Given the two-factor factorial experiment and the ANOVA summary table to the rig

ID: 3174876 • Letter: G

Question

Given the two-factor factorial experiment and the ANOVA summary table to the right, fill in all the missing results. Source Degrees of Freedom (df) Sum of Squares Mean Square left parenthesis Variance right parenthesis F A r minus 1equals1 SSAequals ? MSAequals 14 Upper F Subscript STAT equals ? B cminus 1equals ? SSBequals 12 MSBequals ? Upper F Subscript STAT equals2 AB (rminus 1)(cminus1)equals3 SSABequals ? MSABequals 16 Upper F Subscript STAT equals ? Error rc(n prime minus1)equals24 SSEequals ? MSEequals ? Total nminus 1equals ? SSTequals ? Fill in the missing results of the table. Source Degrees of Freedom Sum of Squares Mean Square left parenthesis Variance right parenthesis F A rminus 1equals1 SSAequals nothing MSAequals 14 Upper F Subscript STAT equalsnothing B cminus 1equalsnothing SSBequals 12 MSBequals nothing Upper F Subscript STAT equals2 AB (rminus 1)(cminus1)equals3 SSABequals nothing MSABequals 16 Upper F Subscript STAT equalsnothing Error rc(n prime minus1)equals24 SSEequals nothing MSEequals nothing Total nminus 1equalsnothing SSTequals nothing

Explanation / Answer

Solution

In ANOVA Table given below, the given data are entered in the normal font and obtained figures for filling the ? cells are given in bold font. Explanation for these obtained figures are given at the end of the table.

NOTE: an additional row named ‘Between cells’ is given for ease in explanation and presentation

Source

Degrees of

Freedom (DF)

Sum of Squares (SS)

Mean Sum of Squares (MS)

F- Statistic (F)

Row (A)

(r – 1) = 1

? 14

? 0.778

Column (B)

(c – 1) = ? 3

? 36

Interaction (AB)

(r – 1) (c – 1) = 3

? 48

? 0.889

Between Cells

Error

? 432

? 18

Total

(n – 1) 31

? 506

Explanations:

Given for A, DF = 1 and MS = 14, SS = MS x DF = 14.

Given (r – 1)(c – 1) = 3 and (r – 1) = 1, r = 2 and (c – 1) = 3 and hence c = 4. Also, MSB = SS x DF = 12 x 3 = 36

For Interaction, given DF = 3 and MS = 16, SS = MS x DF = 48.

Now, for Between Cells, DF and SS are sum of respective DFand SS of

A, B and AB. So, DF = 7 and SS = 74. Also, Between Cells + Error = Total for DF and SS.

Thus, DF for total = 24 + 7 = 31

Again, F for B = MSB/MSE = 2 (given) and so with MSB = 36 (already obtained), MSE = 36/2 = 18 and hence SSE = 18 x 24 = 432 and consequently, SS for Total = 432 + 74 = 506

F for A = MSA/MSE = 14/18 = 0.778 and

F for AB = MSAB/MSE = 16/18 = 0.889

DONE