Here's demo code using tinv to produce the t-critical values for a two-sided test with independent samples (i.e., between-subjects). The example uses a random data set (10x2) with one column biased to occasionally produce a significant difference. If you run this script multiple times, you'll find that t falls within the lower and upper t-critical values when p > .05 and falls outside the lower and upper t-critical values when p < .05.
% design parameters
n = 10; % Note: df = 2*(n-1)
alpha = 0.05;
% test data
M(:,1) = rand(1,n);
M(:,2) = rand(1,n) + 0.3; % add bias to get significance (sometimes)
% perform t-test
[~, p, ~, stats] = ttest2(M(:,1), M(:,2));
% compute lower and upper t-critical values
pLower = alpha/2;
pUpper = 1 - alpha/2;
tCritical = tinv([pLower pUpper], stats.df);
% output t, p, df, and t-critical lower and upper
fprintf('t=%.4f, p=%.4f, df=%d, t-critical: %.4f | %.4f\n', stats.tstat, p, stats.df, tCritical(1), tCritical(2));
