ci_score: Compute Confidence Intervals for Test Scores Adjusted for...

In jazznbass/wmisc: Wilbert miscellaneous functions

Compute Confidence Intervals for Test Scores Adjusted for Reliability

Description

Calculates the confidence interval around an observed test score, adjusting for test reliability. Returns the confidence interval in raw score units, z-scores, and percentiles.

Usage

ci_score(x, rtt, m, s, ci)

Arguments

x	Numeric value representing the observed test score.
rtt	Numeric value between 0 and 1 indicating the reliability coefficient of the test (e.g., test-retest reliability).
m	Numeric value representing the mean of the test scores in the population.
s	Numeric value representing the standard deviation of the test scores in the population.
ci	Numeric value between 0 and 1 indicating the desired confidence level (e.g., 0.95 for a 95% confidence interval).

Details

The standard error (se) is calculated using the formula:

se = s \times \sqrt{1 - rtt}

where s is the standard deviation and rtt is the reliability coefficient.

The confidence interval is computed using the normal distribution quantile corresponding to the specified confidence level.

Value

A list containing the following components:

scale

A named numeric vector with the confidence interval in raw score units:

• lower: Lower bound of the confidence interval.

• x: The observed test score.

• upper: Upper bound of the confidence interval.

• range: Width of the confidence interval.

z

A named numeric vector with the confidence interval in z-score units:

• lower: Lower bound in z-scores.

• x: Observed score in z-scores.

• upper: Upper bound in z-scores.

• range: Width of the confidence interval in z-scores.

percentile

A named numeric vector with the confidence interval in percentiles:

• lower: Lower percentile.

• x: Percentile rank of the observed score.

• upper: Upper percentile.

• range: Width of the confidence interval in percentiles.

parameters

A named numeric vector with additional parameters:

• se: Standard error of measurement adjusted for reliability.

• ci: Confidence level used.

• z: Z-score multiplier corresponding to the confidence level.

Examples

# Calculate a 95% confidence interval for an observed score of 100
ci_score(x = 100, rtt = 0.9, m = 100, s = 15, ci = 0.95)

jazznbass/wmisc documentation built on Jan. 28, 2025, 11:13 p.m.