This is an Incomplete Block Design.

Thirty consumers are asked to rate the softness of clothes washed by ten different detergents, but each consumer rates only four different detergents. The design and responses are given below: Trts Softness 1 ABCD 37 23 37 41 2 ABEF 35 32 39 37 3 ACGH 39 45 39 41 4 ADIJ 44 42 46 44 5 AEGI 44 44 45 50 6 AFHJ 55 45 53 49 7 BCFI 47 50 48 52 8 BDGJ 37 42 40 37 9 BEHJ 32 34 39 29 10 BGHI 36 41 39 43 11 CEIJ 45 44 40 36 12 CFGJ 42 38 39 39 13 CDEH 47 48 46 47 14 DEFG 43 47 48 41 15 DFHI 39 32 32 31 Trts Softness 16 ABCD 52 41 45 48 17 ABEF 46 42 45 42 18 ACGH 44 43 41 36 19 ADIJ 32 42 36 29 20 AEGI 43 42 44 44 21 AFHJ 46 41 43 45 22 BCF I 43 51 40 42 23 BDGJ 38 37 36 34 24 BEH J40 49 43 44 25 BGHI 23 20 27 29 26 CEIJ 46 49 48 43 27 CFGJ 48 43 48 41 28 CDEH 35 35 31 26 29 DEFG 45 47 47 42 30 DFHI 43 39 38 39 Obtain the Source and df columns for the ANOVA table that would test for treatment effects using the Type III SS for treatments. Thirty consumers are asked to rate the softness of clothes washed by ten different detergents, but each consumer rates only four different detergents. The design and responses are given below: Trts Softness 1 ABCD 37 23 37 41 2 ABEF 35 32 39 37 3 ACGH 39 45 39 41 4 ADIJ 44 42 46 44 5 AEGI 44 44 45 50 6 AFHJ 55 45 53 49 7 BCFI 47 50 48 52 8 BDGJ 37 42 40 37 9 BEHJ 32 34 39 29 10 BGHI 36 41 39 43 11 CEIJ 45 44 40 36 12 CFGJ 42 38 39 39 13 CDEH 47 48 46 47 14 DEFG 43 47 48 41 15 DFHI 39 32 32 31 Trts Softness 16 ABCD 52 41 45 48 17 ABEF 46 42 45 42 18 ACGH 44 43 41 36 19 ADIJ 32 42 36 29 20 AEGI 43 42 44 44 21 AFHJ 46 41 43 45 22 BCF I 43 51 40 42 23 BDGJ 38 37 36 34 24 BEH J40 49 43 44 25 BGHI 23 20 27 29 26 CEIJ 46 49 48 43 27 CFGJ 48 43 48 41 28 CDEH 35 35 31 26 29 DEFG 45 47 47 42 30 DFHI 43 39 38 39 Obtain the Source and df columns for the ANOVA table that would test for treatment effects using the Type III SS for treatments