In the mixed world of predictive biology—Contradiction or support

Statistical prediction is a tool and aim in ecology and wildlife management and conservation. A prediction may either be supported by or contradicted by observations of an unknown set of observations. A contradiction occurs if the prediction is not included within the range of the unknown observations, i.e. the prediction misses the cloud of observations completely. Mixed-effects models, frequently used for statistical assessment of clustered data, carry information needed for calculating the probability of such contradictions. Here we present a new versatile statistic, the probability of contradiction (P (Contra)), that describes how often we would anticipate a new cluster of observations contradicting our predictions. Some benefits of P (Contra) are: (1) easy to calculate and intuitive interpretation, (2) comparability between datasets, (3) inclusion of residual correlation, (4) summary of the multitude of information from mixed models into one statistics, and (5) applicable to local mixed-effect models.In this outline of P (Contra) we show through two real data examples, egg-size of Pied Flycatcher, and number of large follicles during the oestrus cycle of mares, the versatility of the statistic both in the context of prediction, as well as a model summary and an interpretational help for the complex outputs of mixed-effect models.