And practices in management accounting reveals a number.Of unsettled issues related to the theorizing and testing of.Contingency hypotheses. After addressing the sub-forms of.Fit we discuss, the appropriateness of various methods to.Conclusively test for them.First we compare, different classifications of forms of.Contingency fit. We find that some forms of fit that have.Been discussed and tested in management accounting literature.Do not belong to contingency theory (mediation form.Of fit) while others have not been addressed (contingency.Theory 's matching form of fit with hetero-performance.On the fit-line (Donaldson 2001), and / or with asymmetric.Effects of mis-fit on performance (Klaas, and Donaldson2009)).Second we evaluate, the main methods discussed in the.Literature for testing contingency theory predictions based.On matching and moderation forms of fit. We build on the.Work of Gerdin and Greve (2008), who discuss the appropriateness.Of various methods to test sub-forms of fit but.Take a more critical view. We find specifically that the traditional.Approaches used to test matching forms of fit are.At high risk of reaching incorrect conclusions. We explain.Why these methods may either not be powerful enough to.Detect existing matching forms of fit or may even lead to.Erroneous acceptance of such a form of fit when the null.Hypothesis or another form of fit is reflected in the dataset.Instead. We propose that extending moderated regression.Analysis (MRA) to polynomial regression analysis (PRA and.)Using response-surface methodology (RSM) offers a powerful.Alternative to testing for matching form of fit hypotheses.(Edwards 2007). We, point to the increasing relevance of.This approach in the organizational, behavior field where.Its use has been the basis for considerable theory progress.Third we address, misconceptions regarding how to.Best test and interpret moderation forms of fit. We challenge.The view that the moderator (contingency variable.)And the independent variable (e.g, management control.Systems) should not be conceptually related (and hence.Correlated). In this regard previous studies, have discussed.The possibility that a path model may instead be the correct.Alternative (Duh et al, 2006; Gerdin 2005a; Gerdin,,And, Greve 2004; Hartmann, and Moers 2003; Shields and.Shields, the 1998). Referring to such arguments Gerdin and,,Greve (2004) argue that if the moderator (contingency).And the independent variables are conceptually related.And hence significantly correlated a statistically, significant.Moderation effect should be ignored and a mediation.Form of fit model should be tested instead. In contrast we,,Argue that contingency theory implies that in the, long.Run the contingency, variable is associated with the independent.Variable (so-called selection forces), (Donaldson2001; Meilich 2006). Therefore, these variables, are likely.To be conceptually related and hence significantly correlated.We outline that statistically significant moderation.Effects should be interpreted and that any path model with.Performance as the dependent variable is outside the scope.Of contingency theory.To corroborate our argument we perform, a Monte Carlo.Simulation. We find that if the moderation form of fit is.Ignored (because moderator and independent variable are.Related) and a mediation form of fit model is, tested insteadTrue moderation forms of fit will be rejected in up to 100%.Of cases and false, mediation form of fit models will erroneously.Be accepted.In, this context we also address Hartmann and Moers.(2003 P. 808), legitimate conjecture that there is a risk.Associated with accepting a spurious moderation effect.If the moderator and independent variable are strongly.Related. However when extending, moderated regression.Analysis (MRA), to PRA thereby adequately controlling for.Non-linear relationships this risk, is, substantially reducedAllowing the moderation form of fit to be interpreted.(MacCallum, and Mar 1995). We also address misconceptions.In the management accounting field about how.To probe for interaction effects in order to differentiate.Between sub-forms of moderation fit.Fourth we provide, recommendations on the possibilities.Of covariance-based structural equation modeling.(SEM) to test contingency-based hypotheses and address.Issues related to avoiding the risk of using these techniques.Inappropriately, (Henri 2007). Particularly in the context.Of testing moderating effects and, quadratic effects these.Advanced statistical techniques can decrease the number.Of type I and type II errors if applied, Conversely correctly.They increase the risk of such errors considerably if applied.Inappropriately. We contribute to the contingency literature.By making researchers in the management accounting.Field aware of when to use (or not use) a specific SEM.Approach to test for matching and moderation forms of fit.The paper proceeds as follows: Section 2 provides an.Overview of different fo.
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