Hypothesis Testing and R-Square Analysis

Explanation

As the sample size increases, it becomes easier to test whether the null hypothesis can be rejected at the specified significance level (Intuitively, it is harder for a false hypothesis to hide its falsity when there are a larger number of observations testing its veracity). In fact, the critical t-statistic required to reject the null decreases as the sample size increases for a given level of significance.

A higher significance level makes it easier to reject the null hypothesis. This is because you are enforcing a looser standard on rejecting the null (recall that the significance level represents the probability thatyou have rejected the null when, in fact, it is true). In fact, significance level and critical t-statistic are inversely related.

R-square is not used in hypothesis testing but in regression analysis, though it does not measure the significance of a regression. A regression with a very low R- square can be highly significant; the low R-square only implies that the behavior of the dependent variable is governed largely by random noise.