The correct way to express the deviation of cata around the mean is to use the standard error of the mean, given by:
where σ is the standard deviation and N are the number of data used to calculate it.
T1 = readtable('datamine.xlsx')
TT1 = table2timetable(T1)
SEM = @(x) std(x)/sqrt(numel(x));
TT1momean = retime(TT1, 'monthly', 'mean')
TT1mosem = retime(TT1, 'monthly', SEM)
TT1monum = retime(TT1, 'monthly', 'count');
[Nmin,Nmax] = bounds(TT1monum{:,1})
% TT1Time = TT1mosem.time;
% TT1SEM = TT1mosem{:,1};
figure
plot(TT1momean.time, TT1momean{:,1}, '-k')
hold on
patch([TT1mosem.time; flip(TT1mosem.time)], [TT1momean{:,1}-TT1mosem{:,1}*1.96; flip(TT1momean{:,1}+TT1mosem{:,1}*1.96)], 'r', 'FaceAlpha',0.25, 'EdgeColor','r')
hold off
grid
xlabel('Time')
ylabel('Value')
title('Mean ±95% CI')
The SEM values are quite small when compared to the mean values (on the order of 
) so they are barely visible. I did a separate accumulation for the number of values in each month, and since they were all above 330, using the 95% confidence intervals from the normal distribution is a safe estimate. It is not necessary to use the t-distribution, since it will closely approximate the normal distribution with this many degrees-of-freedom.
) so they are barely visible. I did a separate accumulation for the number of values in each month, and since they were all above 330, using the 95% confidence intervals from the normal distribution is a safe estimate. It is not necessary to use the t-distribution, since it will closely approximate the normal distribution with this many degrees-of-freedom. .
