Relating alternative forms of contingency fit to the appropriate methods to test them

•Rival forms of contingency fit get easily confused when using the traditional empirical methods.•We re-evaluate some of the recommendations how to differentiate between rival forms of fit.•We present polynomial regression analysis as a powerful alternative.•We provide a discussion regarding the suitability of SEM to test contingency hypotheses.

At the core of contingency theory, a major theory in management accounting, is the concept of fit. We critically discuss forms of fit as presented in overview articles from the management accounting field, highlighting forms of fit that have not appeared in prior overview articles (matching fit with hetero-performance on the fit line and/or asymmetric effects of mis-fit on performance). We also address some confusing arguments in the literature concerning the moderation form of fit and what has been referred as the mediation form of fit. In a second step, we reevaluate the appropriateness of statistical techniques used to test sub-forms of fit, highlighting the difficulties in differentiating conclusively between them. Specifically, we present polynomial regression analysis (PRA) in conjunction with the response surface methodology (RSM) as a powerful methodological alternative and discuss its ability to differentiate between the sub-forms of fit. We also discuss the strengths and weaknesses of structural equation modeling (SEM) to test for forms of fit.