© Buddy Freeman, 2015 H 0 : H 1 : α = Decision Rule: If then do not reject H 0, otherwise reject H 0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that

© Buddy Freeman, 2015 H 0 : H 1 : α = Decision Rule: If then do not reject H 0, otherwise reject H 0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that.025

© Buddy Freeman, 2015 H 0 : H 1 : α = Decision Rule: If then do not reject H 0, otherwise reject H 0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After H 0 :  1 =  2 H 1 :  1 >  2 After Before or

© Buddy Freeman, 2014 # of groups ? Parameter ? Can we make all f e > 5 ? Normal populations ? Hartley’s F max *(not in text) Resample and try again. yes no yes no chi-square df = (R-1)(C-1) pp yes no Kruskal-Wallis *pp way ANOVA pp ANOVA OK ? mean or median proportion variance or standard deviation more than 2 Parameter ? Related Samples ? mean or median proportion variance or standard deviation Normal populations ? yes no Levine-Brown-Forsythe F = S 1 2 /S 2 2 pp Z for proportions pp yes no unequal-variances t-test p pooled-variances t-test pp Wilcoxon Rank Sum *pp no yes Normal populations ? Normal populations ? yes no yes no n 1 > 30 and n 2 > 30 ? Z for means with σ 1 & σ 2 pp yes no σ 1 and σ 2 both known ? no Normal populations ? yes no yes at least interval level data ? yes no Sign Test *pp Wilcoxon Signed-Ranks *pp paired-difference t-test pp chi-square goodness-of-fit test pp. for the Multinomial Experiment and the Normal Distribution Groups and > 2 Groups Flowchart Spearman Rank Correlation test pp yes no n 1 > 30 and n 2 > 30 ? 6 σ 1 = σ 2 ? Levine-Brown-Forsythe Jaggia and Kelly (1 st edition) Default case * means coverage is different from text.

© Buddy Freeman, 2015 H 0 : H 1 : α = Decision Rule: If then do not reject H 0, otherwise reject H 0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After

© Buddy Freeman, 2015 H 0 : H 1 : α = Decision Rule: If then do not reject H 0, otherwise reject H 0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After Do not reject H 0 Reject H t = df = n – 1 = 8

© Buddy Freeman, 2015 H 0 : H 1 : α = Decision Rule: If t computed > then do not reject H 0, otherwise reject H 0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After Do not reject H 0 Reject H t = df = n – 1 = 8

© Buddy Freeman, 2015 H 0 : H 1 : α = Decision Rule: If t computed > then do not reject H 0, otherwise reject H 0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After Do not reject H 0. insufficient Do not reject H 0 Reject H t = df = n – 1 = 8 Do not reject H 0