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How Well Does the Sum Score Summarize the Test? Summability as a Measure of Internal Consistency

Many researchers use Cronbach's alpha to demonstrate internal consistency, even though it has been shown numerous times that Cronbach's alpha is not suitable for this. Because the intention of questionnaire and test constructers is to summarize the test by its overall sum score, we advocate summability, which we define as the proportion of total test variation that is explained by the sum score. This measure is closely related to Loevinger's H. The mathematical derivation of summability as a measure of explained variation is given for both scale and dichotomously scored items. Using computer simulations, we show that summability performs adequately and we apply it to an existing productive vocabulary test. An open-source tool to easily calculate summability is provided online (https://sites.google.com/view/summability).