The usage of the sensitivity parameter doesn't influence the neighborhood statistics. It's simply used as a polarity-independent proxy for the output scaling.
You can open up adaptthresh() and read it, or this is a simplified example of how it works using the default settings.
% an image in unit-scale float
inpict = imread('cameraman.tif');
inpict = im2double(inpict);
% parameters
sensitivity = 0.5; % default
fgpolarity = 'bright'; % default
nhoodsize = size(inpict)/8; % default
% convert normalized sensitivity to polarity-dependent scale factor
switch lower(fgpolarity)
case 'bright'
scalefactor = 0.6 + (1-sensitivity);
case 'dark'
scalefactor = 0.4 + sensitivity;
end
% construct filter kernel
nhoodsize = 2*round(nhoodsize/2) + 1; % round odd
fk = fspecial('average',nhoodsize);
% apply the filter and scale the threshold value
TH = imfilter(inpict,fk,'replicate');
TH = scalefactor*TH;
% compare against the IPT tool
THref = adaptthresh(inpict);
immse(TH,THref)
