Lecture 4 Section 1.4.3 Wed, Sep 1, 2004 What’s in the Bag? Lecture 4 Section 1.4.3 Wed, Sep 1, 2004

How Strong is the Evidence? Rather than give an accept/reject answer, we may ask a different question: How strong is the evidence against H0?

The p-value p-value – The likelihood of getting by chance, if H0 is true, a value at least as extreme as the one observed.

Two Bags Bag A -1000 10 20 30 40 50 60 1000 Bag B -1000 10 20 30 40 50 60 1000

Interpretation of the p-value Smaller p-values Larger p-values 1 p-values

Interpretation of the p-value Larger discrepancy Smaller discrepancy 1 p-values

Interpretation of the p-value Stronger evidence against H0 Weaker evidence against H0 1 p-values

Interpretation of the p-value Statistically significant Statistically insignificant 1 p-values

Let’s Do It! Let’s do it! 1.7, p. 26 – Chromium Supplements. Let’s do it! 1.8, p. 27 – Three Studies.

Let’s Do It! Let’s do it! 1.9, p. 32 – p-value for a One-Sided Rejection Region to the Left. Example 1.8, p. 33 – p-value for a Two-Sided Rejection Region. Let’s do it! 1.10, p. 34 – p-value for a Two-Sided Rejection Region. Example 1.9, p. 36 – Can You Picture the p-value?

Let’s Do It! Let’s do it! 1.11, p. 39 – Machine A or Machine B?