mariposa (version 0.7.3)

w_se: Calculate Population-Representative Standard Errors

Description

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.

Usage

w_se(data, ..., weights = NULL, na.rm = 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.

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)

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: \(SE = s / \sqrt{n}\)

References

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

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)

# Multiple variables
survey_data %>% w_se(age, income, weights = sampling_weight)

# Grouped data
survey_data %>% group_by(region) %>% w_se(age, weights = sampling_weight)

# In summarise context
survey_data %>% summarise(se_age = w_se(age, weights = sampling_weight))

# Unweighted (for comparison)
survey_data %>% w_se(age)