w_se() calculates the standard error of the mean using survey weights.
The standard error tells you how precisely you have estimated the population
mean – a smaller SE means your estimate is more precise. This is essential
for constructing confidence intervals and assessing the reliability of your
weighted mean estimates.
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 standard error.
- na.rm
Remove missing values before calculating? (Default: TRUE)
Value
Population-weighted standard error(s) with sample size information, including the weighted SE, effective sample size (effective N), and the number of valid observations used.
Details
Understanding the Results
Weighted SE: The precision of your weighted mean estimate. Smaller values mean more precise estimates. You can build a 95% confidence interval as: weighted mean +/- 1.96 * weighted SE.
Effective N: How many independent observations your weighted data represents. Weights that vary a lot reduce effective N, increasing the SE.
N: The actual number of observations used.
When to Use This
Use w_se() when:
You need to report precision of mean estimates
You want to construct confidence intervals for weighted means
You need to compare precision across subgroups
You need SPSS-compatible weighted standard errors
Formula
The weighted standard error is calculated as:
\(SE_w = \frac{s_w}{\sqrt{V_1}}\)
where \(s_w\) is the weighted standard deviation (see w_sd)
and \(V_1 = \sum w_i\) is the sum of all weights.
For the unweighted case: \(SE = s / \sqrt{n}\)
See also
w_sd for weighted standard deviation.
w_mean for weighted means.
describe for comprehensive descriptive statistics including SE.
Other weighted_statistics:
w_iqr(),
w_kurtosis(),
w_mean(),
w_median(),
w_modus(),
w_quantile(),
w_range(),
w_sd(),
w_skew(),
w_var()
Examples
# Load required packages and data
library(dplyr)
data(survey_data)
# Basic weighted standard error
survey_data %>% w_se(age, weights = sampling_weight)
#>
#> Weighted Standard Error Statistics
#> ----------------------------------
#>
#> --- age ---
#> Variable weighted_se Effective_N
#> age 0.341 2468.8
#>
# Multiple variables
survey_data %>% w_se(age, income, weights = sampling_weight)
#>
#> Weighted Standard Error Statistics
#> ----------------------------------
#>
#> --- age ---
#> Variable weighted_se Effective_N
#> age 0.341 2468.8
#>
#> --- income ---
#> Variable weighted_se Effective_N
#> income 30.353 2158.9
#>
# Grouped data
survey_data %>% group_by(region) %>% w_se(age, weights = sampling_weight)
#>
#> Weighted Standard Error 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(se_age = w_se(age, weights = sampling_weight))
#> # A tibble: 1 × 1
#> se_age
#> <dbl>
#> 1 0.341
# Unweighted (for comparison)
survey_data %>% w_se(age)
#>
#> Standard Error Statistics
#> -------------------------
#>
#> --- age ---
#> Variable se N
#> age 0.34 2500
#>