normTable.shash: Calculate Norm Tables for Sinh-Arcsinh Distribution

In cNORM: Continuous Norming

Calculate Norm Tables for Sinh-Arcsinh Distribution

Description

Generates norm tables for specific ages based on a fitted SinH-ArcSinH (shash) regression model. Computes probabilities, percentiles, z-scores, and norm scores for a specified range of raw scores. Optionally includes confidence intervals when reliability is provided.

Usage

normTable.shash(
  model,
  ages,
  start = NULL,
  end = NULL,
  step = 1,
  CI = 0.9,
  reliability = NULL
)

Arguments

model	Fitted shash model object of class "cnormShash"
ages	Numeric vector of age points for norm table generation
start	Minimum raw score value for the norm table
end	Maximum raw score value for the norm table
step	Step size between consecutive raw scores (default: 1)
CI	Confidence coefficient (0-1, default: 0.9) for confidence intervals
reliability	Reliability coefficient (0-1) for true score confidence intervals

Details

For continuous shash distributions, probability densities are computed and converted to cumulative probabilities and percentiles. When reliability is specified, confidence intervals include correction for regression to the mean.

Value

List of data frames (one per age) containing:

x	Raw scores
Px	Probability density values
Pcum	Cumulative probabilities
Percentile	Percentile ranks (0-100)
z	Standardized z-scores
norm	Norm scores in specified scale
lowerCI, upperCI	Confidence intervals (if reliability provided)
lowerCI_PR, upperCI_PR	CI as percentile ranks (if reliability provided)

Examples

## Not run: 
# Basic norm table
model <- cnorm.shash(age, score)
tables <- normTable.shash(model, ages = c(7, 8, 9), start = 0, end = 50)

# With confidence intervals and finer granularity
tables_ci <- normTable.shash(model, ages = c(8, 9), start = 10, end = 40,
                             step = 0.5, CI = 0.95, reliability = 0.85)

## End(Not run)

cNORM documentation built on Feb. 27, 2026, 1:07 a.m.