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RAK

RAK. Rancangan Acak Kelompok (RAK) Diterapkan pada percobaan yang dilakukan pada lingkungan tidak homogen (heterogen). Struktur Data RAK.

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RAK

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  1. RAK • Rancangan Acak Kelompok (RAK) Diterapkan pada percobaan yang dilakukan pada lingkungan tidak homogen (heterogen)

  2. Struktur Data RAK

  3. ER untukmemperolehsensitivitas RAL yang samadengan RAK makaulangan yang digunakandalammenerapkan RAL harus ER kali dariulangan yang digunakandalam RAK.

  4. FAKTORIAL - RAL Dr. Ir. Rahmat Kurnia, M.Si

  5. Two-Way ANOVA • Examines the effect of • Two factors of interest on the dependent variable • e.g., Percent carbonation and line speed on soft drink bottling process • Interaction between the different levels of these two factors • e.g., Does the effect of one particular carbonation level depend on which level the line speed is set?

  6. Two-Way ANOVA (continued) • Assumptions • Independent random samples are drawn • Populations have equal variances • Populations are normally distributed

  7. Two-Way ANOVA Sources of Variation Two Factors of interest: A and B a = number of levels of factor A b = number of levels of factor B r = number of replications for each cell n = total number of observations in all cells (n = abr) Xijk = value of the kth observation of level i of factor A and level j of factor B

  8. Two-Way ANOVA Sources of Variation (continued) SST = SSA + SSB + SSAB + SSE Degrees of Freedom: SSA Factor A Variation a – 1 SST Total Variation SSB Factor B Variation b – 1 SSAB Variation due to interaction between A and B (a – 1)(b – 1) n - 1 SSE Random variation (Error) ab(r – 1)

  9. Two Factor ANOVA Equations Total Variation: Factor A Variation: Factor B Variation:

  10. Two Factor ANOVA Equations (continued) Interaction Variation: Sum of Squares Error:

  11. Two Factor ANOVA Equations (continued) where: r = number of levels of factor A c = number of levels of factor B n’ = number of replications in each cell

  12. Mean Square Calculations

  13. Two-Way ANOVA:The F Test Statistic F Test for Factor A Effect H0: μ1.. = μ2.. = μ3..=• • • H1: Not all μi.. are equal Reject H0 if F > FU F Test for Factor B Effect H0: μ.1. = μ.2. = μ.3.=• • • H1: Not all μ.j. are equal Reject H0 if F > FU F Test for Interaction Effect H0: the interaction of A and B is equal to zero H1: interaction of A and B is not zero Reject H0 if F > FU

  14. Two-Way ANOVASummary Table

  15. Features of Two-Way ANOVA FTest • Degrees of freedom always add up • n-1 = rc(n’-1) + (r-1) + (c-1) + (r-1)(c-1) • Total = error + factor A + factor B + interaction • The denominator of the FTest is always the same but the numerator is different • The sums of squares always add up • SST = SSE + SSA + SSB + SSAB • Total = error + factor A + factor B + interaction

  16. Examples:Interaction vs. No Interaction • Interaction is present: • No interaction: Factor B Level 1 Factor B Level 1 Factor B Level 3 Mean Response Mean Response Factor B Level 2 Factor B Level 2 Factor B Level 3 Factor A Levels Factor A Levels

  17. Chapter Summary • Described one-way analysis of variance • The logic of ANOVA • ANOVA assumptions • F test for difference in c means • The Tukey-Kramer procedure for multiple comparisons • Described two-way analysis of variance • Examined effects of multiplefactors • Examined interaction between factors

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