I am analyzing data from different dichotomous variables. When analyzing association between these variables, what is the most recommended method?
I'm aware that this one is far from yes or no question, but I'd like to know which techniques do you prefer in categorical data analysis - i.e. cross tabulation with two categorical variables.  I've come up with:    &chi;2 test - well, this is quite self-explanatory  Fisher's exact test - when n &lt; 40, Yates' continuity correction - when n > 40,  Cramer's V - measure of association for tables which have more than 2 x 2 cells, &Phi; coefficient - measure of association for 2 x 2 tables, contingency coefficient (C) - measure of association for n x n tables, odds ratio - independence of two categorical variables, McNemar marginal homogeniety test,   And my question here is: Which statistical techniques for cross-tabulated data (two categorical variables) do you consider relevant (and why)?
Finding the limit of $(1-\cos(x))/x$ as $x\to 0$ with squeeze theorem How do I find:  $$ \lim_{x\to0}\frac{1-\cos(x)}{x} $$  Using the squeeze theorem.  Particularly, how would I arrive at its bounding functions?   If possible, please try not to use derivatives. How to install brackets.io from the command line? For some reason the gnome installer that handles .deb packages on my system is not working. I'm not concerned.  How would one install the Brackets.io program from the terminal? Singular or plural following a list The Tree of Life in Evangelion I've noticed references to the Kabbalah in a couple of anime I've watched.  One of them is Neon Genesis Evangelion.  Neon Genesis Evangelion has it in the sky in both the opening credits and in the series itself:     I also remember it was on the ceiling at NERV, but the best screencap I could find of that was too tiny to be visible.  So, my question is, Is there any deeper meaning to the use of the Kabbalistic tree of life, or is it just used because it looks cool? Unable to Retrieve Metadata Given this (very) tricky determinant, how can we calculate it easily?  $$\begin{pmatrix} \alpha + \beta &amp; \alpha \beta &amp; 0 &amp; ... &amp; ... &amp; 0 \\ 1 &amp; \alpha + \beta &amp;  \alpha \beta &amp; 0 &amp; ... &amp; 0 \\ 0 &amp; 1 &amp; \alpha + \beta &amp; \alpha \beta &amp; ... &amp; ... \\ ... &amp; ... &amp; ... &amp; ... &amp; ... &amp; 0 \\ ... &amp; ... &amp; .... &amp; ... &amp; ... &amp; \alpha \beta \\ 0 &amp; 0 &amp; 0 &amp; ... &amp; 1 &amp; \alpha + \beta   \\ \end{pmatrix} \in M_{n\times n}$$  EDIT:     I have to prove it is equal to $\frac{{\alpha}^{n+1} - {\beta}^{n+1}}{\alpha - \beta}$   Any help is appreciated, I just could not find a trick to ease it up! Opt out of moderator election notifications I was working on a problem that resulted in the calculation: $20 \equiv 10x \pmod{11}$.  I got the answer $x \equiv 2 \pmod{11}$ with the thought process: Since $10$ is a factor of $20$ I can rewrite $20 \pmod{11}$ as $10x \pmod{11}$ with $x=2$. But isn't this basically the same as using division, which we aren't supposed to do in modular spaces?  If I solve by multiplying $20$ by the multiplicative inverse of $10 \pmod{11}$ which is $10$, I get $200 \pmod{11}$ which simplifies to $2 \pmod{11}$ anyway. Did these numbers just happen to be the same or is my original method valid? How can I make realistic looking potions as handouts ASP.NET Web Site or ASP.NET Web Application? When I start a new ASP.NET project in Visual Studio, I can create an ASP.NET Web Application or I can create an ASP.NET Web Site.  What is the difference between ASP.NET Web Application and ASP.NET Web Site? Why would I choose one over other?  Is the answer different based on which version of Visual Studio I am using? Name tikz pic as if it was a node I'm confused about tikz pics. I can freely define them without issue, and even add coordinates inside that will be available by name inheritance like (-A) as for example in \pic (S) at (0,0) {myPic}; \draw (S-A) -- ++(0,0);. This is all documented around p. 255 of the pgf manual.  However I don' understand why it is not possible to give a name to a pic like the one above if no coordinate is defined inside it. By default it would be great if it could behave like a normal node.  MWE:  \documentclass{minimal} \usepackage{tikz}  \tikzset{     myBlock/.pic = {         \node[draw,minimum width=1cm,minimum height=0.5cm] at (0,0) {};     },     myBlockNamed/.pic = {         \node[draw,minimum height=1cm,minimum width=0.5cm] (-m) at (0,0) {};     }, }  \begin{document} \begin{tikzpicture}     \pic () at (0,0) {myBock}; % can't give it a name     \pic (S) at (3,0) {myBlockNamed}; % can give it a name     \draw (S-A) -- ++(2,0); \end{tikzpicture} \end{document}   The underlying point is I'm working on a control blocs library (so that we can stop the chat below with @Alenanno). For example here is the definition of a math operator  \tikzset{     mySum background/.style = {         circle, minimum size=1.5em, fill=white,     },     mySum edge/.style = {         draw=black, circle, minimum size=1.5em, line width=.5pt,     },     pics/bOp/.style = {     code = {       \node [mySum background] {};       \foreach \t [count=\i] in {#1}{         \pgfmathsetmacro{\angle}{\i*90}         \node[anchor=center, font=\tiny] at (\angle:0.45em) {$\t$};       }       \node [mySum edge] {};     },   }, } How do I get the browser to reask me to integrate with a website? I'm using  and I accidentally clicked "No" when asked if I want to integrate with the website.  How can I have Firefox or Chrome reask me to integrate the site with Ubuntu? How to suppress Terminated message after killing in bash? Exporting video to .mov in Blender 2.79 In the past, Blender (at least the Mac version) has had the ability to encode video files as .mov, the format used by Quicktime Player. However, with Blender 2.79 this feature seems to have vanished, for both the Internal and Cycles render engines. The release log happens to have the entry "Video encoding settings have been simplified, along with the addition of a Constant Rate Factor (CRF) mode" which I suppose could be the cause.  Does anyone know what happened—whether it is the aformentioned reason or something else—and how to export videos as Quicktime .mov in Blender 2.79? What is the physical meaning of commutators in quantum mechanics? This is a question I've been asked several times by students and I tend to have a hard time phrasing it in terms they can understand. This is a natural question to ask and it is not usually well covered in textbooks, so I would like to know of various perspectives and explanations that I can use when teaching.  The question comes up naturally in what is usually students' second course in quantum physics / quantum mechanics. At that stage one is fairly comfortable with the concept of wavefunctions and with the Schrödinger equation, and has had some limited exposure to operators. One common case, for example, is to explain that some operators commute and that this means the corresponding observables are 'compatible' and that there exists a mutual eigenbasis; the commutation relation is usually expressed as $[A,B]=0$ but no more is said about that object.  This naturally leaves students wondering     what is, exactly, the physical significance of the object $[A,B]$ itself?   and this is not an easy question. I would like answers to address this directly, ideally at a variety of levels of abstraction and required background. Note also that I'm much more interested in the object $[A,B]$ itself than what the consequences and interpretations are when it is zero, as those are far easier and explored in much more depth in most resources.    One reason this is a hard question (and that commutators are such confusing objects for students) is that they serve a variety of purposes, with only thin connecting threads between them (at least as seen from the bottom-up perspective).   Commutation relations are usually expressed in the form $[A,B]=0$ even though, a priori, there appears to be little motivation for the introduction of such terminology. A lot of stock is placed behind the canonical commutation relation $[x,p]=i \hbar$, though it is not always clear what it means.  (In my view, the fundamental principle that this encodes is essentially de Broglie's relation $\lambda=h/p$; this is made rigorous by the  but that's quite a bit to expect a student to grasp at a first go.) From this there is a natural extension to the Heisenberg Uncertainty Principle, which in its general form includes a commutator (and an anticommutator, to make things worse). Canonically-conjugate pairs of observables are often introduced, and this is often aided by observations on commutators. (On the other hand, the energy-time and angle-angular momentum conjugacy relations cannot be expressed in terms of commutators, making things even fuzzier.) Commutators are used very frequently, for example, when studying the angular momentum algebra of quantum mechanics. It is clear they play a big role in encoding symmetries in quantum mechanics but it is hardly made clear how and why, and particularly why the combination $AB-BA$ should be important for symmetry considerations.  This becomes even more important in more rigorous treatments of quantum mechanics, where the specifics of the Hilbert space become less important and the algebra of observable operators takes centre stage. The commutator is the central operation of that algebra, but again it's not very clear why that combination should be special. An analogy is occasionally made to the Poisson brackets of hamiltonian mechanics, but this hardly helps - Poisson brackets are equally mysterious. This also ties the commutator in with time evolution, both on the classical side and via the Heisenberg equation of motion.   I can't think of any more at the moment but they are a huge number of opposing directions which can make everything very confusing, and there is rarely a uniting thread. So: what are commutators, exactly, and why are they so important? Where is the Layers panel in Blender 2.8? Resolving a Git conflict with binary files I've been using Git on Windows (msysgit) to track changes for some design work I've been doing.  Today I've been working on a different PC (with remote repo brian) and I'm now trying to merge the edits done today back into my regular local version on my laptop.  On my laptop, I've used git pull brian master to pull the changes into my local version. Everything was fine apart from the main InDesign document - this shows as a conflict.  The version on the PC (brian) is the latest one that I want to keep but I don't know what commands tells the repo to use this one.   I tried directly copying the file across onto my laptop but this seems to break the whole merge process.  Can anyone point me in the right direction? Did the law of conservation of energy apply to the earliest moments of the Big Bang? If so, what theoretical physics supports this?   I hear that Einstein's theory of relativity disputes the law of conservation of energy- so does that mean the law is false, or only some aspect of it? I've been taking photographs for a while, and have started to think about moving to full-frame. I'm on a very limited budget, but I currently have a good macro lens and am quite willing to buy something like a EF 50mm f/1.8 to start off with. I could possibly stretch my budget as far as a 70-200 f/4 L or 24-105 f/4 L.  Primarily, I'm interested in taking photos of small wildlife like reptiles, amphibians and insects, but I have a healthy interest in landscapes, birds and street photography.   I currently have an EOS 30D, and I love the way the camera handles, especially with the dual control dials. For this reason, I think shooting with a Rebel would be a significant step down.   However, I have seen 5Ds and occasionally 1Ds Mark IIs on ebay for roughly the same price as an EOS 650D. I'm sure these cameras have better IQ than my 30D, since they are pro-level bodies from around the same time, and full-frame besides. The question is, are these cameras now so old that the image quality from them is a substantial step down from current Rebels?   I realise I'll be giving up continuous shooting speed and some amount of low-light performance, and that I'd also need to get an external flash, but besides these, are there any substantial caveats I need to be aware of before I go ahead and take the plunge? Can't find the reason why root directory usage is so large