I want to find the correlation between a continous variable with a non normal distribution, positively skewed, and a categorical variable with 4 categories. The only test I can find that fits these variable is the kruskal wallis test, but I am not sure how I can use this test to find the correlation or relationship between my two variables. Can anyone suggest how this relates to correlation or another test to use with my data? Rookie with statistics, so please let me know if any more information is required.
I am wanting to find the correlation between two variables: a categorical vegetation variable (with categories 1-4)  and a continuous variable of erosion (with values anywhere between 0.2 and 9). I think I would be required to use a non parametric test to find the correlation, but bit of a newby to stats so could anyone suggest the best test to use? I also wanted to know how sample size can affect these tests, ie with a sample size of 100 or 1000?
How to find the sum of this series?  $$\sum_{k=0}^{\infty}\cfrac{{2}^{k}}{\binom{2k+1}{k}}$$  It seems very easy. But I still can not work it out, can anyone help? Android Min SDK Version vs. Target SDK Version Where do Orc babies come from? I've not seen/read any female Orcs mentioned in the movies or in the books. In one of the movies, an Uruk-hai is momentarily shown emerging from a giant, grown-Orc sized flesh packet. So are they created with spells, or do they follow the Standard Reproductive Model. Why AUC =1 even classifier has misclassified half of the samples? I only read part of the second book in this series years ago, and am unsure of how many books were in it. It was about a teenage or young adult boy, who was part of the ruling class of this fantasy world. He was gay, and his lover was the heir to the throne. The antagonist of the first book - I haven't read it, but I got the gist from comments in the second - was the current queen, who tricked the boy and his lover into leaving the kingdom for remote outer regions, thus enabling her son to take the throne. She then married her own son to keep herself in power.  The second book had the boy and his lover slowly becoming enemies, as the lover began to corrupt the simple tribesmen they were sheltering with in his quest to regain his throne. He wanted to build an empire in the hinterland and use the army to attack his homeland, killing the queen in the process, and didn't care about the long-term effects his actions were having on the culture or environment of his new followers.   The lover defeats a tribesman by breaking his neck in unarmed combat, then later takes a young boy as his "willing catamite." He also leads raids on neighbouring tribes, establishes alliances with other neighbouring tribes and organises daring and successful raids on the eggs of dinosaurs living in the middle of a swamp. He enslaves the first tribe to turn against him, and gives their children to slavers from the empire in place of those of allied tribes, thus weakening his enemies while ensuring the loyalty of his allies.  The series involved dinosaurs living among humans, being both domesticated and wild, used as livestock, for hunting and as transport. The boy and his lover were much taller than the average humans who were forced to pay tribute to this pseudo-magical empire they came from; all the humans from the empire were much larger than their subjects. The tribesmen have a tradition about not touching the ground with bare feet, as it is an insult to nature, or their god. The boy and his lover both ignore this superstition, but the catamite also begins to ignore it, despite looking ashamed as he does so.  I have absolutely no idea when this series was written, what it is called or who wrote it. All I know is that I read it in 2005-06, though it probably wasn't new. I'm hoping the long description I've given will help someone work it out. How to hide notification center button in Mountain Lion? I am using Mountain Lion.  The only advantage (for me) over the gesture is that Option + clicking the button enables/disables showing alerts and banners (toggles the switch in the notifications center).  Is there a way to hide the button in the status bar that opens notification center? Is CAT5 cable good enough for RS-485 vs "true" RS-485 cable Is the word tenfold a misnomer? There's already a question like this  so that my question could be considered duplicate, but I'll try to make my point clear that this is a different question.   Is there a way to derive  from the Lorentz' Force law or just from Maxwell's Equations?   The point is that we usually define, based on experiments, that the force felt by a moving charge on the presence of a magnetic field is $\mathbf {F} = q\mathbf{v}\times \mathbf{B}$, but in that case the magnetic field is usually left to be defined later.   Now can that force law be used in some way to obtain Biot-Savart law like we obtain the equation for the electric field directly from Coulomb's Force law?  I wanted to know that because as pointed out in the question I've mentioned, although Maxwell's Equations can be considered more fundamental, those equations are obtained after we know Coulomb's and Biot-Savart's laws, so if we start with Maxwell's Equations to obtain Biot-Savart's having use it to find Maxwell's Equations then I think we'll fall into a circular argument.   In that case, without recoursing to Maxwell's Equations the only way to obtain Biot-Savart's law is through observations or can it be derived somehow? Does measurement, quantum in particular, always increase the total entropy? Given $f_{n} : [a,b]\rightarrow \mathbb R$ is uniformly Lipschitz and $f_{n}\rightarrow f$, how can I show that $f$ is Lipschitz?  $f_{n}$ is uniformly Lipschitz $\leftrightarrow \exists K &gt; 0$ such that for all $n$ and for every $x,y\in [a,b]$ we have $|f_{n}(x)-f_{n}(y)| &lt; K|x-y|$.  $f_{n}\rightarrow f \leftrightarrow \forall~\epsilon&gt;0~~\exists~N$ such that $\forall~n&gt;N$ we have $\mid f_{n}(x) - f(x)\mid&lt;\epsilon~~~(=\mid x-y\mid?)$  Then we have  \begin{align} |f(x)-f(y)| &amp;\leq |f(x)- f_{n}(x)| + |f_{n}(y)-f(y)| + |f_{n}(x)-f_{n}(y)| \\ &amp;\leq |x-y| + |x-y| + K|x-y| \\ &amp;\leq (K + 2) |x - y| \end{align}  which shows that $f$ is Lipschitz. Can anybody tell me if this makes sense? Sorry if layout is poor. I'm having a problem finding out a way to project from top view and the side view so I texture better. It just replaces the current projection with the top view    So is it possible to project from view twice on the same image? apt-get update only for a specific repository When I add a PPA and I want to install some of its content, it is quite annoying to re-update all my apt list using apt-get update.  Is it instead possible to only sync the content of a given repository? Why is it called Area 51? According to : "We like the little aliens."  This seems well targeted to appeal to the Stack Overflow / Server Fault / Super User audience, but way off the mark if the goal is to "make the Internet a better place to get expert answers to your questions."    There are experts who aren't interested in or focused on technology oriented topics.  Little aliens are unlikely to be something that someone interested in organizing a site on gardening would gravitate too.  No, I'm not suggesting that no one interested in gardening would be bother to look at a site with little aliens, but won't it be likely that the sort of mass appeal to to a very broad cross section of the internet will be lacking? Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd I read somewhere that     $(a^n - b^n)$         It is always divisible by $a-b$.   When $n$ is even it is also divisible by $a+b$.   When $n$ is odd it is not divisible by $a+b$.      and     $(a^n + b^n)$         It is never divisible by $a-b$.   When $n$ is odd it is divisible by $a+b$.   When $n$ is even it is not divisible by $a+b$.      I wonder what's the proof for this.  First postulate is clear. $(a-b)$ would or would not be a factor. Any light on others? What is the reason that the value "47" is so popular in electrical engineering? Efficiently select beginning and end of multiple contiguous ranges in Postgresql query I've got about a billion rows of data in a table with a name and an integer in the range 1-288.  For a given name, every int is unique, and not every possible integer in the range is present--so there are gaps.  This query generates an example case:  --what I have: SELECT * FROM ( VALUES ('foo', 2),               ('foo', 3),               ('foo', 4),               ('foo', 10),               ('foo', 11),               ('foo', 13),               ('bar', 1),               ('bar', 2),               ('bar', 3)      ) AS baz ("name", "int")   I'd like to generate a lookup table with a row for each name and sequence of contiguous integers.  Each such row would contain:  name   --  the value of the name column start  --  the first integer in the contiguous sequence end    --  the final value in the contiguous sequence span   --  end - start + 1  This query generates example output for the above example:  --what I need: SELECT *  FROM ( VALUES ('foo', 2, 4, 3),               ('foo', 10, 11, 2),               ('foo', 13, 13, 1),               ('bar', 1, 3, 3)      ) AS contiguous_ranges ("name", "start", "end", span)   Because I have so many rows, more efficient is better.  That said, I only have to run this query once, so it isn't an absolute requirement.  Thanks in advance!  Edit:  I should add that PL/pgSQL solutions are welcome (please explain any Fancy Tricks--I'm still new to PL/pgSQL). I'm looking for a way to prove $$\sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)^{2m+1}}=\frac{(-1)^m E_{2m}\pi^{2m+1}}{4^{m+1}(2m)!}$$ I know that $$\sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)^{2m+1}}=\frac{1}{4^{2m+1}}\left(\zeta\left(2m+1,\frac14\right)-\zeta\left(2m+1,\frac34\right)\right)$$ so maybe I could simplify the above more? Capacitor discharging through no load? What exactly would happen in the ideal case where a capacitor were to discharge into a wire with zero resistance?  Like in here:  There is still charge on one plate of the capacitor, which will try to go to the other plate to make $\Delta V = 0$ across the capacitor, so there has to be a current $I$.  But as more charge goes to the other side of the capacitor, the more repulsion these will cause to more coming towards them. So I am assuming current cannot just be constant?  I am starting from $$ I = C \frac{dV}{dt}, $$ but I know neither $V(t)$ nor $I$. Normally, it takes three votes to delete.  It still does, though the mouseover tip for a question with one delete vote cast on it already appears to be stuck at '1'    And then after casting a delete vote on it:    And if I've cast the first delete vote:    The above examples are from P.SE, and while I don't have the privs to verify this being the situation on other sites, this has been confirmed on at least SO and is likely network wide.    Child meta dups:   SO: