Lecture23-2010 - Type I and Type II Errors and the...

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Type I and Type II Errors and the Neyman-Pearson: Lecture XXIII Charles B. Moss October 26, 2010 I. Introduction A. In general there are two kinds of hypotheses: one type concerns the form of the probability distribution (i.e. is the random variable normally distributed) and the second concerns parameters of a distribution function (i.e. what is the mean of a distribution). B. The second kind of distribution is the traditional stuF of econo- metrics. We may be interested in testing whether the eFect of income on consumption is greater than one, or whether the eFect of price on the level consumed is equal to zero. 1. The second kind of hypothesis is termed a simple hypothesis. Under this scenario, we test the value of a parameter against a single alternative. 2. The ±rst kind of hypothesis (whether the eFect of income on consumption is greater than one) is termed a composite hypothesis. Implicit in this test is several alternative values. C. Hypothesis testing involves the comparison between two compet- ing hypothesis, or conjectures. 1. The null hypothesis, denoted H 0 , is sometimes referred to as the maintained hypothesis. 2. The competing hypothesis to be accepted if the null hypoth- esis is rejected is called the alternative hypothesis. 1
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AEB 6571 Econometric Methods I Professor Charles B. Moss Lecture XXIII Fall 2010 D. The general notion of the hypothesis test is that we collect a sam- ple of data X 1 , ··· X n . This sample is a multivariate random vari- able, E n (the text refers to this as an element of a Euclidean space). 1. If the multivariate random variable is contained in space R , we reject the null hypothesis. 2. Alternatively, if the random variable is in the complement of the space R , we fail to reject the null hypothesis.
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Lecture23-2010 - Type I and Type II Errors and the...

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