This paper introduces a new method for change detection in medical and 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 known null and alternative distributions, 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 studies showing that our method outperforms other Tests for a Change Point (TFCP) with both normally distributed and binary data and carry out two real data analyses on genomic data and SAT critical reading data. The proposed test contributes to the framework of medical and 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.