Student's t cumulative distribution function
p = tcdf(x,v)
p = tcdf(x,v,'upper')
p = tcdf(x,v) returns Student's t cdf at each value in x using the corresponding degrees of freedom in v. x and v can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs.
p = tcdf(x,v,'upper') returns the complement of the Student's t cdf at each value in x, using an algorithm that more accurately computes the extreme upper tail probabilities.
The t cdf is
The result, p, is the probability that a single observation from the t distribution with ν degrees of freedom will fall in the interval [–∞, x).
mu = 1; % Population mean sigma = 2; % Population standard deviation n = 100; % Sample size x = normrnd(mu,sigma,n,1); % Random sample from population xbar = mean(x); % Sample mean s = std(x); % Sample standard deviation
t = 0.2489
p = 1-tcdf(t,n-1) % Probability of larger t-statistic
p = 0.4020
This probability is the same as the p value returned by a t-test of the null hypothesis that the sample comes from a normal population with mean μ.
[h,ptest] = ttest(x,mu,0.05,'right')
h = 0 ptest = 0.4020