function?[p?Q]=?chi2test（x）
	
%?Usage:?[p?Q]=?chi2test（x）
%?
%?The?chi-squared?test.?
%?
%?Given?a?number?of?samples?this?function?tests?the?hypothesis?that?the?samples?are?
%?independent.?If?Q?>?chi2（p?nu）?the?hypothesis?is?rejected.?
%?
%?Each?column?represents?a?variables?each?row?a?sample.
%?
%?If?you?find?any?errors?please?let?me?know:?.
%?
%?ARGUMENTS:
%?x?????Absolut?numbers.
%?p?????The?prob?ability?value?calculated?from?Q.
%?Q?????The?resulting?Q-value.
%?
%?EXAMPLE?1
%?In?region?A?324?of?556?cows?were?red?whereas?in?region?B?98?of?260?were?red.
%?[p?Q]=?chi2test（[324?556-324;?98?260-98]）
%?p=
%????4.2073e-08
%?Q=
%????30.0515
%?With?an?error?risk?of?about?4e-08?we?can?claim?that?the?samples?are?independent.
%?
%?EXAMPLE?2
%?Throw?two?different?dices?to?see?if?they?have?the?same?probability?of?1?（and?2?3?4?5?6）.
%?We?don‘t?check?if?they?are?symetrical?only?if?the?both?behave?in?the?same?way.
%?[pQ]?=?chi2test（[1510;?711;?97;?2015;?2621;?1916]）
%?p=
%????0.8200
%?Q?=
%????2.2059
%?The?dices?don‘t?significantly?behave?differently.?That?is?they?seem?to?behave?in?the?same?way.
%
%?HISTORY:????v.1.0?first?working?version?2007-08-30.
%?
%?COPYRIGHT:??（c）?2007?Peder?Axensten.?Use?at?own?risk.

%?KEYWORDS:???chi-squared?test?chi-squared?chi2?test

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	%?Check?the?arguments.
	if（nargin?~=?1）			error（‘One?and?only?one?argument?required!‘）;					end
	if（ndims（x）?~=?2）			error（‘The?argument?（x）?must?be?a?2d?matrix!‘）;					end
	if（any（size（x）?==?1））		error（‘The?argument?（x）?must?be?a?2d?matrix!‘）;					end
	if（any（~isreal（x）））		error（‘All?values?of?the?argument?（x）?must?be?real?values!‘）;	end
	
	%?Calculate?Q?=?sum（?（a-np*）^2/（np*（1-p*））?）
	s=		size（x?1）;
	r=		size（x?2）;
	np=		sum（x?2）/sum（sum（x））?*?sum（x）;		%?p=sum（x?2）/sum（sum（x））?and?n=sum（x）
	Q=		sum（sum（（x-np）.^2./（np）））;
	
	%?Calculate?cdf?of?chi-squared?to?Q.?Degrees?of?freedom?v?is?（r-1）*（s-1）.
	p=		1?-?gammainc（Q/2?（r-1）*（s-1）/2）;
end

?屬性????????????大小?????日期????時間???名稱
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?????文件???????2040??2009-03-25?08:04??chi2test.m

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?????????????????2040????????????????????1