Update holm_sidak.m

CanlabCore/Statistics_tools/holm_sidak.m

@@ -1,4 +1,4 @@
-function sig = holm_sidak(pVector, alpha)
+function [sig, pthr] = holm_sidak(pVector, alpha)
 % performs Holm-Sidak correction for multiple independent comparisons. Sidak correction is a slightly less conservative bonferonni
 % Holm's method is a step down approach implemented by the while loop iterations. More commonly used in the context of bonferonni
 % rather than Sidak, but equally valid in both cases.
@@ -10,14 +10,36 @@
 % Bogdan Petre, 6/19/2023
 %
 % WARNING: This code is an alpha version, not fully tested for all edge cases
+%
+% 1.The P values are ranked from smallest to largest.
+% 2.Set a value for the significance level, alpha. This is often set to 5%.
+% 3.Define k equal to the number of comparisons (length(sortedP) in the code)
+% 4.Start with the smallest P value and set i=k. Ask: Is the smallest P value less than the Šídák corrected value 1-(1-alpha)(1/i)?
+% 
+%   If No: Conclude that none of the comparisons are statistically significant, and you are done.
+%   If Yes: Conclude that this comparison is statistically significant, and continue.
+% 
+% 5.The second to smallest P value is compared next. Set i=K-1. Is the P value less than 1-(1-alpha)(1/i)?
+% 
+% If No: Conclude that this  comparison (and all with larger P values) is not statistically significant. Exit.
+% 
+% If Yes: Conclude that this comparison is statistically significant, and continue step 5 with i = K-2, etc.
+
 
 [sortedP, argsort] = sort(pVector, 'descend'); % pValues sorted from largest to smallest, and indices mapping pVector to sortedP
 
 sig = zeros(length(sortedP),1);
+
+pthr = 1 - (1-alpha)^(1/length(sortedP)); % max P-value for sig results. Anything below this is signficant.
+
 while sortedP(end) < 1 - (1-alpha)^(1/length(sortedP))
+
     sig(argsort(end)) = 1;
     sortedP(end) = [];
     argsort(end) = [];
+
+    pthr = 1 - (1-alpha)^(1/length(sortedP)); % step-down adjustment of P-value.
+
 end
 
 end