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

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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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