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.
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.
- na.rm
Remove missing values before calculating? (Default: TRUE)
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: The actual number of observations used in the calculation.
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.
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
#> ----------------------------
#>
#> --- age ---
#> Variable weighted_var Effective_N
#> age 291.857 2468.8
#>
# Multiple variables
survey_data %>% w_var(age, income, weights = sampling_weight)
#>
#> Weighted Variance Statistics
#> ----------------------------
#>
#> --- age ---
#> Variable weighted_var Effective_N
#> age 291.857 2468.8
#>
#> --- income ---
#> Variable weighted_var Effective_N
#> income 2027678 2158.9
#>
# Grouped data
survey_data %>% group_by(region) %>% w_var(age, weights = sampling_weight)
#>
#> Weighted Variance Statistics
#> ----------------------------
#>
#> Group: region = East
#> Warning: Unknown or uninitialised column: `Variable`.
#>
#> Group: region = West
#> Warning: Unknown or uninitialised column: `Variable`.
#>
# 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
#> -------------------
#>
#> --- age ---
#> Variable var N
#> age 288.185 2500
#>