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Type I and Type II Errors and the
NeymanPearson: 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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View Full DocumentAEB 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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