Thursday, April 19, 2012

Nonparametric Methods for Hypothesis Tests in Investment Analysis



Not all hypothesis tests are parametric. Nonparametric hypothesis tests are not concerned with population parameters and they make minimum assumptions about the population from which the sample is taken. Nonparametric tests are used primarily in three situations:


1.     When the population that is being analyzed is not normal (no assumption of normal distribution)

2.     When the data consists of rankings rather than ordinal measures.
3.     When the characteristic being test is not a population parameter.
Examples include:


·        Runs tests, such as determining whether a series of up and down motions are random or not random. (Used in efficient market hypothesis tests)

·        Tests for randomness between two populations

·        Tests for whether or not two events are independent of each other.
There is a comment about the content of this article. The person who made the comment is an expert in the subject. Hence I have to relook at the concepts involved in this topic.
Richard Levin in his "Statistics for Management", Third edition, Prentice hall International, 1984 has said:
Statisticians have developed useful techniques that do not mkae restrictive assumptions about the shape of population. These are known as distribution-free or, more commonly, nonparametric tests. The hypotheses of a nonparametric test are concerned with something other than the value of a population paramter.
Hence hypothesis tests and nonparametric tests are connected.  Can we say parametric hypothesis tests and nonparametric hypothesis tests? I feel we can use such terms. But still I need to examine the issue.
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