For a research project I have obtained results which I have to test for significance. The two values I am comparing are the true diameter of a certain object versus the calculated diameter of that object. In this case it would be favourable if the t-test showed no significant difference between those results.
However while checking the T-table I came across this problem which just won't reach my brain. When my t-value is higher than a critical value there is a significant difference, but as the probability (alpha) increases that critical value increases. This leads to my misunderstanding that for this reason I can say that:
- There is a 95% probability that there is a significant difference between the true values and calculated results
But since the critical value rises with probability:
- There is a 99.9% probability that there is no significant difference between the two
This is obviously not right, but I cannot grasp what is going wrong.