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\author{igotanA}
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  /Title (statistics.pdf)
  /Creator (Cheatography)
  /Author (igotanA)
  /Subject (Statistics Cheat Sheet)
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Statistics Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{igotanA} via \textcolor{DarkBackground}{\uline{cheatography.com/168892/cs/35345/}}}
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\noindent
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}igotanA \\
  \uline{cheatography.com/igotana} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 10th November, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Basics of Statistics\textasciitilde{}{\emph{Definitions}}}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Statistics \textasciitilde{} {\emph{Oxford Dictionary}}}} & {\emph{"The science of collecting and analysing numerical data in large quantities, especially for the purpose of {\bf{inferring}}... from those in a representative {\bf{sample}}."}} \tn 
% Row Count 9 (+ 9)
% Row 1
\SetRowColor{white}
{\bf{Statistics \textasciitilde{} {\emph{simple}}}} & The practice of {\emph{collecting data from a {\bf{small(er)}} number of individuals to draw conclusions about a {\bf{large(er)}} number of individuals}}. \tn 
% Row Count 16 (+ 7)
% Row 2
\SetRowColor{LightBackground}
{\bf{Descriptive Statistics}} & This involves organizing, and summarizing data through {\emph{numerical, tabular, and graphical means.}} {\bf{Estimation Procedures}} are {\emph{formulas}} used to obtain {\emph{estimates}} (i.e. {\bf{descriptive statistics}}) of {\bf{population}} traits from the {\bf{sample}} data. \tn 
% Row Count 28 (+ 12)
% Row 3
\SetRowColor{white}
{\bf{Inference Procedures}} & The {\emph{formulas used to quantify the magnitude of {\bf{error}} in generalizing}} from a 'part' ({\bf{sample}}) to the 'whole' ({\bf{population}}) e.g., *t-test, *Z-test, *chi-square test, *Wald test, etc. The {\bf{Inference "Statistics"}} obtained may reflect the {\bf{reliability}} of the result or the possibility of {\bf{error}}. \tn 
% Row Count 44 (+ 16)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.76 cm} x{4.24 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Basics of Statistics\textasciitilde{}{\emph{Definitions}} (cont)}}  \tn
% Row 4
\SetRowColor{LightBackground}
{\bf{Inference}} & A conclusion reached based on evidence and reasoning. {\emph{In statistics, we learn things from {\bf{samples}} and infer to the {\bf{population}}}}. \tn 
% Row Count 7 (+ 7)
% Row 5
\SetRowColor{white}
{\bf{Population}} & The {\emph{entire set of individuals}} to which the study are to be extrapolated {\emph{(generalized)}}. \tn 
% Row Count 12 (+ 5)
% Row 6
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{\bf{Parameter}} & This is a {\emph{numerical summary}} of a {\bf{population}}. \tn 
% Row Count 15 (+ 3)
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{\bf{Sample}} & A subset of the population \tn 
% Row Count 17 (+ 2)
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{\bf{Sampling Plan}} & The {\emph{methodology}} for choosing the {\bf{sample}}. \tn 
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{\bf{Statistic}} & This is a {\emph{numerical summary}} of a {\bf{sample}}. \tn 
% Row Count 23 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{p{3.04 cm} x{4.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Types of estimates}}  \tn
% Row 0
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Point & Interval \tn 
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Types of Study Design}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{• Randomized Controlled Trials • Cohort Studies • Case-Control Studies • Cross-Sectional Studies} \tn 
% Row Count 3 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Framework of a Typical Study}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/igotana_1668026841_Framework of a Study.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Exploratory Data Analysis}}  \tn
% Row 0
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 & {\bf{The first step in dealing with data is to organize your thinking about the data. }} \tn 
% Row Count 5 (+ 5)
% Row 1
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{\bf{Exploratory data analysis}} & This is the process of {\emph{using statistical tools and ideas to examine data in order to describe their main features}}. \tn 
% Row Count 11 (+ 6)
% Row 2
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{\bf{Steps of an exploratory data analysis}} & • Examine each variable first. • Then study the relationships among the variables. • Begin with a graph or graphs. • Add numerical summaries of specific aspects of the data \tn 
% Row Count 20 (+ 9)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Variables}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{The characteristics of the individuals within the population} \tn 
% Row Count 2 (+ 2)
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Variables Tree}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/igotana_1668026228_Variable Tree Sheet.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{All about Variables}}  \tn
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{\bf{Categorical Data or Variables}} & Data can only take on {\emph{discrete values}}. It allows for classification of individuals based on some attribute or characteristic. \tn 
% Row Count 7 (+ 7)
% Row 1
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{\bf{Nominal Data or Variables}} & apply in name only – {\emph{no inherent ordering}} (e.g. {\emph{blood type, hair color}}). \tn 
% Row Count 11 (+ 4)
% Row 2
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{\bf{Ordinal Data or Variables}} & Data can be {\emph{ranked in order}} but only take on discrete values (e.g. {\emph{satisfaction score, Glasgow Coma Score}}). \tn 
% Row Count 17 (+ 6)
% Row 3
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{\bf{Continuous/Measured Data or Variables}} & These values can be {\emph{added or subtracted and provide meaningful results}}. \tn 
% Row Count 21 (+ 4)
% Row 4
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{\bf{Interval Data or Variables}} & The difference between each number/value is equal (e.g. temperature in Celsius, IQ score). No absolute 0 {\emph{(Zero has a meaningful value)}} \tn 
% Row Count 28 (+ 7)
% Row 5
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{\bf{Ratio Data or Variables}} & These values are on {\emph{an interval scale with an absolute zero with no meaningful value}} (e.g. weight, temperature in Kelvin) \tn 
% Row Count 35 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
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\begin{tabularx}{8.4cm}{x{3.2 cm} x{4.8 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Graphing Variables}}  \tn
% Row 0
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{\emph{Categorical}}-{\bf{Pie Chart}} & This shows the distribution of a categorical variable as a "pie" whose slices are sized by the counts or percent for the categories. \tn 
% Row Count 6 (+ 6)
% Row 1
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{\emph{Categorical}}-{\bf{Bar Chart}} & This represents each category as a bar whose heights show the category counts or percent. \tn 
% Row Count 10 (+ 4)
% Row 2
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{\emph{Continuous}}-Histograms & Count how many  (or the percentage of individuals) that fall into each interval) \tn 
% Row Count 14 (+ 4)
% Row 3
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{\emph{Continuous}}-Boxplot & • The Lower Inner Fence (LIF) • LIF = Q1 – 1.5{\emph{IQR • The Upper Inner Fence (UIF) • UIF= Q3 + 1.5}}IQR • The Lower Adjacent Value • The actual data value just inside the LIF • The Upper Adjacent Value • The actual data value just inside the UIF \tn 
% Row Count 25 (+ 11)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
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\begin{tabularx}{8.4cm}{x{2.64 cm} x{5.36 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{\seqsplit{Tables-Continuous/categorical} variables}}  \tn
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{\bf{Advantages}} :) & • Gives the reader a compact and structured synthesis of information • Shows a lot of detail in a small amount of space \tn 
% Row Count 5 (+ 5)
% Row 1
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{\bf{Disadvantages}} :( & • Because the reader only sees numbers, the table may not be readily understood without comparing it with other tables \tn 
% Row Count 10 (+ 5)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Skew}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/igotana_1668030625_egoldstein710_1572117377_Screen Shot 2019-10-26 at 3.16.01 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Skewness}}  \tn
% Row 0
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Right or positively skewed distributions will yield skewness values \textgreater{} 0 & Left or negatively skewed distributions will yield skewness values \textless{} 0 \tn 
% Row Count 4 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Kurtosis}}  \tn
% Row 0
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This is often made in comparison to a Bell Shaped/Normal distribution & Kurtosis is a measure of how "peaked" or "flat" a distribution is \tn 
% Row Count 4 (+ 4)
% Row 1
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– If a distribution has an excessive amount of observations close to the mean (meaning fewer observations in the tails) it will have a more peaked appearance (Platykurtic Kurtosis \textless{} 3) & – If a distribution has an excessive amount of observations which are further away from the mean (ex. in the tails) it will have a flattened appearance as if it really has no tails at all (Leptokurtic Kurtosis \textgreater{} 3) \tn 
% Row Count 15 (+ 11)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{So, about sampling...}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Probability sampling}} & Random selection-equal chance for selection for every member of the {\bf{population}} \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
{\bf{Non-probability sampling}} & Convenience or voluntary self-selection increases the likelyhood of selection of one or more participants \tn 
% Row Count 10 (+ 6)
% Row 2
\SetRowColor{LightBackground}
{\bf{Parametric tests}} & In these tests, reasonable and evidence-supported assumptions must be made about the distribution. They can be used to make strong statistical inferences when data are collected using probability sampling. \tn 
% Row Count 20 (+ 10)
% Row 3
\SetRowColor{white}
{\bf{Non-parametric tests}} & Very few assumptions are made, if any, about the population distribution. They are more appropriate for non-probability samples, but they result in weaker inferences about the population. \tn 
% Row Count 29 (+ 9)
% Row 4
\SetRowColor{LightBackground}
{\bf{Significance level (alpha)}} & The risk of rejecting a true null hypothesis that you are willing to take, usually set at 5\%. \tn 
% Row Count 34 (+ 5)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{So, about sampling... (cont)}}  \tn
% Row 5
\SetRowColor{LightBackground}
{\bf{Statistical power}} & The probability of your study detecting an effect of a certain size if there is one, usually 80\% or higher. \tn 
% Row Count 5 (+ 5)
% Row 6
\SetRowColor{white}
{\bf{Expected effect size}} & A standardized indication of how large the expected result of your study will be, usually based on other similar studies. \tn 
% Row Count 11 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{So, about sampling...}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Probability sampling}} & Random selection-equal chance for selection for every member of the {\bf{population}} \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
{\bf{Non-probability sampling}} & Convenience or voluntary self-selection increases the likelyhood of selection of one or more participants \tn 
% Row Count 10 (+ 6)
% Row 2
\SetRowColor{LightBackground}
{\bf{Parametric tests}} & In these tests, reasonable and evidence-supported assumptions must be made about the distribution. They can be used to make strong statistical inferences when data are collected using probability sampling. \tn 
% Row Count 20 (+ 10)
% Row 3
\SetRowColor{white}
{\bf{Non-parametric tests}} & Very few assumptions are made, if any, about the population distribution. They are more appropriate for non-probability samples, but they result in weaker inferences about the population. \tn 
% Row Count 29 (+ 9)
% Row 4
\SetRowColor{LightBackground}
{\bf{Significance level (alpha)}} & The risk of rejecting a true null hypothesis that you are willing to take, usually set at 5\%. \tn 
% Row Count 34 (+ 5)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{So, about sampling... (cont)}}  \tn
% Row 5
\SetRowColor{LightBackground}
{\bf{Statistical power}} & The probability of your study detecting an effect of a certain size if there is one, usually 80\% or higher. \tn 
% Row Count 5 (+ 5)
% Row 6
\SetRowColor{white}
{\bf{Expected effect size}} & A standardized indication of how large the expected result of your study will be, usually based on other similar studies. \tn 
% Row Count 11 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
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\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{So, about sampling...}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Probability sampling}} & Random selection-equal chance for selection for every member of the {\bf{population}} \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
{\bf{Non-probability sampling}} & Convenience or voluntary self-selection increases the likelyhood of selection of one or more participants \tn 
% Row Count 10 (+ 6)
% Row 2
\SetRowColor{LightBackground}
{\bf{Parametric tests}} & In these tests, reasonable and evidence-supported assumptions must be made about the distribution. They can be used to make strong statistical inferences when data are collected using probability sampling. \tn 
% Row Count 20 (+ 10)
% Row 3
\SetRowColor{white}
{\bf{Non-parametric tests}} & Very few assumptions are made, if any, about the population distribution. They are more appropriate for non-probability samples, but they result in weaker inferences about the population. \tn 
% Row Count 29 (+ 9)
% Row 4
\SetRowColor{LightBackground}
{\bf{Significance level (alpha)}} & The risk of rejecting a true null hypothesis that you are willing to take, usually set at 5\%. \tn 
% Row Count 34 (+ 5)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{So, about sampling... (cont)}}  \tn
% Row 5
\SetRowColor{LightBackground}
{\bf{Statistical power}} & The probability of your study detecting an effect of a certain size if there is one, usually 80\% or higher. \tn 
% Row Count 5 (+ 5)
% Row 6
\SetRowColor{white}
{\bf{Expected effect size}} & A standardized indication of how large the expected result of your study will be, usually based on other similar studies. \tn 
% Row Count 11 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{So, about sampling...}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Probability sampling}} & Random selection-equal chance for selection for every member of the {\bf{population}} \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
{\bf{Non-probability sampling}} & Convenience or voluntary self-selection increases the likelyhood of selection of one or more participants \tn 
% Row Count 10 (+ 6)
% Row 2
\SetRowColor{LightBackground}
{\bf{Parametric tests}} & In these tests, reasonable and evidence-supported assumptions must be made about the distribution. They can be used to make strong statistical inferences when data are collected using probability sampling. \tn 
% Row Count 20 (+ 10)
% Row 3
\SetRowColor{white}
{\bf{Non-parametric tests}} & Very few assumptions are made, if any, about the population distribution. They are more appropriate for non-probability samples, but they result in weaker inferences about the population. \tn 
% Row Count 29 (+ 9)
% Row 4
\SetRowColor{LightBackground}
{\bf{Significance level (alpha)}} & The risk of rejecting a true null hypothesis that you are willing to take, usually set at 5\%. \tn 
% Row Count 34 (+ 5)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{So, about sampling... (cont)}}  \tn
% Row 5
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{\bf{Statistical power}} & The probability of your study detecting an effect of a certain size if there is one, usually 80\% or higher. \tn 
% Row Count 5 (+ 5)
% Row 6
\SetRowColor{white}
{\bf{Expected effect size}} & A standardized indication of how large the expected result of your study will be, usually based on other similar studies. \tn 
% Row Count 11 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}