Calculate standard deviation for different groups

I want to plot a Measurement with a bar figure. Therefore I want to create different groups and calculate the standard deviation for each group. I have a vector "Measurement" which is sorted according to increasing values. I get group IDs for the Measurement values by the use of the histc function.

[~,Measure_ID]=histc(Measurement_x,0:200:max);

In the next step I try to calculate the standard deviation with the accumarray function.

group_std = accumarray(Measure_ID,Measurement_y,[],@std);

The std command uses the follow mathematical formula:

The problem is that accumarray calculates the arithmetic average for each group separately. But I want to see the standard deviation regarding to the global arithmetic average. Is there a way to solve my issue?

Version: 2012b

[Jan]

Do you mean:

std(Measurement_y)

? What exactly is "standard deviation regarding to the global arithmetic average"?

Answer 1

[Jan]

If you want to set the x_bar values of the formula to mean(Measurement_y), why not implementing this as function?

function s = specialStd(x, m)
s = sqrt(sum((x - m) .^ 2) / (length(x) - 1));
end

and call it like:

m         = mean(Measurement_x);
group_std = accumarray(Measure_ID, Measurement_y, [], @(x) specialStd(x, m));

[Guillaume]

specialStd, notexactlystd, I think we can agree that this thing shouldn't be called plain std!

Answer 2

[Guillaume]

"The problem is that accumarray calculates the arithmetic average for each group separately".

It's not accumarray doing that, it's std, because that the definition of the standard eviation.

To do what you want, you'll have to implement your own standard deviation calculation:

whole_mean = mean(Mesurement_y);
group_notexactlystd = accumarray(Measure_ID, Measurement_y, [], @(v) sum((v - whole_mean).^2)/(numel(v)-1));