Example: Contingency Table. Contingency Tables: Context 1 Samples are “drug” and “placebo” ; observed variable “improve” or “don’t improve” Observed Treatment.

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Presentation transcript:

Example: Contingency Table

Contingency Tables: Context 1 Samples are “drug” and “placebo” ; observed variable “improve” or “don’t improve” Observed Treatment DrugPlaceboTotal Improve15419 Don’t Improve Total262147

Contingency Tables: Context 2 Observe eye color( red/purple) and wing shape (normal/vestigial) eye color redpurple wing shape normal3911 vestigial1832

Example: Context 1 (cont) Are patients who take the drug more likely to improve than those who take the placebo at a significance level of 0.01? p 1 = probability that a patient will improve if they take the drug p 2 = probability that a patient will improve if they take the placebo

Example: Context 1 (cont) H 0 : p 1 = p 2 ; the probability of improving is the same whether drug or placebo is taken H A : p 1 > p 2 ; the probability if improving is greater if the drug is taken than if the placebo is taken

Contingency Tables: Context 1 (cont) Observed Treatment DrugPlaceboTotal Improve15419 Don’t Improve Total Observed (Expected) Treatment DrugPlaceboTotal Improve15 (10.5)4 (8.5)19 Don’t Improve11(15.5)17 (12.5)28 Total262147

Example: Context 1(cont) This study provides evidence at the 0.01 significance level that the probability of improving is greater if the drug is taken than if the placebo is taken.

Example: Context 2 Are eye color and wing shape independent in this back-cross population? p 1 = probability that a fly has red eyes if it has normal wings p 2 = probability that a fly has red eyes if it has vestigial wings

Example: Context 2 (cont) H 0 : p 1 = p 2 ; eye color and wing shape are independent H A : p 1  p 2 : eye color and wing shape are associated

Example: Context 2 (cont) eye color redpurpleTotal wing shape normal vestigial total eye color redpurpleTotal wing shape normal39 (28.5)11 (21.5)50 vestigial18 (28.5)32 (21.5)50 total

Example: Context 2 (cont) This study provides evidence at the 0.05 significance level that eye color and wing shape are associated.

Example: r x k Contingency Table Hair Color eye color BrownGrey/GreenBlueTotal Brown Black Fair Red Total This table shows the relationship between hair color and eye color for 6800 German men. Is there an association between hair color and eye color for German men to a significance level of 0.01.

Example: r x k Contingency Table (cont) Hair Color eye color BrownGrey/GreenBlueTotal Brown438 (331.7) 1387 (1212.3) 807 (1088.0)2632 Black288 (154.1)746 (563.3)189 (505.6)1223 Fair115 (356.5)946 (1303.0)1768 (1169.5)2829 Red16 (14.6)53(53.4)47 (48.0)116 Total

Example: Confidence Interval What is the 95% Confidence Interval for the study of the treatment of a drug vs. a placebo below? Observed Treatment DrugPlaceboTotal Improve15419 Don’t Improve Total262147

Summary