ANOVA. Effect due type, company. Independence. Show steps thinking, and hand cal

Question

ANOVA. Effect due type, company. Independence.

Show steps thinking, and hand calculations.

It is later learned that there were actually 3 companies and 4 different paper types. The table below represents the paper porosity from three replicates of a 4 times 3 factorial design. Run a complete ANOVA analysis and answer the following: a) Is there an effect due to the paper type? b) Is there an effect due to the companies? c) Are the companies and paper types independent? C)ijk = 381.44 C_j = 310.58 C_i = 323.26 C_ij = 359.64 C = 295.84

Explanation / Answer

a) as p value(5.7*10-5) for paper type is less then 0.05 ; hence there is effect due to paper type

b)p value(0.005487) for comany type is less then 0.05there is effect due to company type

c) as pvalue of interaction is less then 0.05 ; they are not independent

SUMMARY type 1 type 2 type 3 type 4 Total Company 1 Count 3 3 3 3 12 Sum 4.8 4.8 6.6 8 24.2 Average 1.6 1.6 2.2 2.666667 2.016667 Variance 0.01 0.01 0.19 0.093333 0.274242 Company 2 Count 3 3 3 3 12 Sum 5.5 7.1 9.4 8.2 30.2 Average 1.833333 2.366667 3.133333 2.733333 2.516667 Variance 0.093333 0.003333 2.143333 0.643333 0.774242 Company 3 Count 3 3 3 3 12 Sum 8.7 15.8 6.3 18 48.8 Average 2.9 5.266667 2.1 6 4.066667 Variance 0.16 3.843333 1.27 2.44 4.240606 Total Count 9 9 9 9 Sum 19 27.7 22.3 34.2 Average 2.111111 3.077778 2.477778 3.8 Variance 0.426111 3.769444 1.144444 3.5175 ANOVA Source of Variation SS df MS F P-value F crit Sample 27.42 2 13.71 15.09358 5.7E-05 3.402826 Columns 14.74 3 4.913333 5.409174 0.005487 3.008787 Interaction 21.64 6 3.606667 3.970642 0.006719 2.508189 Within 21.8 24 0.908333 Total 85.6 35

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