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\author{Cerulean}
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  /Title (analysis-of-covariance-ancova.pdf)
  /Creator (Cheatography)
  /Author (Cerulean)
  /Subject (Analysis of Covariance - ANCOVA Cheat Sheet)
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Analysis of Covariance - ANCOVA Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Cerulean} via \textcolor{DarkBackground}{\uline{cheatography.com/35405/cs/11131/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Cerulean \\
  \uline{cheatography.com/cerulean} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 10th March, 2017.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{When to use ANCOVA in place of ANOVA}}  \tn
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To reduce within-group error variance & Elimination of confounds \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Reducing SS{\emph{residual}} through covariates & Variables known to influence DV (and not IV) \tn 
% Row Count 5 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{ASSUMPTIONS}}  \tn
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\mymulticolumn{2}{x{8.4cm}}{Additivity and Linearity} \tn 
% Row Count 1 (+ 1)
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 & Is the relationship linear? \tn 
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\mymulticolumn{2}{x{8.4cm}}{Normally Distributed Sampling Distribution of Means} \tn 
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S-W and K-S tests & Q-Q plots and histograms \tn 
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\mymulticolumn{2}{x{8.4cm}}{Homogeneity of Variance} \tn 
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\mymulticolumn{2}{x{8.4cm}}{Levene's Test} \tn 
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\mymulticolumn{2}{x{8.4cm}}{Independence of scores} \tn 
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 & Are the groups independent? \tn 
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\mymulticolumn{2}{x{8.4cm}}{No Univariate Outliers} \tn 
% Row Count 13 (+ 1)
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Tested with Z-score conversion & Above or below +/- 3.29 (Field, 2013) \tn 
% Row Count 15 (+ 2)
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\mymulticolumn{2}{x{8.4cm}}{Independence of Covariate (CV) and Treatment Effect} \tn 
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Tested using ANOVA or t-test for Covariate and Treatment & CV should not share variance with treatment IV \tn 
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\mymulticolumn{2}{x{8.4cm}}{Homogeneity of Regression Slopes} \tn 
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Tested using custom model, including interaction for CV and DV & Does the relationship CV and outcome apply to all treatment groups \tn 
% Row Count 25 (+ 4)
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\par\addvspace{1.3em}

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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Effect Size}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{Partial Eta Squared} \tn 
% Row Count 1 (+ 1)
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\mymulticolumn{1}{x{8.4cm}}{= SS\textasciicircum{}effect\textasciicircum{}/ (SS\textasciicircum{}effect\textasciicircum{} + SS\textasciicircum{}residual\textasciicircum{})} \tn 
% Row Count 2 (+ 1)
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\mymulticolumn{1}{x{8.4cm}}{= variance explained/ (variance explained + error variance)} \tn 
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\mymulticolumn{1}{x{8.4cm}}{Eta Squared uses SS\textasciicircum{}total\textasciicircum{} in place of (SS\textasciicircum{}effect\textasciicircum{} + SS\textasciicircum{}residual\textasciicircum{}). Partial eta squared removes the variance explained by the covariate from SS\textasciicircum{}total\textasciicircum{}}  \tn 
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Contrasts}}  \tn
% Row 0
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SPSS: {\emph{Contrasts}} button in {\emph{Univariate}} dialog box & Several \seqsplit{possibilities} \tn 
% Row Count 2 (+ 2)
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{{\emph{Post hoc}} Tests}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{{\emph{Options}} button. {\emph{Display Means}} for IV.} \tn 
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\mymulticolumn{1}{x{8.4cm}}{Tick {\emph{Compare main effects}}} \tn 
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\mymulticolumn{1}{x{8.4cm}}{Confidence interval adjustment} \tn 
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\mymulticolumn{1}{x{8.4cm}}{Bonferroni (recommended); Sidak is conservative; LSD liberal (not recommended).} \tn 
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\mymulticolumn{1}{x{8.4cm}}{Contrasts are effectively {\emph{t}}-tests} \tn 
% Row Count 1 (+ 1)
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\mymulticolumn{1}{x{8.4cm}}{Can calculate {\emph{r}}} \tn 
% Row Count 2 (+ 1)
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\mymulticolumn{1}{x{8.4cm}}{{\emph{r}}\textasciicircum{}contrast\textasciicircum{} = Square root {[}{\emph{t}}\textasciicircum{}2\textasciicircum{}/ ({\emph{t}}\textasciicircum{}2\textasciicircum{} +{\emph{df}}){]}} \tn 
% Row Count 4 (+ 2)
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\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}