Question

Suppose that the researchers drop the temperature from the study and add a new factor, size of bacteria', as a blocking factor. The size may be Small, Medium, or Large. They now have nine colonies of bacteria, randomly assigned to each exposure- size combination. The resulting ANOVA table is reported in Table 5. SS df MS Source of Variation Blocks Treatments Error Total SSBL=13.10 T - 1= SSTR = 26.05 T-1=2 SSBL.TR = 12.89 (no - 1)(-1)= SSTO = 52.04 nyt-1= MSBL MSTR = 13.02 MSBL.TR le 5: ANOVA table for the doubling time wrt to the size of bacteria as a blocking factor. . Which experimental design is this? Identify the number of blocks no, and complete Table 5. (3p) Test the equality of the effects of the different exposure levels onto the doubling time at a significance level of 5%. Comment. (4p)

Answer 1

It is a randomized block design (RB D) - → There are 3 blocks, rather block size. (Small, medium, large) The ANOVA table is A table is court) * Source of Variation ss df Crisisse Blocks 13:10 Botz 2 6.55 Treatments 26.05 r122 13.02 Emor 3.22 x . 12.89 52.04 (16-1)(N-1) 24 nor-128 Total Based on the given design we consider our model is Yüz M + Li + ß; & Ey, where yij is the doubling time corresponding to ith exposure lend and ith block size , Liz additional effect due to ith exposure level, B; 2 additional effect due to ith block size, tj a random error. iz 1, 2, 3, j21, 2, 3

Asstemptione molt wit s tora di 20, Š Bj 20., Ej "CN10,8") Sad Here on 23 2 andra3 A We are to test for equality of effects of the exposure levels into doubling time. 1. Ho: There are are no differential effect of exposure levels on doubling time. Ho 4 222 223 her Not Ho against To test the above heypothesis the appropiate test statistic is given by - Mato Ho MSTR MSBL.TR v segt. exp. Fri; not New Testrule, we reject to ag Hi ist Feap y Food r. 1; ngt at 5 % level of significance Here 8.3. np.3, and Feup 2 13:02 2 4.04 3.22 and R0.05; 2,2 2 19.00

Thus we get Feup < Fo.os; 2,2 The Honce we conclude based on the diven data there is no differential effect of exposure lee levels at 5% level of significance,