cNORM (version 3.6.2)

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

Description

Generates norm tables for specific ages based on a fitted Sinh-Arcsinh (shash) regression model. Computes interval 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
)

Value

List of data frames (one per age) containing:

x

Raw scores

Px

Approximate interval probabilities (density times step width). These are consistent with Pcum but do not necessarily sum to 1 over the tabulated score range.

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)

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, densities are converted to interval probabilities (density times step width) and cumulative probabilities. When reliability is specified, confidence intervals include correction for regression to the mean.

Examples

if (FALSE) {
# 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)
}