Drawing upon previous research, a mathematical model for understanding the , relationship between causal attributions for success and failure and future expectations was developed. Four hypotheses were generated from the model: (a) The stability of attributions is a function of the difference between the person's initial expectations and the actual outcome, (b) The more an outcome is attributed to stable causes, the greater the weight that will be given to that outcome in determining predictions for the future, (c) Change in expectations will be a quadratic function of the difference between initial expectations and the actual performance, (d) By manipulating the causal attributions it is possible to lessen or increase the amount of weight given to an outcome when making predictions for the future. Two studies are reported that tested and supported these hypotheses.

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A model of the attribution process based upon an observer's probability estimates is presented. Four hypotheses were tested using hypothetical achievement situations. Subjects were presented with a student's present quiz grade, the class average, and the student's average on past quizzes. Five levels for each of these three independent variables created a 5 × 5 × 5 factorial design. The model assumed that the results of achievement behavior can be attributed either internally or externally and either stably or unstably. The dependent variables were subjects' ratings of the level and importance of ability, effort, task difficulty, and luck as possible causes for the student's present quiz grade. Three of the four hypotheses were strongly supported. The advantages and implications of this approach are discussed.

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