## Related questions with answers

An experiment to determine the effect of mold temperature on tensile strength involved three different alloys and five different mold temperatures. Four specimens of each alloy were cast at each mold temperature. With mold temperature as the row factor and alloy as the column factor, the sums of squares were: SSA = 69,738, SSB = 8958, SSAB = 7275, and SST = 201,816. a. Construct an ANOVA table. You may give ranges for the P-values. b. Is the additive model plausible? Explain. c. Is it plausible that the main effects of mold temperature are all equal to 0? Provide the value of the test statistic and the P-value. d. Is it plausible that the main effects of alloy are all equal to 0? Provide the value of the test statistic and the P-value.

Solution

VerifiedGiven:

$\begin{align*} SSA&=69738 \\ SSB&=8958 \\ SSAB&=7275 \\ SST&=201816 \\ I&=5 \\ J&=3 \\ K&=4 \end{align*}$

(a) $SSE$ is the total sum of squares $SST$ decreased by all other sum of squares.

$\begin{align*} SSE&=SST-SSA-SSB-SSAB \\ &=201816-69738-8958-7275 \\ &=115845 \end{align*}$

The degrees of freedom for the effect of a variable is the number of categories of the variable decreased by 1.

$df_A=I-1=5-1=4$

The degrees of freedom for the effect of a variable is the number of categories of the variable decreased by 1.

$df_B=J-1=3-1=2$

The degrees of freedom for the interactions is the product of the degrees of freedom for the effect of each variable.

$df_{AB}=df_A\cdot df_B=4\cdot 2=8$

The degrees of freedom for error is the product of the number of categories for each variable, and the number of replicates per treatment decreased by 1.

$df_E=IJ(K-1)=5\cdot 3\cdot (4-1)=15\cdot 3=45$

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