mariposa (version 0.7.3)

w_skew: Measure Population-Representative Skewness

Description

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)

Usage

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

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)

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)

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

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

# In summarise context
survey_data %>% summarise(skew_age = w_skew(age, weights = sampling_weight))

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