Two-Sided Testing and C.I. s; Choosing the Levels of Significance Chapter 8
[Pages:13]Two-Sided Testing and C.I. s; Choosing the Levels of Significance
Chapter 8
3/19/12
Lecture 18 - Xuanyao He
1
Two-sided hypothesis testing and confidence intervals
? A two-sided significance test rejects the null hypothesis exactly when the claim falls outside the corresponding confidence interval for ?.
? If the claim is in the CI ? fail to reject H0 ? If the claim is not in the CI ? reject H0
? NOTE: must have "" in Ha!
3/19/12
Lecture 18 - Xuanyao He
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3/19/12
Lecture 18 - Xuanyao He
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Let's revisit a few examples
? Metabolism
? C.I.? ? P-Value?
? Module
? C.I.? ? P-Value?
[-560.629, -169.171] 0.002
[-.11, 3.31] .124
? A confidence interval can be used as a basis for testing hypotheses, and
? there is a confidence interval procedure (with C = 1 ? ) corresponding to any particular test procedure with significance .
? Remark: for two-sided test, use two-sided C.I.;
for one-sided test, use C.I. in the same direction.
3/19/12
Lecture 18 - Xuanyao He
4
8.5 Choosing the level of significance
? =0.05 is accepted standard, but... ? if the conclusion that Ha is true has
"costly" implications, smaller may be appropriate ? not always need to make a decision: describing the evidence by P-value may be enough
? no sharp border between statistically significant and insignificant
3/19/12
Lecture 18 - Xuanyao He
5
Statistical vs. practical significance
? Statistically significant effect may be small: ? Example ("Executive" blood pressure):
? ?0 = 128 ? = 15 ? n = 1000 obs. ? sample mean = 127
? Z = (127-128)/ (15/sqrt(1000)) = -2.11
? P-value for two sided Ha = 2*0.0174=0.0348
Significant??
Stat. significance is not necessarily practical
3/19/1s2ignificance.
Lecture 18 - Xuanyao He
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Significance vs. practical significance
? Plot your results and confidence interval, to see if the effect is worth your attention.
? Important effects may have large P-value if sample size too small. Converse also true.
? Outliers may produce or destroy statistical significance.
3/19/12
Lecture 18 - Xuanyao He
7
Lack of significance may be informative...
..for other researchers, as a warning not to invest more time in a given study.
But..., did your survey have a chance to detect the size of effect you were looking for? (e.g. maybe too small a sample size?).
3/19/12
Lecture 18 - Xuanyao He
8
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