Question

Exercise 13-45 Algo

A researcher conducts a two-way ANOVA test with interaction and provides the following ANOVA table.

a. Find the missing values in the ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "MS" to 4 decimal places and "F" to 3 decimal places.)

	ANOVA Source of Variation SS df MS F p-value Sample 776.84 2 MSB = F Factor B = 0.010 Columns 12,425.44 1 MSA = F Factor A = 4.57E-09 Interaction 56.25 2 MSAB = F Interaction = 0.621 Within 681.72 12 MSE = Total 13,940.25 17

Answer 1

Answer

we know that the formula for MS is given as MS = SS/df

so, MSB = SSB/df

df is degree of freedom corresponding to SSB only.

MSB = SSB/df

we have SSB = 776.84 and df = 2

So, MSB = (776.84/2)= 388.4200

MSA = SSA/df

we have SSA = 12425.44 and df = 1

So, MSA = (12425.44/1)= 12425.4400

MSAB = SSAB/df

we have SSAB = 56.25 and df = 2

So, MSAB = (56.25/2)= 28.1250

MSE = SSE/df

we have SSE = 681.72 and df = 12

So, MSE = (681.72/12)= 56.8100

We know that the formula for F factor B statistics is given as MSB/MSE

setting the given values, we get

F factor B = 388.4200/56.8100 = 6.837

We know that the formula for F factor A statistics is given as MSA/MSE

setting the given values, we get

F factor A = 12425.44/56.8100 = 218.719

We know that the formula for F factor AB statistics is given as MSAB/MSE

setting the given values, we get

F factor AB = 28.1250/56.8100 = 0.495