The article by Brian H. Toby discusses the definitions and significance of various Rietveld error indices, such as $\chi^2$, $R$ factors, and the expected $R$ factor ($R_{exp}$). It emphasizes that while smaller error index values generally indicate a better fit of a model to the data, they can be misleading if the data quality is poor. The author explains that wrong models with low-quality data may show smaller error index values than well-fitted models with high-quality data. The article also highlights the importance of graphical analysis and the chemical reasonableness of the model in assessing the quality of Rietveld fits. It discusses the impact of background levels, data quality, and instrumental resolution on these indices, and notes that no single rule-of-thumb can determine the reliability of a fit based on these indices alone. The reflection-based $R$ factor is introduced as a valuable tool for assessing the accuracy of peak integration, but it is noted that it has no statistical validity. The article concludes by emphasizing the importance of visual inspection and chemical plausibility in determining the quality of a Rietveld fit.The article by Brian H. Toby discusses the definitions and significance of various Rietveld error indices, such as $\chi^2$, $R$ factors, and the expected $R$ factor ($R_{exp}$). It emphasizes that while smaller error index values generally indicate a better fit of a model to the data, they can be misleading if the data quality is poor. The author explains that wrong models with low-quality data may show smaller error index values than well-fitted models with high-quality data. The article also highlights the importance of graphical analysis and the chemical reasonableness of the model in assessing the quality of Rietveld fits. It discusses the impact of background levels, data quality, and instrumental resolution on these indices, and notes that no single rule-of-thumb can determine the reliability of a fit based on these indices alone. The reflection-based $R$ factor is introduced as a valuable tool for assessing the accuracy of peak integration, but it is noted that it has no statistical validity. The article concludes by emphasizing the importance of visual inspection and chemical plausibility in determining the quality of a Rietveld fit.