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\author{Jeremy Morris}
\title{Chapter 4 Example 2}

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Chapter 4 Example 2

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The Model for this example is defined by the following equation.

\noindent $y_{ijklmnop} = \mu$ + $P_{i}$  + $L_{j}$  + $PL_{ij}$  + $S_{k(ij)}$  + $D_{l(ijk)}$  + $O_{m}$  + $PO_{im}$  + $LO_{jm}$  + $PLO_{ijm}$  + $SO_{km(ij)}$  + $DO_{lm(ijk)}$  + $A_{n}$  + $PA_{in}$  + $LA_{jn}$  + $PLA_{ijn}$  + $SA_{kn(ij)}$  + $DA_{ln(ijk)}$  + $OA_{mn}$  + $POA_{imn}$  + $LOA_{jmn}$  + $PLOA_{ijmn}$  + $SOA_{kmn(ij)}$  + $DOA_{lmn(ijk)}$  + $C_{o}$  + $PC_{io}$  + $LC_{jo}$  + $PLC_{ijo}$  + $SC_{ko(ij)}$  + $DC_{lo(ijk)}$  + $OC_{mo}$  + $POC_{imo}$  + $LOC_{jmo}$  + $PLOC_{ijmo}$  + $SOC_{kmo(ij)}$  + $DOC_{lmo(ijk)}$  + $AC_{no}$  + $PAC_{ino}$  + $LAC_{jno}$  + $PLAC_{ijno}$  + $SAC_{kno(ij)}$  + $DAC_{lno(ijk)}$  + $OAC_{mno}$  + $POAC_{imno}$  + $LOAC_{jmno}$  + $PLOAC_{ijmno}$  + $SOAC_{kmno(ij)}$  + $DOAC_{lmno(ijk)}$  + $\varepsilon_{p(i j k l m n o)}$

\begin{center}
\begin{longtable}{l|l| p{11.5cm} |l}
Source & df & EMS & $F_{calc}$ \\ \hline \endhead
	$P_{i}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{POC}^{2} + 8\sigma_{DC}^{2} + 16\sigma_{SC}^{2} + 32\sigma_{PLC}^{2} + 64\sigma_{PC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{SO}^{2} + 32\sigma_{PLO}^{2} + 64\sigma_{PO}^{2} + 16\sigma_{D}^{2} + 32\sigma_{S}^{2} + 64\sigma_{PL}^{2} + 128\sigma_{P}^{2}$&$- -$\\
	$L_{j}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{LOC}^{2} + 8\sigma_{DC}^{2} + 16\sigma_{SC}^{2} + 32\sigma_{PLC}^{2} + 64\sigma_{LC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{SO}^{2} + 32\sigma_{PLO}^{2} + 64\sigma_{LO}^{2} + 16\sigma_{D}^{2} + 32\sigma_{S}^{2} + 64\sigma_{PL}^{2} + 128\sigma_{L}^{2}$&$- -$\\
	$PL_{ij}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 8\sigma_{DC}^{2} + 16\sigma_{SC}^{2} + 32\sigma_{PLC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{SO}^{2} + 32\sigma_{PLO}^{2} + 16\sigma_{D}^{2} + 32\sigma_{S}^{2} + 64\sigma_{PL}^{2}$&$- -$\\
	$S_{k(ij)}$ &4&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 8\sigma_{DC}^{2} + 16\sigma_{SC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{SO}^{2} + 16\sigma_{D}^{2} + 32\sigma_{S}^{2}$&$- -$\\
	$D_{l(ijk)}$ &8&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{DC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{D}^{2}$&$- -$\\
	$O_{m}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{LOC}^{2} + 32\sigma_{POC}^{2} + 64\sigma_{OC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{SO}^{2} + 32\sigma_{PLO}^{2} + 64\sigma_{LO}^{2} + 64\sigma_{PO}^{2} + 128\sigma_{O}^{2}$&$- -$\\
	$PO_{im}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{POC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{SO}^{2} + 32\sigma_{PLO}^{2} + 64\sigma_{PO}^{2}$&$- -$\\
	$LO_{jm}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{LOC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{SO}^{2} + 32\sigma_{PLO}^{2} + 64\sigma_{LO}^{2}$&$- -$\\
	$PLO_{ijm}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{SO}^{2} + 32\sigma_{PLO}^{2}$&$- -$\\
	$SO_{km(ij)}$ &4&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 8\sigma_{DO}^{2} + 16\sigma_{SO}^{2}$&$- -$\\
	$DO_{lm(ijk)}$ &8&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{DO}^{2}$&$MS(DO)/MS(DOC)$\\
	$A_{n}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{LOAC}^{2} + 16\sigma_{POAC}^{2} + 32\sigma_{OAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2} + 16\sigma_{PLAC}^{2} + 32\sigma_{LAC}^{2} + 32\sigma_{PAC}^{2} + 64\sigma_{AC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2} + 16\sigma_{PLOA}^{2} + 32\sigma_{LOA}^{2} + 32\sigma_{POA}^{2} + 64\sigma_{OA}^{2} + 8\sigma_{DA}^{2} + 16\sigma_{SA}^{2} + 32\sigma_{PLA}^{2} + 64\sigma_{LA}^{2} + 64\sigma_{PA}^{2} + 128\sigma_{A}^{2}$&$- -$\\
	$PA_{in}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{POAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2} + 16\sigma_{PLAC}^{2} + 32\sigma_{PAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2} + 16\sigma_{PLOA}^{2} + 32\sigma_{POA}^{2} + 8\sigma_{DA}^{2} + 16\sigma_{SA}^{2} + 32\sigma_{PLA}^{2} + 64\sigma_{PA}^{2}$&$- -$\\
	$LA_{jn}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{LOAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2} + 16\sigma_{PLAC}^{2} + 32\sigma_{LAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2} + 16\sigma_{PLOA}^{2} + 32\sigma_{LOA}^{2} + 8\sigma_{DA}^{2} + 16\sigma_{SA}^{2} + 32\sigma_{PLA}^{2} + 64\sigma_{LA}^{2}$&$- -$\\
	$PLA_{ijn}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2} + 16\sigma_{PLAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2} + 16\sigma_{PLOA}^{2} + 8\sigma_{DA}^{2} + 16\sigma_{SA}^{2} + 32\sigma_{PLA}^{2}$&$- -$\\
	$SA_{kn(ij)}$ &4&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2} + 8\sigma_{DA}^{2} + 16\sigma_{SA}^{2}$&$- -$\\
	$DA_{ln(ijk)}$ &8&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{DAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{DA}^{2}$&$- -$\\
	$OA_{mn}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{LOAC}^{2} + 16\sigma_{POAC}^{2} + 32\sigma_{OAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2} + 16\sigma_{PLOA}^{2} + 32\sigma_{LOA}^{2} + 32\sigma_{POA}^{2} + 64\sigma_{OA}^{2}$&$- -$\\
	$POA_{imn}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{POAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2} + 16\sigma_{PLOA}^{2} + 32\sigma_{POA}^{2}$&$- -$\\
	$LOA_{jmn}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{LOAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2} + 16\sigma_{PLOA}^{2} + 32\sigma_{LOA}^{2}$&$- -$\\
	$PLOA_{ijmn}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2} + 16\sigma_{PLOA}^{2}$&$- -$\\
	$SOA_{kmn(ij)}$ &4&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 4\sigma_{DOA}^{2} + 8\sigma_{SOA}^{2}$&$- -$\\
	$DOA_{lmn(ijk)}$ &8&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{DOA}^{2}$&$MS(DOA)/MS(DOAC)$\\
	$C_{o}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{LOC}^{2} + 32\sigma_{POC}^{2} + 64\sigma_{OC}^{2} + 8\sigma_{DC}^{2} + 16\sigma_{SC}^{2} + 32\sigma_{PLC}^{2} + 64\sigma_{LC}^{2} + 64\sigma_{PC}^{2} + 128\sigma_{C}^{2}$&$- -$\\
	$PC_{io}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{POC}^{2} + 8\sigma_{DC}^{2} + 16\sigma_{SC}^{2} + 32\sigma_{PLC}^{2} + 64\sigma_{PC}^{2}$&$- -$\\
	$LC_{jo}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{LOC}^{2} + 8\sigma_{DC}^{2} + 16\sigma_{SC}^{2} + 32\sigma_{PLC}^{2} + 64\sigma_{LC}^{2}$&$- -$\\
	$PLC_{ijo}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 8\sigma_{DC}^{2} + 16\sigma_{SC}^{2} + 32\sigma_{PLC}^{2}$&$- -$\\
	$SC_{ko(ij)}$ &4&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 8\sigma_{DC}^{2} + 16\sigma_{SC}^{2}$&$- -$\\
	$DC_{lo(ijk)}$ &8&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{DC}^{2}$&$MS(DC)/MS(DOC)$\\
	$OC_{mo}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{LOC}^{2} + 32\sigma_{POC}^{2} + 64\sigma_{OC}^{2}$&$- -$\\
	$POC_{imo}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{POC}^{2}$&$MS(POC)/MS(PLOC)$\\
	$LOC_{jmo}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2} + 32\sigma_{LOC}^{2}$&$MS(LOC)/MS(PLOC)$\\
	$PLOC_{ijmo}$ &1&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2} + 16\sigma_{PLOC}^{2}$&$MS(PLOC)/MS(SOC)$\\
	$SOC_{kmo(ij)}$ &4&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2} + 8\sigma_{SOC}^{2}$&$MS(SOC)/MS(DOC)$\\
	$DOC_{lmo(ijk)}$ &8&$\sigma_{\varepsilon}^{2} + 4\sigma_{DOC}^{2}$&$MS(DOC)/MS(\varepsilon)$\\
	$AC_{no}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{LOAC}^{2} + 16\sigma_{POAC}^{2} + 32\sigma_{OAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2} + 16\sigma_{PLAC}^{2} + 32\sigma_{LAC}^{2} + 32\sigma_{PAC}^{2} + 64\sigma_{AC}^{2}$&$- -$\\
	$PAC_{ino}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{POAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2} + 16\sigma_{PLAC}^{2} + 32\sigma_{PAC}^{2}$&$- -$\\
	$LAC_{jno}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{LOAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2} + 16\sigma_{PLAC}^{2} + 32\sigma_{LAC}^{2}$&$- -$\\
	$PLAC_{ijno}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2} + 16\sigma_{PLAC}^{2}$&$- -$\\
	$SAC_{kno(ij)}$ &4&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 4\sigma_{DAC}^{2} + 8\sigma_{SAC}^{2}$&$- -$\\
	$DAC_{lno(ijk)}$ &8&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{DAC}^{2}$&$MS(DAC)/MS(DOAC)$\\
	$OAC_{mno}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{LOAC}^{2} + 16\sigma_{POAC}^{2} + 32\sigma_{OAC}^{2}$&$- -$\\
	$POAC_{imno}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{POAC}^{2}$&$MS(POAC)/MS(PLOAC)$\\
	$LOAC_{jmno}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2} + 16\sigma_{LOAC}^{2}$&$MS(LOAC)/MS(PLOAC)$\\
	$PLOAC_{ijmno}$ &1&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2} + 8\sigma_{PLOAC}^{2}$&$MS(PLOAC)/MS(SOAC)$\\
	$SOAC_{kmno(ij)}$ &4&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2} + 4\sigma_{SOAC}^{2}$&$MS(SOAC)/MS(DOAC)$\\
	$DOAC_{lmno(ijk)}$ &8&$\sigma_{\varepsilon}^{2} + 2\sigma_{DOAC}^{2}$&$MS(DOAC)/MS(\varepsilon)$\\
	$\varepsilon_{p(i j k l m n o)}$&28&$\sigma_{\varepsilon}^{2}$&$- -$\\
\end{longtable}
\end{center}

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