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Lecture

Latin and Graeco-Latin Squares.pdf

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Department
Statistics
Course
STAT368
Professor
Douglas Wiens
Semester
Winter

Description
88 12. Latin and Graeco-Latin Squares For the Latin square design the LSEs are ˆ = ¯ ¯ ˆ = ¯ ¯ ˆ = ¯ ¯ as usual, with (as usual) X 2 X 2 X ˆ2 = ˆ = ˆ = =1 =1 =1 = The d.f. of these are 1 1 1 and 2 1 3( 1) = ( 2)( 1). Theoretical ANOVA table: Source SS df MS F0 Treat. 1 = 1 0= Rows 1 = 1 Col. 1 = ( 1)· 1 Error ( 2) = 2 Total 1 89 The value of 0 is of course compared to 1 : ( 1)( 2) p-vaµue for the hypot¶esis of equal treatments e ects is 1 . ( 1)( 2) 0 > y operators coupons tips data data y operators coupons tips 1 9.3 1 1 A 2 9.4 1 2 B 3 9.2 1 3 C 4 9.7 1 4 D 5 9.3 2 1 B 6 9.4 2 2 A 7 9.6 2 3 D 8 9.4 2 4 C 9 9.5 3 1 C etc. 90 > g anova(g) Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) tips 3 0.38500 0.12833 38.5 0.0002585 *** operators 3 0.82500 0.27500 82.5 2.875e-05 *** coupons 3 0.06000 0.02000 6.0 0.0307958 * Residuals 6 0.02000 0.00333 --- From the ANOVA table the means are signicantly di erent treatment.means treatment.means [1] 9.600 9.625 9.700 9.575 # These are the averages for tips A, B, C, D > qtukey(.95,4,6)*sqrt(.0033/4) [1] 0.1406154 91 • Tukey’s procedure says that and are sig- nicantly di erent ( = 05) if s |¯ ¯ | qtukey ( 95 4 6) = 141 so again we conclude that tip 4 gives signicantly di erent readings. Tips 2 and 3 seem signi- cantly di erent as well. Now the coupons don’t seem to
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