Statistical methods are based on model assumptions, and it is statistical folklore that a method's model assumptions should be checked before applying it. This can be formally done by running one or more misspecification tests of model assumptions before running a method that requires these assumptions; here we focus on model-based tests. A combined test procedure can be defined by specifying a protocol in which first model assumptions are tested and then, conditionally on the outcome, a test is run that requires or does not require the tested assumptions. Although such an approach is often taken in practice, much of the literature that investigated this is surprisingly critical of it. Our aim is to explore conditions under which model checking is advisable or not advisable. For this, we review results regarding such "combined procedures" in the literature, we review and discuss controversial views on the role of model checking in statistics, and we present a general setup in which we can show that preliminary model checking is advantageous, which implies conditions for making model checking worthwhile.

翻译：统计方法基于模型假设，而统计学的常规认知是在应用方法前应检验其模型假设。这一过程可通过在运行需要某些假设的方法之前，先执行一个或多个模型假设的设定错误检验来正式实现；本文聚焦于基于模型的检验。通过规定一个协议，即先检验模型假设，再根据检验结果有条件地运行需要或不需要这些假设的检验，可以定义一种组合检验程序。尽管这种方法在实践中常被采用，但许多相关文献却对其持出人意料的批评态度。本文旨在探究模型检验可取或不可取的条件。为此，我们回顾了文献中关于此类“组合程序”的研究结果，梳理并讨论了统计学中关于模型检验角色的争议性观点，并提出了一个通用框架，在该框架下可证明初步的模型检验具有优势，从而明确使模型检验有价值所需的条件。