Slides23-2010 - 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 Charles B. Moss () Neyman-Pearson October 26, 2010 1 / 22
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1 Introduction 2 Type I and Type II Errors 3 Neyman-Pearson Lemma Charles B. Moss () Neyman-Pearson October 26, 2010 2 / 22
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Introduction 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). The second kind of distribution is the traditional stuF of econometrics. 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. I The second kind of hypothesis is termed a simple hypothesis. Under this scenario, we test the value of a parameter against a single alternative. I 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. Charles B. Moss () Neyman-Pearson October 26, 2010 3 / 22
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Hypothesis testing involves the comparison between two competing hypothesis, or conjectures. I The null hypothesis, denoted H 0 , is sometimes referred to as the maintained hypothesis. I The competing hypothesis to be accepted if the null hypothesis is rejected is called the alternative hypothesis. Charles B. Moss () Neyman-Pearson October 26, 2010 4 / 22
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The general notion of the hypothesis test is that we collect a sample of data X 1 , ··· X n . This sample is a multivariate random variable, E n (the text refers to this as an element of a Euclidean space). I If the multivariate random variable is contained in space R , we reject the null hypothesis. I Alternatively, if the random variable is in the complement of the space R , we fail to reject the null hypothesis.
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This note was uploaded on 07/15/2011 for the course AEB 6180 taught by Professor Staff during the Spring '10 term at University of Florida.

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Slides23-2010 - Type I and Type II Errors and the...

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