w_skew() measures how asymmetric your data's distribution is, using
survey weights for population-representative results. Skewness tells you
whether values tend to trail off more to the left or right:
Positive skew: A long tail to the right (e.g., income – many low, few very high)
Negative skew: A long tail to the left (e.g., exam scores – many high, few very low)
Near zero: Roughly symmetric (e.g., height in a 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 skewness.
- na.rm
Remove missing values before calculating? (Default: TRUE)
Value
Population-weighted skewness value(s) with sample size information, including the weighted skewness, effective sample size (effective N), and the number of valid observations used.
Details
Understanding the Results
Weighted Skewness: The population-representative skewness value.
Near 0: Distribution is roughly symmetric
Between -0.5 and 0.5: Approximately symmetric
Between -1 and -0.5 or 0.5 and 1: Moderately skewed
Beyond -1 or 1: Highly skewed
Effective N: How many independent observations your weighted data represents.
N: The actual number of observations used.
High skewness suggests you might want to use the median instead of the mean as a measure of center, and non-parametric tests instead of t-tests.
When to Use This
Use w_skew() when:
You need to check if a variable is normally distributed
You want to decide between parametric and non-parametric tests
You need to assess whether the mean is a good summary measure
You need SPSS-compatible weighted skewness values
Formula
Uses the SPSS Type 2 (sample-corrected) skewness formula. First, the population skewness (\(g_1\)) is calculated:
\(g_1 = \frac{m_3}{m_2^{3/2}}\)
where \(m_2 = \sum w_i(x_i - \bar{x}_w)^2 / V_1\) and \(m_3 = \sum w_i(x_i - \bar{x}_w)^3 / V_1\) with \(V_1 = \sum w_i\).
Then, the bias-corrected (Type 2) skewness is:
\(G_1 = g_1 \cdot \frac{\sqrt{n(n-1)}}{n-2}\)
where \(n = V_1\) for weighted data.
References
Joanes, D. N., & Gill, C. A. (1998). Comparing measures of sample skewness and kurtosis. The Statistician, 47(1), 183-189.
IBM Corp. (2023). IBM SPSS Statistics 29 Algorithms. IBM Corporation.
See also
w_kurtosis for weighted kurtosis (tail heaviness).
describe for comprehensive descriptive statistics including skewness.
Other weighted_statistics:
w_iqr(),
w_kurtosis(),
w_mean(),
w_median(),
w_modus(),
w_quantile(),
w_range(),
w_sd(),
w_se(),
w_var()
Examples
# Load required packages and data
library(dplyr)
data(survey_data)
# Basic weighted skewness
survey_data %>% w_skew(age, weights = sampling_weight)
#>
#> Weighted Skewness Statistics
#> ----------------------------
#>
#> --- age ---
#> Variable weighted_skew Effective_N
#> age 0.159 2468.8
#>
# Multiple variables
survey_data %>% w_skew(age, income, life_satisfaction, weights = sampling_weight)
#>
#> Weighted Skewness Statistics
#> ----------------------------
#>
#> --- age ---
#> Variable weighted_skew Effective_N
#> age 0.159 2468.8
#>
#> --- income ---
#> Variable weighted_skew Effective_N
#> income 0.725 2158.9
#>
#> --- life_satisfaction ---
#> Variable weighted_skew Effective_N
#> life_satisfaction -0.499 2390.9
#>
# Grouped data
survey_data %>% group_by(region) %>% w_skew(age, weights = sampling_weight)
#>
#> Weighted Skewness 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(skew_age = w_skew(age, weights = sampling_weight))
#> # A tibble: 1 × 1
#> skew_age
#> <dbl>
#> 1 0.159
# Unweighted (for comparison)
survey_data %>% w_skew(age)
#>
#> Skewness Statistics
#> -------------------
#>
#> --- age ---
#> Variable skew N
#> age 0.172 2500
#>