  This paper introduces a new method for change detection in psychometric
studies based on the recently introduced pseudo Score statistic, for which the
sampling distribution under the alternative hypothesis has been determined. Our
approach has the advantage of simplicity in its computation, eliminating the
need for resampling or simulations to obtain critical values. Additionally, it
comes with a known null/alternative distribution, facilitating easy
calculations for power levels and sample size planning. The paper indeed also
discusses the topic of power analysis in segmented regression, namely the
estimation of sample size or power level when the study data being collected
focuses on a covariate expected to affect the mean response via a piecewise
relationship with an unknown breakpoint. We run simulation results showing that
our method outperforms other Tests for a Change Point (TFCP) with both normally
distributed and binary data and carry out a real SAT Critical reading data
analysis. The proposed test contributes to the framework of psychometric
research, and it is available on the Comprehensive R Archive Network (CRAN) and
in a more user-friendly Shiny App, both illustrated at the end of the paper.
