Traditional course condensed 2. Traditional course regular length 3. Online course condensed 4. Online course regular length Chap 11-53 DCOV A
Excel Analysis Of Collapsed Data Chap 11-54 DCOV A Group is a significant effect. p-value of 0.0003 < 0.05 1. Traditional regular > Traditional condensed 2. Online condensed > Traditional condensed 3. Traditional regular > Online regular 4. Online condensed > Online regular If the course is take online should use the condensed version and if the course is taken by traditional method should use the regular.
The Randomized Block Design Is Often Useful The randomized block design is an on-line topic Chap 11-55
Chap 11-56 Chapter Summary In this chapter we discussed The 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 The Levene test for homogeneity of variance The two-way analysis of variance Examined effects of multiple factors Examined interaction between factors
RBD - 1 Online Topic The Randomized Block Design Statistics for Managers Using Microsoft Excel 7 th Edition
RBD - 2 Learning Objective To learn the basic structure and use of a randomized block design
RBD - 3 The Randomized Block Design Like One-Way ANOVA, we test for equal population means (for different factor levels, for example)... ...but we want to control for possible variation from a second factor (with two or more levels) Levels of the secondary factor are called blocks DCOV A
RBD - 4 Partitioning the Variation Total variation can now be split into three parts: SST = Total variation SSA = Among-Group variation SSBL = Among-Block variation SSE = Random variation SST = SSA + SSBL + SSE DCOV A
RBD - 5 Sum of Squares for Blocks Where: c = number of groups r = number of blocks X i. = mean of all values in block i X = grand mean (mean of all data values) r 1 i 2 i. ) X X ( c SSBL SST = SSA + SSBL + SSE DCOV A
RBD - 6 Partitioning the Variation Total variation can now be split into three parts: SST and SSA are computed as they were in One-Way ANOVA SST = SSA + SSBL + SSE SSE = SST – (SSA + SSBL) DCOV A
RBD - 7 Mean Squares 1 c SSA groups among square Mean MSA 1 r SSBL blocking square Mean MSBL ) 1 )( 1 ( c r SSE MSE error square Mean DCOV A
RBD - 8 Randomized Block ANOVA Table Source of Variation df SS MS Among Groups SSA MSA Error (r–1)(c-1) SSE MSE Total rc - 1 SST c - 1 MSA MSE F c = number of populations rc = total number of observations r = number of blocks df = degrees of freedom Among Blocks SSBL r - 1 MSBL MSBL MSE DCOV A
RBD - 9 Main Factor test: df 1 = c – 1 df 2 = (r – 1)(c – 1) MSA MSE c . .3 .2 .1 0 μ μ μ μ : H equal are means population all Not : H 1 F STAT = Reject H 0 if F STAT > F α Testing For Factor Effect DCOV A
RBD - 10 Test For Block Effect Blocking test: df 1 = r – 1 df 2 = (r – 1)(c – 1) MSBL MSE r. 3. 2. 1. 0
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