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A z score (or standardized value) is measured in units of the standard deviation. It tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a zero z score. It is important to note that the mean of the z scores is zero, and the standard deviation is one.
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The z score is one of the three measures of relative standing. It describes the location of a value in a dataset relative to the mean. z scores are obtained after the standardization of the values in a dataset. The z score for the mean is 0.
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IRT scoring procedures for TIMSS data.

Gregory Camilli1, John A Dossey2

  • 1Rutgers University, United States.

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|July 16, 2019
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Summary

This study introduces empirical subscores using item response theory (IRT) for analyzing mathematics proficiency in international assessments like TIMSS. This method offers richer diagnostic feedback than traditional subscores.

Keywords:
Diagnostic informationEmpirical subscore estimationEmpirical subscoresExploratory factor analysisIRTInternational assessmentItem response theoryMathematics achievementMultidimensional scoringTIMSS

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • International Large-Scale Assessments

Background:

  • Traditional scoring in international assessments uses predefined content subdomains.
  • Overall scores and subscores are standard, but may lack nuanced diagnostic information.
  • Item response theory (IRT) offers advanced statistical modeling for educational data.

Purpose of the Study:

  • To present an alternative method for deriving empirical subscores in mathematics proficiency.
  • To augment traditional scoring with data-driven insights from IRT.
  • To validate these empirical subscores using Trends in International Mathematics and Science Study (TIMSS) data.

Main Methods:

  • An exploratory IRT factor analysis is employed to identify empirical subscores.
  • The method leverages the TIMSS jackknife resampling design for robust analysis.
  • Factor scores are estimated for sampling units and aggregated to jurisdictional levels using sampling weights.

Main Results:

  • Empirical subscores reveal naturally occurring item clusters, providing diagnostic feedback.
  • Jurisdictional achievement ranks can differ based on the empirical subscore considered.
  • The proposed method offers a valuable supplement to traditional subscore reporting.

Conclusions:

  • Empirical subscores derived from IRT provide a more nuanced understanding of mathematics proficiency.
  • This approach enhances diagnostic capabilities beyond content-based subdomains.
  • The method is validated for use in large-scale international assessments like TIMSS.