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H 0 : H 1 : α = Decision Rule: If then do not reject H 0 , otherwise reject H 0 . Test Statistic:

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 . H 0 : H 1 : α = Decision Rule: If

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H 0 : H 1 : α = Decision Rule: If then do not reject H 0 , otherwise reject H 0 . Test Statistic:

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  1. H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that

  2. H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that .05 .05

  3. ρ = 0 (no correlation) ρ≠ 0 (correlation exists) H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that correlation exists between speed ranking and power-hitting ranking. .05 .05

  4. * means coverage is different from text. 2 Groups and > 2 Groups Flowchart 3 4 6 5 7 8 9 10 11 12 13 14 15 paired-difference t-test pp. 315-322 Spearman Rank Correlation test pp. 625-630 yes 1 yes yes Normal populations ? Wilcoxon Signed-Ranks *pp. 614-616 chi-square goodness-of-fit test pp. for the Multinomial Experiment 362-368 and the Normal Distribution 374-376 at least interval level data ? no no 2 Sign Test *pp. 631-634. mean or median yes Z for means with σ1 & σ2 pp. 307-315 yes n1> 30 and n2> 30 ? Related Samples ? yes Normal populations ? Jaggia and Kelly (1stedition) no no Wilcoxon Rank Sum *pp. 616-621 no no σ1 and σ2 both known ? n1> 30 and n2> 30 ? no yes pooled-variances t-test pp. 307-315 yes Normal populations ? no yes σ1 = σ2 ? no unequal-variances t-test p. 307-315 proportion 2 Z for proportions pp. 322-328 Parameter ? variance or standard deviation yes # of groups ? F = S12/S22 pp. 344-354 Normal populations ? no Levine-Brown-Forsythe mean or median yes 1-way ANOVA pp. 386-395 ANOVA OK ? no Kruskal-Wallis *pp. 621-625 more than 2 chi-square df = (R-1)(C-1) pp. 368-374 yes Can we make all fe> 5 ? proportion Parameter ? no Resample and try again. variance or standard deviation yes Hartley’s Fmax *(not in text) Normal populations ? no Default case Levine-Brown-Forsythe

  5. ρ = 0 ρ≠ 0 H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Spearman Rank Correlation Coefficient Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that correlation exists between speed ranking and power-hitting ranking. .05 .05

  6. ρ = 0 ρ≠ 0 Reject H0 Do not reject H0 Reject H0 .025 .025 H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Spearman Rank Correlation Coefficient Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that correlation exists between speed ranking and power-hitting ranking. .05 n = 8 rS = -.738 0 rS = .738 .05

  7. ρ = 0 ρ≠ 0 Reject H0 Do not reject H0 Reject H0 .025 .025 H0: H1: α = Decision Rule: If -.738 < rScomputed < .738 then do not reject H0, otherwise reject H0. Test Statistic: Spearman Rank Correlation Coefficient Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that correlation exists between speed ranking and power-hitting ranking. .05 n = 8 rS = -.738 0 rS = .738 .05

  8. Calculation of the Spearman Rank Correlation Coefficient Seconds # of Balls Player X RX Y RY di = RXi - RYi (di)2 A 4.44 10 8 -7 49 B 4.52 25 5 -3 9 C 4.56 33 6 -3 9 D 4.64 42 7 -3 9 E 4.67 513 2 +3 9 F 4.80 610 3 +3 9 G 4.96 77 4 +3 9 H 4.99 815 1 +7 49 rs = 1 - (6)(å(di)2) = 1 - (6)(152) = 1 - 912 = 1 - 1.80952381 n(n2-1) 8(64-1) 504 rs» -.8095

  9. ρ = 0 ρ≠ 0 Reject H0 Do not reject H0 Reject H0 .025 .025 H0: H1: α = Decision Rule: If -.738 < rScomputed < .738 then do not reject H0, otherwise reject H0. Test Statistic: Spearman Rank Correlation Coefficient Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that correlation exists between speed ranking and power-hitting ranking. .05 n = 8 Reject H0 rS = -.738 0 rS = .738 Reject H0. .05 sufficient

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