In a two-tailed t-test for a P of 0.1 and a one-tailed test for a P of 0.05, is the t value to show significance the same? I understand that the two-tailed test is looking for significance at either end on the curve and the one-tailed is looking for significance in only one direction, in fact, that is why I ask the question.
In two-tailed situation where the type I error rate, $\alpha$, is set at 10%, the 10% is evenly placed at the two ends, cutting at the first 5% and the last 5% of the t-distribution.
In one-tailed with $\alpha$ is set at 5%, this 5% will just be placed at one end.
So, the critical values are of the same magnitude. But to be technically correct they are not all the same. Because in the two-tailed situation the critical value can be both positive and negative; in the one-tailed situation it has to be either positive or negative, depending on your hypothesis.