**CODE**

% We are going to measure 40 different conditions.

% For the first twenty conditions, the true signal will be 0.

% For the second twenty conditions, the true signal will be 1.

numconditions = 40;

% We will make 30 different measurements for each condition.

n = 30;

% Let's perform a simulation, visualize the results,

% and then do it again (ad nauseum).

while 1

% these are the true signal values

signal = [zeros(1,numconditions/2) ones(1,numconditions/2)];

% this is the noise (random Gaussian noise)

noise = randn(n,numconditions);

% these are the measurements

measurement = bsxfun(@plus,signal,noise);

% given the measurements, let's calculate the mean

% and standard error for each condition.

mn = mean(measurement,1);

se = std(measurement,[],1)/sqrt(n);

% now, let's visualize the results

figure(999); clf; hold on;

bar(1:numconditions,mn);

errorbar2(1:numconditions,mn,se,'v','r-','LineWidth',2);

plot(1:numconditions,signal,'b-','LineWidth',2);

axis([0 numconditions+1 -1 2]);

title('Black is the mean; red is the standard error; blue is the true signal');

pause;

end

**OBSERVATIONS**

If you use +/- 1 standard error to visualize results, it may subjectively look like there are differences, even though there aren't any. For this reason, it may be useful to instead plot error bars that reflect +/- 2 standard errors.

It is quite common to find measurements that are several error bars away from the true value. Of course, this is completely expected given the nature of standard errors (e.g. 5% of the time, you will find a data point that is more than 2 standard errors away from the true value).

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