Significance Tests: Yet Another Introduction

The great chess grandmaster Siegbert Tarrasch once said that if you pay careful attention to development, then when the time came that you needed a combination, it will be there. Tarrasch's comment came to mind as I was reevaluating, yet again, the way I introduce hypothesis testing.

Recall the comments in Is Statistics Hard?

Statistical methods are convoluted! In order to show an effect exists,

Before considering formal hypothesis testing, let's see how those quoted comments relate to confidence intervals. We wished to compare two population means. We did so by constructing a confidence interval for their difference.

The way the game is played, the data are said to be consistent with any value for the population mean difference that is in the CI.

Insofar as comparing population means is concerned, a formal test of the hypothesis that the means are equal will be equivalent to looking at whether 0 is in the confidence interval.

Confidence Intervals Significance Tests
construct interval calculate test statistic
is 0 in interval? is statistic far enough
away from 0?

Copyright © 2006 Gerard E. Dallal