MSB MSW k 3 2 1 \u03bc \u03bc \u03bc \u03bc H equal are means population all Not H A F Reject H if

Msb msw k 3 2 1 μ μ μ μ h equal are means

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  • STATS 401
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MSB MSW k 3 2 1 0 μ ... μ μ μ : H equal are means population all Not : H A F = Reject H 0 if F > F Main Factor Test
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Chap 12-64 Fisher’s Least Significant Difference Test To test which population means are significantly different e.g.: μ 1 = μ 2 μ 3 Done after rejection of equal means in randomized block ANOVA design Allows pair-wise comparisons Compare absolute mean differences with critical range x = 1 2 3
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Chap 12-65 Fisher’s Least Significant Difference (LSD) Test where: t /2 = Upper- tailed value from Student’s t -distribution for /2 and (k - 1)(b - 1) degrees of freedom MSW = Mean square within from ANOVA table b = number of blocks k = number of levels of the main factor b 2 MSW t LSD /2
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Chap 12-66 ... etc x x x x x x 3 2 3 1 2 1 Fisher’s Least Significant Difference (LSD) Test (continued) b 2 MSW t LSD /2 If the absolute mean difference is greater than LSD then there is a significant difference between that pair of means at the chosen level of significance. Compare: ? LSD x x Is j i
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Chap 12-67 Example of Blocking
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Chap 12-68 Example of Blocking
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Chap 12-69 Example of Blocking
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Chap 12-70 Example of Blocking
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Chap 12-71 Example of Blocking
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Chap 12-72 Example of Blocking
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Chap 12-73 Example of Blocking
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Chap 12-74 Fisher’s Least Significant Difference (LSD) Test where: t /2 = Upper- tailed value from Student’s t -distribution for /2 and (k - 1)(b - 1) degrees of freedom MSW = Mean square within from ANOVA table b = number of blocks k = number of levels of the main factor b 2 MSW t LSD /2
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Chap 12-75 Fisher’s Least Significant Difference (LSD) Test
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Chap 12-76 Fisher’s Least Significant Difference (LSD) Test
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Chap 12-77 Fisher’s Least Significant Difference (LSD) Test
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Chap 12-78 Fisher’s Least Significant Difference (LSD) Test
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