Kentaro,
Pearsonīs Chi2 is a non-parametric test in the sense that the theoretical
distribution of the general population must be deduced from the sample itself.
Check Pearsonīs explanation in his original paper here:
http://www.economics.soton.ac.uk/staff/aldrich/1900.pdf
Carlos
PS: yet of course all "significance tests" must have some parameters... note
here that for df = 1, chi2 = z2 (i.e. for p = 0.5, chi2 = 3.84; which equals
Z*Z = 1.96*1.96)
>
>>-- Mensaje Original --
>>Date: Fri, 9 Jan 2009 00:45:20 +0900
>>Reply-To: Political Methodology Society <[log in to unmask]>
>>From: Kentaro Fukumoto <[log in to unmask]>
>>Subject: [POLMETH] (why or in what sense) is chi-square test non-parametric?
>>To: [log in to unmask]
>>
>>
>>Dear Political Methodologists,
>>
>>I have a question: (why or in what sense) is chi-square test non-parametric?
>>
>>Even though I often heard that it is non-parametric, I suspect it is
>>parametric.
>>
>>Suppose N people are divided into J categories. While we expect that the
>>
>>j-th category has E_j (not necessarily integer) people, we observe the
j-th
>>
>>category has O_j people. (Sum E_j = Sum O_j = N). The chi-square statistic
>>
>>is Sum (E_j - O_j )^2/E_j. This asympototically follows chi-square
>>distribution with J-1 degree of freedom.
>>
>>But in order to derive this asympototic distribution, it is assumed that
>>the
>>vector (O_1,O_2, ... , O_J) follows multinomial distribution, J!/(Prod
O_j!)
>>
>>Prod p_j^{O_j}, which contains parameters p_j (the probabilty a person
falls
>>
>>in the j -th category). Thus, I think chi-square test is parametric.
>>
>>I'm afraid I'm wrong, though I don't know why chi-square test is said to
>>be
>>non-parametric. Does anyone help me?
>>
>>Kentaro
>>
>><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
>>Kentaro FUKUMOTO, Ph. D.
>>Professor, Department of Political Science, Gakushuin Univ.
>>E-mail: [log in to unmask]
>>http://www-cc.gakushuin.ac.jp/~e982440/index_e.htm
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>
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>
>
>
>Anexo: Pearson 1900.pdf
>
>Fin del mensaje anexo
>
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