Testing the Significance of Regression Coefficients: The t Test
An alternative but complementary approach to the confidence-interval method of testing statistical hypotheses is the test-of-significance approach developed along independent lines by R. A. Fisher and jointly by Neyman and Pearson.9 Broadly speaking, a test of significance is a procedure by which sample results are used to verify the truth or falsity of a null hypothesis. The key idea behind tests of significance is that of a test statistic (estimator) and the sampling distribution of such a statistic under the null hypothesis. The decision to accept or reject H0 is made on the basis of the value of the test statistic obtained from the data at hand.
As an illustration, recall that under the normality assumption the variable t =
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