MATLAB: How to calculate the confidence interval

confidence intervalconfidence intervallmeant-distribution

I have a vector x with e.g. 100 data point. I can easy calculate the mean but now I want the 95% confidence interval. I can calculate the 95% confidence interval as follows:

CI = mean(x)+- t * (s / square(n))

where s is the standard deviation and n the sample size (= 100).

Is there a method in matlab where I just can feed in the vector and then I get the confidence interval?

Or I can write my own method but I need at least the value of t (critical value of the t distribution) because it depends on the number of samples and I don't want to lookup it in a table everytime. Is this possible?

Would be very nice if somebody could give an example.

Last but not least, I want 95% confidence in a 5% interval around the mean. For checking that I just have to calculate the 95% confidence interval and then check if the retrieved value is less than 5% of my mean, right?

Best Answer

This works:

x = randi(50, 1, 100);                      % Create Data
SEM = std(x)/sqrt(length(x));               % Standard Error
ts = tinv([0.025  0.975],length(x)-1);      % T-Score
CI = mean(x) + ts*SEM;                      % Confidence Intervals

You have to have the Statistics Toolbox to use the tinv function. If you do not have it, I can provide you with a few lines of my code that will calculate the t-probability and its inverse.

Related Solutions

MATLAB: Standard error of Weibull MLE estimates

The standard error is basically 1/4 of the length of the confidence interval.

MATLAB: How to draw 95% CI plot in the data

Replace the second plot call with:

patch([x, fliplr(x)], [yCI95(1,:) fliplr(yCI95(2,:))], 'b', 'EdgeColor','none', 'FaceAlpha',0.25)

so the full code is now:

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,'p')                                  % Plot Mean Of All Experiments
hold on
% plot(x, yCI95+yMean,'-r')                           % Plot 95% Confidence Intervals Of All Experiments
patch([x, fliplr(x)], [yCI95(1,:) fliplr(yCI95(2,:))], 'b', 'EdgeColor','none', 'FaceAlpha',0.25)
hold off
grid

That should do what you want. (I appreciate your quoting my code!)

Best Answer

Related Solutions

MATLAB: Standard error of Weibull MLE estimates

MATLAB: How to draw 95% CI plot in the data

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