NetNews Usenet Archive 1992 #19/NN_1992_19.iso/spool/sci/math/10679

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From: [e-mail] (Chuck Haas)
Newsgroups: sci.math
Subject: Re: Additional info on "trends" question
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Date: 28 Aug 92 17:55:38 GMT
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Use of Mann's test for trend (see Kotz and Johnson, Ency. of
Statistical Sciences, vol5, p 207).

sort paired observations (Xi, Yi) according to X (in your case, year)

compute sign(Yj-Yi) for all i<j;  sign(arg) = arg/absolute value(arg)

define S* = sum of sign(Yj-Yi)

For large samples, S* null distribution is normal with zero mean and
variance given by:

(1/18) [n(n-1)(2n+5)- SIGMA u(u-1)(2u+5)]

where n = number of observations
           u = multiplicity of ties (if two observations Y are equal,
u=2; if three are equal
                 then u=3, etc.) for each "tuple"

Reject null hypothesis (i.e. trend is statistically significant) based on
comparison
to tables of the standard normal distribution.

Comment:
    This test obviously neglects the information contained in your year
intervals, however does not require many assumptions that exist for
example in regression analysis.

Perhaps someone else would have information on the relative power of this
test to  regression.

==============
Charles N. Haas
Betz Chair Professor of Environmental Engineering
Drexel University
Philadelphia PA