%%
% The project assigned to students in BME1300 class several semesters ago was
% to test the precision of a pedometer.
%
% One group organized the experiment as follows. The subjects would walk on a treadmill
% for some time under different conditions and the pedometer count was contrasted to the
% human count obtained by several designated student-counters who simultaneously
% counted the steps.
% The human count was considered exact.
%
% There were 4 treatments defined by two treadmill speeds and two types of gait.
%
% Speeds: Normal at 2.7 mi/h and Slow at 2 mi/h.
% Under both speeds the subject will walk with unconstrained gait and
% constrained gait (Steps constrained by stepping marks on the treadmill)
%
% 1 = NU (Normal -- Unconstrained)
% 2 = NC (Normal -- Constrained)
% 3 = SU (Slow -- Unconstarined)
% 4 = SC (Slow -- Constrained)
%
% The student-researchers wanted to test that the differences between the
% pedometer count and the human count were equal under all 4 regimes
% of walking thus statistically confirming the constant precision of the pedomemer
% under this experimental design.
%
% To account for differences among the subjects, each subject went through all
% 4 treatments, making this design repeated measures design.
% In total n=24 subjects, N=4 * 24 = 96 differences (pedometer count - human count)
% were measured.
%
clear all
close all
disp('Pedometer')
set(0, 'DefaultAxesFontSize', 16);
lw =2.5; fs = 16; msize = 10;
load 'C:/BESTAT/ANOVA/ANOVAdat/pmr1300.mat'
%
% reading count diffs treat subject
% 223 224 -1 1 1
% 215 223 -8 1 2
% 150 153 -3 1 3
% ...
% total 96 rows = 4 treatments x 24 subjects
reading = pmr(:,1);
count = pmr(:,2);
diffs = reading - count;
n=length(diffs);
%
treat = pmr(:,4);
subject = pmr(:,5);
%
hist(diffs,15)
%%
% Nonsolution 1
%If 96 subjects involved and
%for each we had pair of measures
%without respect to treatments:
t=mean(diffs)/(std(diffs)/sqrt(n))
pval = 2 * tcdf(-abs(t), n-1)
% Solution
varnames ={'Treatment','Subject'};
[p, table, sts] = anovan( diffs, {treat, subject}, 1,3, varnames)
multcompare(sts, 'dimension',1)
%%