Понятие о критерии согласия (проверка гипотезы о соответствии эмпирического распределения нормальному)

Закон нормального распределения лежит в основе многих теорем и методов статистики при оценке репрезентативности выборки (расчете ошибки выборки и распространении характеристик выборки на генеральную совокупность); измерении степени тесноты связи и составлении модели регрессии; построении и использование статистических критериев и др.
Как показывают многочисленные статистические исследования, частоты (частости) эмпирических распределений за редким исключением будут отличаться от значений теоретического распределения. Расхождения между частотами (частостями) эмпирического и теоретического распределения могут быть несущественными и объяснены случайностями выборки и существенными при несоответствии выбранного и эмпирического законов распределения.
Для проверки гипотезы о соответствии эмпирического распределения теоретическому закону нормального распределения используются особые статистические показатели-критерии согласия (или критерии соответствия). К ним относятся критерии Пирсона, Колмогорова, Романовского, Ястремского и др.
Большинство критериев согласия базируется на использовании отклонений эмпирических частот то теоретических. Очевидно, что чем больше эти отклонения, тем хуже теоретическое распределения соответствует (описывает) эмпирическому (эмпирическое). Статистические характеристики таких критериев согласия являются некоторыми функциями этих отклонений.


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