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--- analysis:stat:fisherexacttest [2014/12/15 18:10] – igorkagan
+++ analysis:stat:fisherexacttest [2014/12/16 12:27] – igorkagan
@@ Line 8: / Line 8: @@
 <code matlab>
-% Fisher's exact test
-Ns1 = 10; % status 1 (e.g. control)
+%% Fisher's exact test on proportions of two outcomes
-Ns2 = 10; % status 2 (e.g. stimulation)
+Ns1 = 10; % condition, or status 1 (e.g. control)
-status1_prop = 8/2;	% outcome 1 / outcome 2
+Ns2 = 10; % condition, or status 2 (e.g. stimulation)
-status2_prop = 1/9;	% outcome 1 / outcome 2
+% Let's assign arbitrary outcome 2 ("1") as "success"
+p_suc1 = 0.2; % probability success in status 1
+p_suc2 = 0.9; % probability success in status 2
 y1 = zeros(1,Ns1);
 y2 = ones(1,Ns2);
-x1 = [zeros(1,round(  status1_prop*Ns1 / (1 + status1_prop) )) ones( 1,round(  Ns1 - status1_prop*Ns1 / (1 + status1_prop)  ))];	% status 1 outcome
+x1 = [zeros(1,round(  (1-p_suc1)*Ns1 )) ones( 1, round(p_suc1*Ns1) )];	% status 1 outcome
-x2 = [zeros(1,round(  status2_prop*Ns2 / (1 + status2_prop) )) ones( 1,round(  Ns2 - status2_prop*Ns2 / (1 + status2_prop)  ))];	% status 2 outcome
+x2 = [zeros(1,round(  (1-p_suc2)*Ns2 )) ones( 1, round(p_suc2*Ns2) )];	% status 2 outcome
-p = fexact( [x1 x2]', [y1 y2]' )
+p = fexact( [x1 x2]' , [y1 y2]' )
+% approximating by Binomial distribution, 100 times
+% http://www.stat.yale.edu/Courses/1997-98/101/binom.htm
+count_success1 = binornd(Ns1,p_suc1,1,100); % this draws a count of success
+count_success2 = binornd(Ns2,p_suc2,1,100);
+y1 = zeros(1,Ns1);
+y2 = ones(1,Ns2);
+for i = 1:100,
+	x1 = [zeros(1,Ns1-count_success1(i)) ones( 1, count_success1(i) )];	% status 1 outcome
+	x2 = [zeros(1,Ns1-count_success2(i)) ones( 1, count_success2(i) )];	% status 1 outcome
+	p(i) = fexact( [x1 x2]' , [y1 y2]' );
+end
+hist(p<0.05);
 </code>