TPS4e_Ch9_9.1.ppt.pptVIP

Statistical Significance The final step in performing a significance test is to draw a conclusion about the competing claims you were testing. We will make one of two decisions based on the strength of the evidence against the null hypothesis (and in favor of the alternative hypothesis) -- reject H0 or fail to reject H0. If our sample result is too unlikely to have happened by chance assuming H0 is true, then we’ll reject H0. Otherwise, we will fail to reject H0. Significance Tests: The Basics Note: A fail-to-reject H0 decision in a significance test doesn’t mean that H0 is true. For that reason, you should never “accept H0” or use language implying that you believe H0 is true. In a nutshell, our conclusion in a significance test comes down to P-value small → reject H0 → conclude Ha (in context) P-value large → fail to reject H0 → cannot conclude Ha (in context) Statistical Significance There is no rule for how small a P-value we should require in order to reject H0 — it’s a matter of judgment and depends on the specific circumstances. But we can compare the P-value with a fixed value that we regard as decisive, called the significance level. We write it as α, the Greek letter alpha. When our P-value is less than the chosen α, we say that the result is statistically significant. Significance Tests: The Basics Definition: If the P-value is smaller than alpha, we say that the data are statistically significant at level α. In that case, we reject the null hypothesis H0 and conclude that there is convincing evidence in favor of the alternative hypothesis Ha. When we use a fixed level of significance to draw a conclusion in a significance test, P-value α → reject H0 → conclude Ha (in context) P-value ≥ α → fail to reject H0 → cannot conclude Ha (in context) Example: Better Batteries Significance Tests: The Basics What conclusion can you make for the significance level α = 0.05? b) What conclusion can you make for the significance level α = 0.01? Since the P-value