Statistical significance versus fit: estimating the importance of individual factors in ecological analysis of variance

Although analysis of variance (ANOVA) is widely used by ecologists, the ful l potential of ANOVA as a descriptive tool has not been realized in most ec ological studies. As questions addressed by ecologists become more complex, and experimental and sampling designs more complicated, it is necessary fo r ecologists to estimate both statistical significance and fit when compari ng the relative importance of individual factors in an explanatory model, e specially when models are multi-factorial. Yet,,vith few exceptions, ecolog ists are only presenting significance values with ANOVA results. Here we re view methods for estimating statistical fit (magnitude of effect) for indiv idual ANOVA factors based on variance components and provide examples of th eir application to field data. Furthermore, we detail the potential occurre nce of negative variance components when determining magnitude of effects i n ANOVA and describe simple remediation procedures. The techniques we advoc ate are efficient and will greatly enhance analyses of a wide variety of AN OVA models used in ecological studies, Estimation of magnitude of effects w ill particularly benefit the analysis of complex multi-factorial ANOVAs whe re emphasis is on interpreting the relative importance of many individual f actors.