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The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic is calculated from the standard deviation, mean, and number of measurements in the data set at a selected confidence interval and then compared to a table of critical values at this confidence level. If the test statistic is smaller than the critical value, the null hypothesis is accepted. In this case, we state that the difference between the...
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The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
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Friedman Two-way Analysis of Variance by Ranks01:21

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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
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Behrens–Fisher Test00:57

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The Behrens-Fisher test is a statistical method designed to address the Behrens-Fisher problem, which arises when comparing the means of two normally distributed populations with unequal variances. Unlike the Student's t-test, which assumes equal variances, the Behrens-Fisher test allows for mean comparison without this restrictive assumption. This flexibility makes it particularly valuable in scenarios where two independent samples exhibit normality but lack variance homogeneity.
This test...
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Group Design02:01

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The most basic experimental design involves two groups: the experimental group and the control group. The two groups are designed to be the same except for one difference— experimental manipulation. The experimental group gets the experimental manipulation—that is, the treatment or variable being tested—and the control group does not. Since experimental manipulation is the only difference between the experimental and control groups, we can be sure that any differences between...
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Using Group Differences in True Score Relationships to Evaluate Measurement Bias.

Michael T Kane1, Joanne Kane2

  • 1Retired from Educational Testing Service, Princeton, NJ, USA.

Applied Psychological Measurement
|July 10, 2025
PubMed
Summary

This study introduces a new linear model for measurement bias, distinct from predictive bias models. It highlights how ignoring differences can lead to incorrect conclusions about test bias, particularly in college admissions and employment testing.

Keywords:
errors-in-variables modelfairnessmeasurement biaspredictive biasregression toward the mean

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Measurement bias and predictive bias are critical in standardized testing.
  • Existing models like the Cleary model primarily address predictive bias.
  • Understanding these biases is essential for fair assessment in admissions and employment.

Purpose of the Study:

  • To develop a novel linear model for assessing measurement bias using Errors-in-Variables (EIV) regression.
  • To differentiate measurement bias from predictive bias, especially when true-score means differ between groups.
  • To re-examine empirical findings on test bias in college admissions and employment contexts.

Main Methods:

  • Development of a linear Errors-in-Variables (EIV) regression model for measurement bias.
  • Comparative analysis of measurement bias and predictive bias under varying true-score means.
  • Re-evaluation of existing empirical data on test performance prediction for minority groups.

Main Results:

  • The proposed EIV model offers a new approach to measurement bias assessment.
  • Ignoring the distinction between measurement and predictive bias can lead to misinterpretations due to regression toward the mean.
  • Empirical findings on over-prediction for minorities are consistent with significant measurement bias against them.

Conclusions:

  • The study provides a refined framework for understanding and quantifying measurement bias.
  • It underscores the importance of distinguishing between measurement and predictive bias for accurate test evaluation.
  • Results suggest that observed over-prediction in minority groups may stem from inherent measurement bias rather than solely predictive issues.