Calculations
Explicit expressions that can be used to carry out various t-tests are given below. In each case, the formula for a test statistic that either exactly follows or closely approximates a t-distribution under the null hypothesis is given. Also, the appropriate degrees of freedom are given in each case. Each of these statistics can be used to carry out either a one-tailed test or a two-tailed test.
Once a t value is determined, a p-value can be found using a table of values from Student's t-distribution. If the calculated p-value is below the threshold chosen for statistical significance (usually the 0.10, the 0.05, or 0.01 level), then the null hypothesis is rejected in favor of the alternative hypothesis.
Read more about this topic: Student's t-test
Famous quotes containing the word calculations:
“He who is conversant with the supernal powers will not worship these inferior deities of the wind, waves, tide, and sunshine. But we would not disparage the importance of such calculations as we have described. They are truths in physics because they are true in ethics.”
—Henry David Thoreau (1817–1862)
“Nowhere are our calculations more frequently upset than in war.”
—Titus Livius (Livy)
“What, really, is wanted from a neighborhood? Convenience, certainly, an absence of major aggravation, to be sure. But perhaps most of all, ideally, what is wanted is a comfortable background, a breathing space of intermission between the intensities of private life and the calculations of public life.”
—Joseph Epstein (b. 1937)