6

Hi dear TeX community!

I hope you can help me out a bit with some matrices I have drawn (with the community's help of course) using the TIKZ package.

I think that I need to post almost the whole code so that you get an appropriate picture of the problem, so sorry for that.

\documentclass[12pt]{article} 

\usepackage{tikz}
\usetikzlibrary{positioning,matrix}

\newcommand{\mb}[1]{{\bullet #1}} % mean with bullet; dbl brackets to maintain subscript
\newcommand{\xq}{\bar{x}}
\begin{document}

    \begin{tikzpicture}

\matrix [matrix of math nodes,left delimiter=(, right delimiter=)] (mat1) {
  x_{11} & x_{22} & \ldots & x_{1j} & \ldots & x_{1k} \\ 

  x_{22} & x_{22} & \ldots & x_{2j} & \ldots & x_{2k} \\ 

  \vdots & \vdots &        & \vdots &        & \vdots \\ 

  x_{i1} & x_{i2} & \ldots & x_{ij} & \ldots & x_{ik} \\ 

  \vdots & \vdots &        & \vdots &        & \vdots \\

  x_{n1} & x_{n2} & \ldots & x_{nj} & \ldots & x_{nk} \\

};

\matrix[matrix of math nodes, left delimiter=(, right delimiter= ), below=7em of 

mat1, xshift=-8em] (mat2) {

  \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\

  \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\

  \vdots     & \vdots     &        & \vdots     &        & \vdots     \\

  \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\

  \vdots     & \vdots     &        & \vdots     &        & \vdots     \\

  \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
};

\node[anchor=west] at (mat2.south east){$\overline{x}_{\bullet \bullet} $};


\matrix[matrix of math nodes, right=4em of mat2, left delimiter=(, right delimiter=)] (mat3) {
  r_{11} & r_{12} & \ldots & r_{1j} & \ldots & r_{1k} \\

  r_{21} & r_{22} & \ldots & r_{2j} & \ldots & r_{2k} \\

  \vdots & \vdots &        & \vdots &        & \vdots \\

  r_{i1} & r_{i2} & \ldots & r_{ij} & \ldots & r_{ik} \\

  \vdots & \vdots &        & \vdots &        & \vdots \\

  r_{n1} & r_{n2} & \ldots & r_{nj} & \ldots & r_{nk} \\

};

\foreach \X/\Y in {2/{\mathrm{IN}},3/{\mathrm{ZW}}}

{\draw[-latex] (mat1) -- (mat\X);

 \draw[-latex] (mat\X.south) -- ++ (0,-4em) node[below] (G\X) 

               {$\widehat{\sigma}^2_{\Y}$};}

 \path (mat2) -- (mat3) node[midway]{$+$} (G2) -- (G3) node[midway,below=3.5em] 
(F) 

{$ \displaystyle 

F = \frac{\hat{\sigma}^2_{\mathrm{ZW}}}

         {\hat{\sigma}^2_{\mathrm{IN}}}

  = \frac{\frac{1}{k-1} \sum_{j=1}^{k} \sum_{i=1}^{n} (\xq_\mb{j} - \xq_{\bullet

\bullet})^2}


         {\frac{1}{N-k} \sum_{j=1}^{k} \sum_{i=1}^{n} (  x_{ij}   - \xq_{\bullet 
j}      )^2} 

$};

\foreach \X/\Y in {2,3}

{\draw[-latex] (G\X) -- (F);}

\end{tikzpicture}

\end{document} 

So the questions that I have are

1.) Is it possible to insert this equation centered in between the uppermost two arrows?

and

2.) to draw a red "double-arrow" going from $\bar{x}_{\bullet 1}$ to $\bar{x}_{\bullet \bullet}$ and one from $r_{11}$ to \bar{x}_{\bullet 1}?

Thank you guys so so much!

This is what it looks like at the moment: enter image description here

This is the output I kind of imagined (roughly): Desired output (roughly)

  • 3
    Welcome to TeX.SE! For the first request, which formula are you referring to? Also how should the red line be placed? I hope if you could you paint or another program to show us the desired output (make it rough, it doesn't need to be fancy, but meaningful) :) – M. Al Jumaily Jun 15 at 19:45
  • If you like an answer and it was helpful, please consider upvoting (by clicking on the arrows next to the score) and marking it as accepted answer (by clicking on the checkmark ✓). @Ñako surely deserves a tick after all of the work that they have put in! – Andrew Jun 26 at 0:44
4

Further attempts with full information

My fourth attempt:

Customizing arrows style.

There are many ways to costumize the arrow style with tikz, see the documentation, Chapter 16 (p.186). In this case, by editing the double arrow/.style in the preamble and/or the options of the last two draw commands of the code you can display "more elegant" arrows:

  • custom-based double-headed arrow:

    enter image description here

    Code:

    % From https://tex.stackexchange.com/a/72793/89320, customize for double-headed arrows
    \tikzset{
    double arrow/.style args={#1 colored by #2 and #3}{
        stealth-stealth,line width=#1,#2, % first arrow
        postaction={draw,stealth-stealth,#3,line width=(#1)/3,
            shorten <=2*(#1)/3,shorten >=2*(#1)/3}, % second arrow
      }
    }
    

      \draw[double arrow=2pt colored by red and white!80!, opacity=0.75,] (mat2-1-1.north) to [in=80,out=30]  (xpp.north);
      \draw[double arrow=2pt colored by red and white!80!, opacity=0.75,] ([yshift=2pt]mat3-1-1.north) to [in=20,out=160] (mat2-1-1.north);
    
  • double and <->:

    enter image description here

    Code:

    \draw[red, double,<->] (mat2-1-1.north) to [in=80,out=30]  (xpp.north);
    \draw[red, double,<->] ([yshift=2pt]mat3-1-1.north) to [in=20,out=160] (mat2-1-1.north);
    
    • double and Latex-Latex:

      enter image description here

    Code:

    \draw[red, {Latex[length=2mm, width=2mm]}-{Latex[length=2mm, width=2mm]} ,double, double distance=.5pt] (mat2-1-1.north) to [in=80,out=30]  (xpp.north);
    \draw[red, {Latex[length=2mm, width=2mm]}-{Latex[length=2mm, width=2mm]} ,double, double distance=.5pt] ([yshift=2pt]mat3-1-1.north) to [in=20,out=160] (mat2-1-1.north);
    

My third attempt:

The desired output is yet known:

Here is my approach:

enter image description here

Code:

\documentclass[12pt]{article} 

\usepackage{tikz}
\usetikzlibrary{positioning,matrix}
\usetikzlibrary{arrows, arrows.meta, calc,fadings}

\newcommand{\mb}[1]{{\bullet #1}} % mean with bullet; dbl brackets to maintain subscript
\newcommand{\xq}{\bar{x}}

% From https://tex.stackexchange.com/a/72793/89320
\tikzset{
    double arrow/.style args={#1 colored by #2 and #3}{
        -stealth,line width=#1,#2, % first arrow
        postaction={draw,-stealth,#3,line width=(#1)/3,
            shorten <=(#1)/3,shorten >=2*(#1)/3}, % second arrow
    }
}
%---------------------------------------------------

\begin{document}

    \begin{tikzpicture}

    \matrix [anchor=center,matrix of math nodes,left delimiter=(, right delimiter=)] (mat1) {
      x_{11} & x_{22} & \ldots & x_{1j} & \ldots & x_{1k} \\ 
      x_{22} & x_{22} & \ldots & x_{2j} & \ldots & x_{2k} \\ 
      \vdots & \vdots &        & \vdots &        & \vdots \\ 
      x_{i1} & x_{i2} & \ldots & x_{ij} & \ldots & x_{ik} \\ 
      \vdots & \vdots &        & \vdots &        & \vdots \\
      x_{n1} & x_{n2} & \ldots & x_{nj} & \ldots & x_{nk} \\
    };


    \matrix[anchor=center,matrix of math nodes, left delimiter=(, right delimiter= ), below=7em of mat1, xshift=-8em] (mat2) {
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
      \vdots     & \vdots     &        & \vdots     &        & \vdots     \\
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
      \vdots     & \vdots     &        & \vdots     &        & \vdots     \\
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
    };

    \node[anchor=west] (xpp) at (mat2.south east){$\overline{x}_{\bullet \bullet} $};


    \matrix[anchor=center,matrix of math nodes, right=4em of mat2, left delimiter=(, right delimiter=)] (mat3) {
      r_{11} & r_{12} & \ldots & r_{1j} & \ldots & r_{1k} \\
      r_{21} & r_{22} & \ldots & r_{2j} & \ldots & r_{2k} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      r_{i1} & r_{i2} & \ldots & r_{ij} & \ldots & r_{ik} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      r_{n1} & r_{n2} & \ldots & r_{nj} & \ldots & r_{nk} \\
    };

    \coordinate (aux) at ($ (mat1) !.5! (mat2) $);
    \node[anchor=center,](xij) at (mat1 |- aux) {$ \displaystyle 
        x_{ij}=\xq_\mb{j}+r_{ij}$};
    \node[anchor=center, below =-2pt of xij] (rij) {$ \displaystyle
        r_{ij}=\xq_\mb{j}-x_{ij}$};
    %
    \foreach \X/\Y in {2/{\mathrm{IN}},3/{\mathrm{ZW}}}
    {\draw[-latex] (mat1) -- (mat\X); 
    \draw[-latex] (mat\X.south) -- ++ (0,-4em) node[below] (G\X) {$\widehat{\sigma}^2_{\Y}$};}
    \path (mat2) -- (mat3) node[midway]{$+$} (G2) -- (G3) node[midway,below=3.5em] (F) 
    {$ \displaystyle 
        F = \frac{\hat{\sigma}^2_{\mathrm{ZW}}}
        {\hat{\sigma}^2_{\mathrm{IN}}}
        = \frac{\frac{1}{k-1} \sum_{j=1}^{k} \sum_{i=1}^{n} (\xq_\mb{j} - \xq_{\bullet\bullet})^2}
        {\frac{1}{N-k} \sum_{j=1}^{k} \sum_{i=1}^{n} (x_{ij}-\xq_{\bullet j})^2}
    $};
    \foreach \X/\Y in {2,3} {\draw[-latex] (G\X) -- (F);}

    \draw[double arrow=10pt colored by blue!50!white and red!50!white,opacity=0.75] (mat2-1-1.north) to[in=80,out=30]  (xpp.north);
    \draw[double arrow=10pt colored by blue!50!white and red!50!white,opacity=0.75] ([yshift=2pt]mat3-1-1.north) to[in=20,out=160] (mat2-1-1.north);

    \end{tikzpicture}

\end{document} 

First attempts with partial information

I have tried to figure out what it could be your desired output. For this purpose:

To your questions:

  1. I have placed the equation F between the matrices and commented %\displaystyle so that it passes between the uppermost two arrows:

    \coordinate (aux) at ($ (mat1) !.5! (mat2) $);
    \node[anchor=center,](F) at (mat1 |- aux) {$ %\displaystyle 
        F = \frac{\hat{\sigma}^2_{\mathrm{ZW}}}
        {\hat{\sigma}^2_{\mathrm{IN}}}
        = \frac{\frac{1}{k-1} \sum_{j=1}^{k} \sum_{i=1}^{n} (\xq_\mb{j} - \tikznode{xpp2}{$\xq_{\bullet\bullet}$})^2}
        {\frac{1}{N-k} \sum_{j=1}^{k} \sum_{i=1}^{n} (x_{ij}-\xq_{\bullet j})^2}
        $};
    
  2. There are two $\xq_{\bullet \bullet}$ (I mean $\bar{x}_{\bullet \bullet}$). Which one do you mean? The matrix (red arrow) or the equation (orange arrow) one?

Could you please specify or better include an image of your desired output?

My second attempt:

1st improvements:

  • Direct referencing the matrix cells with matname-rownumber-columnnumber instead of \tikznode, which is the approach/solution of Andrew (with your permission of course)
  • Added round corners and the arrows go around the matrices for better readability

Output:

enter image description here

Code:

\documentclass[12pt]{article} 

\usepackage{tikz}
\usetikzlibrary{positioning,matrix}
\usetikzlibrary{arrows, arrows.meta, calc, tikzmark}

\newcommand{\mb}[1]{{\bullet #1}} % mean with bullet; dbl brackets to maintain subscript
\newcommand{\xq}{\bar{x}}

    %Tikznode -> https://tex.stackexchange.com/a/361392/89320
\newcommand\tikznode[3][]%
{\tikz[remember picture,baseline=(#2.base)]
    \node[minimum size=0pt,inner sep=0pt,#1](#2){#3};%
}
%-----

\begin{document}

    \begin{tikzpicture}[remember picture]

    \matrix [anchor=center,matrix of math nodes,left delimiter=(, right delimiter=)] (mat1) {
      x_{11} & x_{22} & \ldots & x_{1j} & \ldots & x_{1k} \\ 
      x_{22} & x_{22} & \ldots & x_{2j} & \ldots & x_{2k} \\ 
      \vdots & \vdots &        & \vdots &        & \vdots \\ 
      x_{i1} & x_{i2} & \ldots & x_{ij} & \ldots & x_{ik} \\ 
      \vdots & \vdots &        & \vdots &        & \vdots \\
      x_{n1} & x_{n2} & \ldots & x_{nj} & \ldots & x_{nk} \\
    };


    \matrix[anchor=center,matrix of math nodes, left delimiter=(, right delimiter= ), below=7em of mat1, xshift=-8em] (mat2) {
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
      \vdots     & \vdots     &        & \vdots     &        & \vdots     \\
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
      \vdots     & \vdots     &        & \vdots     &        & \vdots     \\
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
    };

    \node[anchor=west] (xpp) at (mat2.south east){$\overline{x}_{\bullet \bullet} $};


    \matrix[anchor=center,matrix of math nodes, right=4em of mat2, left delimiter=(, right delimiter=)] (mat3) {
      r_{11} & r_{12} & \ldots & r_{1j} & \ldots & r_{1k} \\
      r_{21} & r_{22} & \ldots & r_{2j} & \ldots & r_{2k} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      r_{i1} & r_{i2} & \ldots & r_{ij} & \ldots & r_{ik} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      r_{n1} & r_{n2} & \ldots & r_{nj} & \ldots & r_{nk} \\
    };

    \coordinate (aux) at ($ (mat1) !.5! (mat2) $);
    \node[anchor=center,](F) at (mat1 |- aux) {$ %\displaystyle 
        F = \frac{\hat{\sigma}^2_{\mathrm{ZW}}}
        {\hat{\sigma}^2_{\mathrm{IN}}}
        = \frac{\frac{1}{k-1} \sum_{j=1}^{k} \sum_{i=1}^{n} (\xq_\mb{j} - \tikznode{xpp2}{$\xq_{\bullet\bullet}$})^2}
        {\frac{1}{N-k} \sum_{j=1}^{k} \sum_{i=1}^{n} (x_{ij}-\xq_{\bullet j})^2}
        $};
     %                      
    \foreach \X/\Y in {2/{\mathrm{IN}},3/{\mathrm{ZW}}}
    {\draw[-latex] (mat1.south) -- ++(0,-1.5em) -|  ([yshift=0.1em]mat\X.north);
     \draw[-latex] (mat\X.south) -- ++ (0,-4em) node[below] (G\X) {$\widehat{\sigma}^2_{\Y}$};}
     \path (mat2) -- (mat3) node[midway]{$+$} (G2) -- (G3) node[midway,below=3.5em] {}; %(F)

    \draw[latex'-latex',red,rounded corners=2mm] (mat2-1-1.north) -- +(0,0.4) -|(xpp.north);
    \draw[latex'-latex',red,rounded corners=2mm] (mat2-1-1.north) -- +(0,0.4) -|(mat3-1-1.north);
    \draw[latex'-latex',orange,rounded corners=2mm] (mat2-1-1.north)-- +(0,2.25) -| (xpp2.north);
    \end{tikzpicture}

\end{document} 

My first attempt:

Output: enter image description here Code:

\documentclass[12pt]{article} 

\usepackage{tikz}
\usetikzlibrary{positioning,matrix}
\usetikzlibrary{arrows, arrows.meta, calc}

\newcommand{\mb}[1]{{\bullet #1}} % mean with bullet; dbl brackets to maintain subscript
\newcommand{\xq}{\bar{x}}

%Tikznode -> https://tex.stackexchange.com/a/361392/89320
\newcommand\tikznode[3][]%
{\tikz[remember picture,baseline=(#2.base)]
    \node[minimum size=0pt,inner sep=0pt,#1](#2){#3};%
}
%-----

\begin{document}

    \begin{tikzpicture}

    \matrix [anchor=center,matrix of math nodes,left delimiter=(, right delimiter=)] (mat1) {
      x_{11} & x_{22} & \ldots & x_{1j} & \ldots & x_{1k} \\ 
      x_{22} & x_{22} & \ldots & x_{2j} & \ldots & x_{2k} \\ 
      \vdots & \vdots &        & \vdots &        & \vdots \\ 
      x_{i1} & x_{i2} & \ldots & x_{ij} & \ldots & x_{ik} \\ 
      \vdots & \vdots &        & \vdots &        & \vdots \\
      x_{n1} & x_{n2} & \ldots & x_{nj} & \ldots & x_{nk} \\
    };


    \matrix[anchor=center,matrix of math nodes, left delimiter=(, right delimiter= ), below=7em of mat1, xshift=-8em] (mat2) {
      \tikznode{xp1}{$\xq_\mb{1}$} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
      \vdots     & \vdots     &        & \vdots     &        & \vdots     \\
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
      \vdots     & \vdots     &        & \vdots     &        & \vdots     \\
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
    };

    \node[anchor=west] at (mat2.south east){\tikznode{xpp}{$\overline{x}_{\bullet \bullet} $}};


    \matrix[anchor=center,matrix of math nodes, right=4em of mat2, left delimiter=(, right delimiter=)] (mat3) {
      \tikznode{r11}{$r_{11}$} & r_{12} & \ldots & r_{1j} & \ldots & r_{1k} \\
      r_{21} & r_{22} & \ldots & r_{2j} & \ldots & r_{2k} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      r_{i1} & r_{i2} & \ldots & r_{ij} & \ldots & r_{ik} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      r_{n1} & r_{n2} & \ldots & r_{nj} & \ldots & r_{nk} \\
    };

    \coordinate (aux) at ($ (mat1) !.5! (mat2) $);
    \node[anchor=center,](F) at (mat1 |- aux) {$ %\displaystyle 
    F = \frac{\hat{\sigma}^2_{\mathrm{ZW}}}
    {\hat{\sigma}^2_{\mathrm{IN}}}
    = \frac{\frac{1}{k-1} \sum_{j=1}^{k} \sum_{i=1}^{n} (\xq_\mb{j} - \tikznode{xpp2}{$\xq_{\bullet\bullet})^2$}}
    {\frac{1}{N-k} \sum_{j=1}^{k} \sum_{i=1}^{n} (x_{ij}-\xq_{\bullet j})^2}
    $};


    \foreach \X/\Y in {2/{\mathrm{IN}},3/{\mathrm{ZW}}}
    {\draw[-latex] (mat1.south) -- ++(0,-1.5em) -|  ([yshift=0.4em]mat\X.north);
     \draw[-latex] (mat\X.south) -- ++ (0,-4em) node[below] (G\X) {$\widehat{\sigma}^2_{\Y}$};}
     \path (mat2) -- (mat3) node[midway]{$+$} (G2) -- (G3) node[midway,below=3.5em] {}; %(F)

    \end{tikzpicture}
    \begin{tikzpicture}[remember picture,overlay]
    \draw[latex'-latex',red] (xp1)--(xpp);
    \draw[latex'-latex',red] (xp1.north) |- +(0,0.4) -|(r11.north);
    \draw[latex'-latex',orange] (xp1)--(xpp2);
    \end{tikzpicture}

\end{document} 
  • 1
    There is no need to use a \tikznode in a TikZ matrix (and in some cases could lead to errors), you can simply reference the cell with matname-rownumber-columnnumber, for example mat1-1-1, or adding |[name=nodename]| before the cell content, for example |[name=r11]|r_11. – CarLaTeX Jun 16 at 4:51
  • @CarLaTeX, I was editing my answer and after posting it I saw Andre´s one with this easy referencing. One learn always new things :) – Ñako Jun 16 at 8:01
  • 1
    Yes, there's always something to learn on TeX.SE! :) – CarLaTeX Jun 16 at 8:07
  • @CarLaTeX, what about referencing the equation´s term $\bar{x}_{\bullet \bullet}$ with the matrix´s term? With tikzmark I get Package tikz Error: Cannot parse this coordinate. ...\sum_{i=1}^{n} (x_{ij}-\xq_{\bullet j})^2}, but it works with tikznode. Then using tikznode and the matrix cell referencing, i.e., adding \draw[latex'-latex',orange] (mat2-1-1)--(xpp2); to the same tikzpicture or just to a new tikzpicture with [remember picture,overlay] it does not give the desired output – Ñako Jun 16 at 8:49
  • 1
    @Ñako Sorry for not having replied early but I had no time before. Btw, +1! – CarLaTeX Jun 16 at 19:55
2

I am not sure what you mean by "inserting the equation" in (1) but the arrows you can draw using the node coordinates of the matrices. For example, the \bar{x}_{\bullet 1} entry is the node (mat2-1-1) and the r_{11} entry is (mat3-1-1). Below I have named the \bar{x}_{\bullet \bullet} entry BB so you can draw a double red line from r_{11} to \bar{x}_{\bullet \bullet} using

  \draw[red, double,->](mat2-1-1)--(BB);

I am not sure if this is really what you want however as the arrow will go through the other matrix entries. Instead, if you use

\draw[red, double,->](mat3-1-1) to[out=150,in=30] (mat2-1-1);

the the arrow will go around the matrices. The code below gives red and blue arrows to give you different options:

enter image description here

If you can explain in more detail what you want for (1) I will try and answer that too. Here is the code:

\documentclass[12pt]{article}

\usepackage{tikz}
\usetikzlibrary{positioning,matrix}

\newcommand{\mb}[1]{{\bullet #1}} % mean with bullet; dbl brackets to maintain subscript
\newcommand{\xq}{\bar{x}}
\begin{document}

  \begin{tikzpicture}

    \matrix[matrix of math nodes,left delimiter=(, right delimiter=)] (mat1) {
      x_{11} & x_{22} & \ldots & x_{1j} & \ldots & x_{1k} \\
      x_{22} & x_{22} & \ldots & x_{2j} & \ldots & x_{2k} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      x_{i1} & x_{i2} & \ldots & x_{ij} & \ldots & x_{ik} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      x_{n1} & x_{n2} & \ldots & x_{nj} & \ldots & x_{nk} \\
    };

    \matrix[matrix of math nodes, left delimiter=(, right delimiter= ),
             below=7em of mat1, xshift=-8em] (mat2) {
      \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
    \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
    \vdots     & \vdots     &        & \vdots     &        & \vdots     \\
    \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
    \vdots     & \vdots     &        & \vdots     &        & \vdots     \\
    \xq_\mb{1} & \xq_\mb{2} & \ldots & \xq_\mb{2} & \ldots & \xq_\mb{j} \\
  };

  \node[anchor=west] (BB) at (mat2.south east){$\overline{x}_{\bullet \bullet} $};
  \matrix[matrix of math nodes, right=4em of mat2, left delimiter=(, right delimiter=)] (mat3) {
    r_{11} & r_{12} & \ldots & r_{1j} & \ldots & r_{1k} \\
      r_{21} & r_{22} & \ldots & r_{2j} & \ldots & r_{2k} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      r_{i1} & r_{i2} & \ldots & r_{ij} & \ldots & r_{ik} \\
      \vdots & \vdots &        & \vdots &        & \vdots \\
      r_{n1} & r_{n2} & \ldots & r_{nj} & \ldots & r_{nk} \\
    };

  \foreach \X/\Y in {2/{\mathrm{IN}},3/{\mathrm{ZW}}} {
   \draw[-latex] (mat1) -- (mat\X);
   \draw[-latex] (mat\X.south) -- ++ (0,-4em) node[below] (G\X)
                 {$\widehat{\sigma}^2_{\Y}$};
                 }
   \path (mat2) -- (mat3) node[midway]{$+$} (G2) -- (G3) node[midway,below=3.5em] (F)
  {$ \displaystyle
  F = \frac{\hat{\sigma}^2_{\mathrm{ZW}}}
           {\hat{\sigma}^2_{\mathrm{IN}}}
    = \frac{\frac{1}{k-1} \sum_{j=1}^{k} \sum_{i=1}^{n} (\xq_\mb{j} - \xq_{\bullet\bullet})^2}
           {\frac{1}{N-k} \sum_{j=1}^{k} \sum_{i=1}^{n} (  x_{ij}   - \xq_{\bullet j})^2}
  $};

  \foreach \X/\Y in {2,3}
     {\draw[-latex] (G\X) -- (F);}

  \draw[red, double,->](mat2-1-1)--(BB);
  \draw[red, double,->](mat3-1-1)--(mat2-1-1);

  \draw[blue, double,->](mat2-1-1) to[out=210, in=150] (mat2-6-1.south west) to[out=330, in=190] (BB);
  \draw[blue, double,->](mat3-1-1) to[out=150,in=30] (mat2-1-1);

  \end{tikzpicture}

\end{document}
  • I guess "inserting the equation" means something like this ----- equation here ---> – user64789 Jun 16 at 15:37

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