P = tcdf(X,V) computes Student's t cdf at each of the values 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.

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).

Examples

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 = (xbar-mu)/(s/sqrt(n)) % t-statistic
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

tcdf - Student's t cumulative distribution function

Syntax

Description

Examples

See Also

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