I am trying to find the correlation or association  between a categorical variable - classes from 1 -4 from a GIS (geographic information system) classification - and a continuous variable with values between 0 and 9. What would be the best test to use for this?
I would like to find the correlation between a continuous (dependent variable) and a categorical (nominal: gender, independent variable) variable. Continuous data is not normally distributed. Before, I had computed it using the Spearman's $\rho$. However, I have been told that it is not right.  While searching on the internet, I found that the boxplot can provide an idea about how much they are associated; however, I was looking for a quantified value such as Pearson's product moment coefficient or Spearman's $\rho$. Can you please help me on how to do this? Or, inform on which method would be appropriate?  Would Point Biserial Coefficient be the right option?
I've been informed by those who know much more about Harry Potter than I that Hogwarts is protected with a Disillusionment Charm so all muggles will see is ruins with a "Danger: Keep out!" sign around them.  (Apparently this was in one of the first three books, but I'm not sure where it was.)  My first thought was, "Well, a danger sign would encourage some muggles to investigate!"  Which leads to what I think is an obvious question: Will a disillusionment charm on a place like that still work when a person is real close to the location?  Will it work from inside the location?  For example, if a curious muggle made it to the gates of Hogwarts and started walking around inside, would they still see it as abandon and in ruins, or once they entered, would they see it as it is? GCD in a PID persists in extension domains Let $R$ be subring of integral domain $S.$ Suppose $R$ is $\text{PID}.$ Let $a\in R$ be a greatest common divisor of $r_1,r_2$ in $R$. ($r_1,r_2 \in R$, not both zero). Could anyone advise me on how to prove $a$ is greatest common divisor of $r_1,r_2$ in $S?$   Hints will suffice, thank you. Difference between I and Me I am quite confused with the usage of I and me, Can anybody tell me what should be used in the following sentence: Your husband doesn't believe that You're older than (I / Me). Proof for two sequences producing the maximum value when sorted I am trying to improve my discrete Math skills by doing some proof exercises. But I am struggling to understand how to start proving the following hypothesis:  $$ S = {x}_1{y}_1 + {x}_2{y}_2 + \ldots + {x}_n{y}_n $$ Where ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are ordering of two different sequences of positive real numbers, each containing n elements. S takes its maximum value when ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are sorted in non decreasing order.  I was thinking that I should maybe use a proof by contradiction. Where the negation of the hypothesis is: S takes it minimum value over all ordering of the two sequences when both sequences are sorted into non increasing order.  However I am not sure my negation of the hypothesis is correct or how proceed from there. I do not want the complete proof because I am trying to learn how to do it myself but if some one can tell me how to make a start on this I would be grateful. Why do some questions in question lists have a yellow background? On SO, when I'm scrolling through "questions" some have a yellow background.  Is this intuitive to everyone but me?  What is the yellow background trying to tell me about this particular question? How to tell if a site is using Drupal 7 I know how to check , but is there a way to tell if a site is built with Drupal 7? Find all the values of $w$ ∈ C that satisfy the equation. Determine if the convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ is uniform. $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ converges pointwise in a set $E = [0, \infty)$ to $f(x) = x$.   This problem reminds me a lot of how $\frac{x}{n}$ fails to converge uniformly to $f=0$ on $[0,\infty]$, but does converge uniformly on $[0,a]$. However, when we proved that we used the definition of uniform convergence. I do not wish to do that here.  I wish to use the Weierstrass test here. And that is where I'm stuck. I cannot find $M_n = \sup\limits_{x \in E} |f_n(x)-f(x)|$. Can someone help me out here? Force new users to go through animated tutorial before they post for the first time Do not allow people to post the minute they created an account.  Let them ask the question but not allow them to post.  Let them stew for 30 minutes and force them through a nice animated tutorial on what they should do before they post and enforcing the fact that bad questions will not get an answer.  If they had a Need to know! basic rules introduction forced on them asking them at the end to check a box I understand! some might ask better questions and help the community instead of flooding the site with bad questions.  The presentation should be on a timer without the ability to skip and highlight the similar questions asked before that might give them the answer.  Also for the first next 9 posts they should have to check a box next to the first 5 of each similar questions before posting.  I do not mean to be harsh, but the truth is I see more negative votes on questions then positive. It's like 90% of the time people give -1 to first questions. How to extract a number from a string Im a newbie in Apex and im developing a page using Visualforce.  My string format is always like this "xx-xx-999999". In this format I need to get only the integer. For example the string is  "RO-W1-445567". I want to get only the integer 445567 in the string. Can someone willing to share a piece of apex code in my problem.  Your help is vey much appreciated.  Thanks in advance!  Ferdie Banu Delegates: Predicate vs. Action vs. Func Can someone provide a good explanation (hopefully with examples) of these 3 most important delegates:   Predicate Action Func Reward for Passing Review tests? Just wanted to see what the community thought of adding a reward to passing the review tests? Maybe a 1 point reward?  I know seeing the tests in the review area has helped me be extra careful when reviewing, but I thought perhaps a little boost in incentive would be cool. I want to have both KDE and Gnome shells on Ubuntu. Ubuntu only has Gnome installed by default. How do I install KDE? Epsilon Delta Proof: How do I use the definitions to prove Is there a word with phobia suffix for fear of waking others up? I usually come home after basketball at like 12:30 a.m. and at this time my mom and sister usually sleep (my Dad though is usually up). When I come home, I don't go to sleep right away and will sometimes eat or do something else. When I do so, I do it in stealth, so that I don't wake up anyone. I do out of two things, to be polite as I do not want to wake anybody up and also the fact that if I make a loud noise and wake my mom up, my mom will get mad and lecture me. Does this count as a phobia? In addition, if it does what would the name of it be. I see these two expressions are used almost identically in different contexts. Is there a difference between I have got and I have gotten? How to reduce fireflies in Cycles? I often use Cycles' built in Glass BSDF shader to achieve realistic refraction effects, but in many cases, it seems that Cycles' glass caustics creates an unfortunately large number of fireflies (pixels that are abnormally bright relative to their surroundings). In some models of mine, even when I render for 3000 or more samples/pixel, my final image is still covered in fireflies. While I can improve this in many cases by increasing the total amount of light available in the scene, this loses a lot of the potency of the refractive effects I'm looking for, especially in scenes with low light levels.  So my question is, how can I reduce the amount of fireflies while using Cycles' caustics without sacrificing the quality of the refractive effects?  Note: I am aware that Cycles' caustics will perform much better once Cycles has full support for bidirectional path-tracing, but it looks unlikely that that will become , unfortunately. Earlier this year, I read a huge (1000+ pg) novel about a cloistered group of monks that sort of worshiped math. The story involved alternate dimensions or time travel or something. A big thing in the book was coordinates, containing data like for speed or something as an alternate axis. There were several rings of the monastery.   At some point the main character was called out of his monastery to never return. I'm hoping to figure out the name so I can discuss it with my book club. Best way to implement keyboard shortcuts in a Windows Forms application? Responsive Web Design - what should happen when the mobile device is rotated? Currently, the standard behaviour for viewing web pages on a mobile is that:   If viewed in portrait the text is smaller because the width of the device is small and the whole page width needs to fit into view. If viewed in landscape the view 'zooms in' as the width is now wider so that the text is larger and more readable, but with less content on screen as a result.   So, this brings a dilemma. When creating a responsive website what should happen on device rotation? (Not on initial page load, I am referring to what should happen once the site is loaded and you decide to then rotate the screen)   When rotated from portrait to landscape should you:   a) Re-detect the device widths and map the contents according to the new dimensions (thereby retaining the same font / images sizes as when viewing portrait). b) Keep the same dimensions and on rotation just bring the content to fit the window (thereby zooming in the content to make it more readable for viewers if the portrait orientation text is too small).          &ndash; Wireframes created with   Bear in mind that with a traditional web-page viewed in the mobile you have the option of pinch-to-zoom the text, so if it's too small you can zoom in. With a responsive site this isn't an option because the site will fit the dimensions so there is nothing to zoom into.  (I guess there is a third option too - use responsive fonts so that the font sizes change according to the screen width. But that's probably a different question altogether).