Setting the conventional null hypothesis as the alternative?
Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?
Help ID this plant, quite possibly a weed I found this plant near my South Indian home in , India. Most probably it could be some sort of weed. Anyhoo, is this plant of any medical or commercial value? Is it a remedy for something?   It has a white tap root with little veins off the main root It has a really small yellow flower It's leaves are similar to that of a clover, except for that it has three to five leaves        Merci d'avance!  (P.S. Forgive me if this is some very common plant that I should know about, I'm in 7th grade.) When is the limit of a sum equal to the sum of limits? I was trying to solve a problem and got stuck at the following step:  Suppose ${n \to \infty}$ .  $$\lim \limits_{n \to \infty} \frac{n^3}{n^3} = 1$$  Let us rewrite $n^3=n \cdot n^2$ as $n^2 + n^2 + n^2 + n^2 \dots +n^2$,$\space$ n times.  Now we have  $$\lim \limits_{n \to \infty} \frac{n^3}{n^3} = \frac {n^2 + n^2 + n^2 + n^2 + n^2 \dots +n^2}{n^3} $$  As far as I understand, we can always rewrite the limit of a sum as the sum of limits ...  $$\dots = \lim \limits_{n \to \infty} \left(\frac{n^2}{n^3} + \frac{n^2}{n^3} + \dots + \frac{n^2}{n^3}\right)$$  ...but we can only let ${n \to \infty}$ and calculate the limit if all of the individual limits are of defined form (is this correct?). That would be the case here, so we have:  $= \dots \lim \limits_{n \to \infty} \left(\frac{1}{n} + \frac{1}{n} + \dots + \frac{1}{n}\right) =$[ letting ${n \to \infty}]$ $= 0 + 0 + \dots + 0 = 0$  and the results we get are not the same.  Where did I go wrong? Is there a missing definite article before caliph in 'the group's leader, XYZ, as (the) caliph'? I read news on the BBC (on its website) this morning. When I was reading the news I noticed the definite article the was missing in a sentence. As per my opinion, the reporter missed the article the. But I also thought that the reporter also had some point as he did not use the article there. So I just wanted to confirm so landed here to get some help on it.     On the website:      It also proclaimed the group's leader, XYZ  (name), as caliph and   "leader for Muslims everywhere".      As per my opinion it should have been:      It also proclaimed the group's leader, XYZ  (name), as the caliph and   "leader for Muslims everywhere".   Source link: How to remove the lines which appear on file B from another file A? Setting: Let $\sum a_n z^n$ have radius of convergence $R$.  We have that  $$ R = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} $$  via Hadamard's formula for the radius of convergence.  Question: What are the radii of convergence for (i) $\sum a_n z^{2n}$ and (ii) $\sum a_n^2 z^n$?  Attempt for $\sum a_n^2 z^n$:   For ease of notation, let $R_1$ and $R_2$ denote the radii of convergence for power series $\sum a_n z^{2n}$ and $\sum a_n^2 z^n$ respectively. From Hadamard's formula, we then have  $$ R_2 = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n^2 \right|^{1/n}} = \left( \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} \right)^2 = R^2 $$   But what about $R_1$? How can I host my own Minecraft server? When documenting a style file, it would be nice to be able to easily put side by side different examples of code, side-by-side with the output they produce.  What recommendations to people have to do this efficiently, and &aelig;sthetically? Kinetic energy conservation in collision.  In any type of collision type of collision if we take the system to comprised of both bodies then the net external force is zero. So the work done by external force is also zero. By the relation $W=K_f-K_i$ as $W$ is zero hence kinetic energy is conserved. But this not the case.   Can you tell me what is the flaw in my argument? Some people say that the argument has neglected the fact that some kinetic energy is transformed into heat. But heat is created due to the interactions between bodies during collision which is thus an internal force and thus shouldn't affect kinetic energy. How do I set up a Godox X2Tc to control a Canon Speedlite 430 EXII I have a Godox X2Tc and a Godox X1Rc. I want to control my Canon Speedlite 430 EXII. (I also have a Godox V1, which is a beautiful thing!) I have the Canon Speedlite attached to the Godox receiver, so it should fire. It just wont! How do I set it up correctly so the receiver makes the Canon Speedlite fire?  Update: Michael C answered this question. I had the ID numbers set differently on the transmitter and receiver. I made them the same and now it all works. Perfect! Thanks Michael!! Is it safe to check floating point values for equality to 0? I know you can't rely on equality between double or decimal type values normally, but I'm wondering if 0 is a special case.  While I can understand imprecisions between 0.00000000000001 and 0.00000000000002, 0 itself seems pretty hard to mess up since it's just nothing.  If you're imprecise on nothing, it's not nothing anymore.  But I don't know much about this topic so it's not for me to say.  double x = 0.0; return (x == 0.0) ? true : false;   Will that always return true? Install 18.04 server without network connection Fundamental group of a torus with points removed Question 5.33 from "Topology and its Applications"  by Baesner is to compute the fundamental group of the torus ($T^2$) with $n$ points removed. I can "see" in my mind that if we remove one point we get a bouquet of two circles. Less clear is what happens when we remove two (or more) points. Any hints? Enable Careers and Jobs in app The current top-voted to  states:     Another one that's not so much a security issue, although it is security-related, is complete and abject failure to grok the difference between hashing a password and encrypting it. Most commonly found in code where the programmer is trying to provide unsafe "Remind me of my password" functionality.   What exactly is this difference? I was always under the impression that hashing was a form of encryption. What is the unsafe functionality the poster is referring to? I'm examining a part of my dataset containing 46840 double values ranging from 1 to 1690 grouped in two groups. In order to analyze the differences between these groups I started by examining the distribution of the values in order to pick the right test.  Following a guide on testing for normality, I did a qqplot, histogram &amp; boxplot.       This doesn't seem to be a normal distribution. Since the guide states somewhat correctly that a purely graphical examination isn't sufficient I also want to test the distribution for normality.   Considering the size of the dataset and the limitation of the shapiro-wilks test in R , how should the given distribution be tested for normality and considering the size of the dataset, is this even reliable? ()  Edit:  The limitation of the Shapiro-Wilk test I'm referring to is that the dataset to be tested is limited to 5000 points.  To cite  concerning this topic:     An additional issue with the Shapiro-Wilk's test is that when you feed   it more data, the chances of the null hypothesis being rejected   becomes larger. So what happens is that for large amounts of data even   very small deviations from normality can be detected, leading to   rejection of the null hypothesis event hough for practical purposes   the data is more than normal enough.      [...] Luckily shapiro.test protects the user from the above described   effect by limiting the data size to 5000.   As to why I am testing for normal distribution in the first place:  Some hypothesis tests assume normal distribution of the data. I want to know whether or not I can use these tests. I'd like to find an analogue of  or any other fps counter on Ubuntu 12.10.  After some googling I found 2 solutions:   To use  (I found it from ). This solution didn't work for me because after launching the game:  mumble-overlay game   I got this error:  game: symbol lookup error: /usr/lib/mumble/libmumble.so.1: undefined symbol: glPopClientAttrib   And I didn't find any fix of this error in the WEB. To use WINEDEBUG=fps with osd_cat. It works only with  (only Windows games). Found from reading  and . It shows FPS during play but the output is definitely wrong - 0.15-0.18 fps. And it doesn't matter if game really runs slow or fast - the result is always the same.   Does anyone know how to fix these errors? Or are there any other solutions? Thanks for the help. the numer of partial function between two sets in combinatoric way $A$ and $B$ two sets. $|A|=k, |B|=n.$ I need to prove in a combinatoric way that the number of partial function from $A$ to $B$ is $(n+1)^k.$ I thing the number is $Σ(n^i),$ for $i=0$ to $k.$ but I have no idea how to show equality, and how to prove it in a combinatoric way.  If someone can show me the way or guide me that will be great!  thanks for helpers. I'm porting a module that currently works with Blocks/BlockForms to Paragraphs/NodeForms. I'm inserting an embedded form inside a Paragraph inside a Node Edit page using a hook_field_widget_entity_reference_paragraphs_form_alter. The general structure where the form gets inserted is: $form['field']['widget'][0]['settings'][form here]  After this the form displays as expected on the node edit page. The inserted form goes through a number of #process steps. The element in question is a select form that when the button underneath it is pressed, is supposed to retrieve some data via a custom submit handler and place it on the page with ajax:  The array for this element looks like this:  You can see the custom submit handler that is supposed to fire when 'Select Segment Set' is pressed After debugging, I've found that the entire NodeForm appears to be submitted to the backend, and the only handler that is found is from some other field that uses ajax. In short 'updateSegmentSet' is never discovered as a submit handler. When I debug the original module based on block/blockforms, I do see the correct submit handler being discovered. Now in the latter case, of course a blockForm is submitted to the back end with the correct plugin. Given that this is basically a form within a form within a form, is there something special I have to do to get the custom submit handler to run? I've read a few things online e.g. the 'settings' key and '#tree' = true. EDIT The Ajax property looks like this:       '#ajax' =&gt; [         'callback' =&gt; [$this, 'updateSegmentSetAjax'],         'wrapper' =&gt; $wrapper_id,       ],    public function updateSegmentSetAjax(array &amp;$form, FormStateInterface $form_state) {     $button = $form_state-&gt;getTriggeringElement();     // Go one level up in the form, to the widgets container.     return NestedArray::getValue($form, array_slice($button['#array_parents'], 0, -2));   }  As best I can tell, this is never called either. Blurry Text On Model After Render I cannot easily figure out which one is more appropriate to use:     It's important to me.        It's important for me.   Are they the same? If not, what's the difference?