ANOVA Analysis for Stat 875 HW05: Comparing Solutions and Block Effects - Prof. Xiaomi Hu, Assignments of Statistics

Download ANOVA Analysis for Stat 875 HW05: Comparing Solutions and Block Effects - Prof. Xiaomi Hu and more Assignments Statistics in PDF only on Docsity! Stat 875 HW05 p157 4.4 (a) Fill out ANOVA table. Do the calculation using calculator and check the results with SAS. Source DF SS MS F p Model 5 1810.4167 362.0833 41.91 0.0001 Error 6 51.8333 8.6389 C.Total 11 1862.2500 Factor A 2 707.5 351.75 40.72 0.0003 Block 3 1106.9167 368.9722 42.71 0.0002 (b) Is the blocking technique effective? Draw your conclusion based on a test at level 0.05. Let βj , j = 1, 2, 3, 4, be the block effects. • H0 : βj = 0 for all j versus H1 : βj 6= 0 for some j • Test Statistic F = MSBMSE • p-value P (F (3, 12n− 6) > Fob) • Fob = 42.71, p-value: P (F (3, 6) > 42.71) = 0.0002 • Reject H0 We conclude that the blocking technique is effective. (c) Are three solutions equally effective? Draw your conclusion from a test at level 0.05. Let τi, i = 1, 2, 3, be the treatment effects. • H0 : τi = 0 for all i versus H1 : τi 6= 0 for some i • Test Statistic F = MSAMSE • p-value P (F (2, 12n− 6) > Fob) • Fob = 40.71, p-value: P (F (2, 6) > 40.72) = 0.0003 • Reject H0 We conclude that three solutions are not equally effective. 1