mariposa (version 0.7.3)

w_iqr: Measure Population-Representative Spread (IQR)

Description

w_iqr() calculates the interquartile range using survey weights. The IQR is the distance between the 25th and 75th percentiles -- it tells you the range that contains the middle 50% of your population. Unlike the standard deviation, the IQR is not affected by outliers, making it a robust measure of spread.

Usage

w_iqr(data, ..., weights = NULL, na.rm = TRUE)

Value

Population-weighted IQR(s) with sample size information, including the weighted IQR, 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("income")

weights

Survey weights to make results representative of your population. Without weights, you get the simple sample IQR.

na.rm

Remove missing values before calculating? (Default: TRUE)

Details

Understanding the Results

• Weighted IQR: The range that covers the middle 50% of the weighted population. A larger IQR means more spread in the central part of the data.

• Effective N: How many independent observations your weighted data represents.

• N: The actual number of observations used.

The IQR is especially useful when your data is skewed. For example, with income data, the IQR gives a better sense of "typical spread" than the SD because extreme incomes do not distort it.

When to Use This

Use w_iqr() when:

• Your data has outliers or is skewed (e.g., income, response times)

• You want a robust measure of spread that is not influenced by extremes

• You need to describe the spread of the middle 50% of your population

• You need SPSS-compatible weighted IQR values

Formula

\(IQR_w = Q_{3,w} - Q_{1,w}\)

where \(Q_{1,w}\) and \(Q_{3,w}\) are the weighted 25th and 75th percentiles, calculated using cumulative weights (see w_quantile).

References

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

See Also

IQR for the base R IQR function.

w_quantile for arbitrary weighted percentiles.

w_sd for weighted standard deviation (another spread measure).

w_range for the full weighted range.

describe for comprehensive descriptive statistics including IQR.

Validation status

Unweighted values use quantile Type 6 (SPSS HAVERAGE). Weighted values apply the HAVERAGE position to cumulative weights with linear interpolation - an R-internal extension (Tier 4 of the Validation Charter); SPSS reference validation for weighted percentiles is pending.

Other weighted_statistics: w_kurtosis(), w_mean(), w_median(), w_modus(), w_quantile(), w_range(), w_sd(), w_se(), w_skew(), w_var()

Examples

# Load required packages and data
library(dplyr)
data(survey_data)

# Basic weighted IQR
survey_data %>% w_iqr(age, weights = sampling_weight)

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

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

# In summarise context
survey_data %>% summarise(iqr_age = w_iqr(age, weights = sampling_weight))

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