>% w_var(age, weights = sampling_weight)
#> 
#> Weighted Variance Statistics
#> ----------------------------
#> Weights: sampling_weight
#> 
#> Group: region = East
#> --------------------
#> 
#>   --------------------------------
#>   Variable  Variance    N  Missing
#>   --------------------------------
#>   age        309.601  509        0
#>   --------------------------------
#> 
#> Group: region = West
#> --------------------
#> 
#>   ---------------------------------
#>   Variable  Variance     N  Missing
#>   ---------------------------------
#>   age        286.520  2007        0
#>   ---------------------------------

# In summarise context
survey_data %>% summarise(var_age = w_var(age, weights = sampling_weight))
#> # A tibble: 1 × 1
#>   var_age
#>     <dbl>
#> 1    292.

# Unweighted (for comparison)
survey_data %>% w_var(age)
#> 
#> Variance Statistics
#> -------------------
#> 
#>   ---------------------------------
#>   Variable  Variance     N  Missing
#>   ---------------------------------
#>   age        288.185  2500        0
#>   ---------------------------------