MATLAB: Plot confidence interval of a signal

confidenceintervalintervalsignalstatistics

Hi all,
i have a signal so it's just data, that i load on Matlab and I have to plot 95% confidence interval according to student t-distribution of my signal. Exactly like photo, that i added. When i am reading some solutions about that, i am confuse because i am not good about statistics. If you help me, at least how can i start to make something, i would be very appreciated that.
Thank you!

Best Answer

In order to calculate the 95% confidence intervals of your signal, you first will need to calculate the mean and *|std| (standard deviation) of your experiments at each value of your independent variable. The standard way to do this is to calculate the standard error of the mean at each value of your independent variable, multiply it by the calculated 95% values of the t-distribution (here), then add and subtract those values from the mean. The plot is then straightforward. (The tinv function is in the Statistics and Machine Learning Toolbox.)
Example —
x = 1:100;                                          % Create Independent Variable
y = randn(50,100);                                  % Create Dependent Variable ‘Experiments’ Data
N = size(y,1);                                      % Number of ‘Experiments’ In Data Set
yMean = mean(y);                                    % Mean Of All Experiments At Each Value Of ‘x’
ySEM = std(y)/sqrt(N);                              % Compute ‘Standard Error Of The Mean’ Of All Experiments At Each Value Of ‘x’
CI95 = tinv([0.025 0.975], N-1);                    % Calculate 95% Probability Intervals Of t-Distribution
yCI95 = bsxfun(@times, ySEM, CI95(:));              % Calculate 95% Confidence Intervals Of All Experiments At Each Value Of ‘x’
figure
plot(x, yMean)                                      % Plot Mean Of All Experiments
hold on
plot(x, yCI95+yMean)                                % Plot 95% Confidence Intervals Of All Experiments
hold off
grid
This should get you started.
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