This book provides a comprehensive and unified framework for evaluating whether statistical models are adequate representations of real data and fit for their intended purpose. Rather than treating goodness-of-fit as the mechanical calculation of a test statistic and p-value, it presents it as a broader diagnostic process that asks a fundamental question: Does the model describe the observed data well enough for the decisions, inferences, or predictions we wish to make?

The book emphasizes that no model is perfectly correct, but some models are sufficiently adequate for particular purposes. By integrating theory, practical examples, graphical diagnostics, simulation methods, and modern applications into a single coherent treatment, the book makes the vast field of goodness-of-fit methodology accessible, systematic, and directly useful in real-world statistical practice. The book covers classical goodness-of-fit testing, regression diagnostics, calibration assessment, survival analysis, multivariate methods, and modern simulation-based approaches. It introduces a unifying perspective in which every goodness-of-fit procedure consists of two key elements: a measure of discrepancy between observed data and model predictions, and a calibration procedure that determines whether that discrepancy is larger than would be expected under the model. Through this framework, the book connects seemingly disparate methods such as chi-square tests, Kolmogorov-Smirnov tests, Anderson-Darling tests, residual diagnostics, calibration plots, bootstrap methods, and graphical techniques, showing them to be variations of the same underlying problem.

The book is designed to help statisticians, researchers, data scientists, and applied analysts become better model critics rather than merely model users. It teaches readers not only how to detect lack of fit, but also how to understand why a model fails, how the failure affects inference and prediction, and how to improve the model in response.

Ayman Baklizi is an applied statistician and associate professor affiliated with Yarmouk University in Jordan, specializing in Likelihood methods, lifetime data analysis and nonparametrics.