This question comes from a .  One user asked a question:     Given $p=0.05$ in one study, what is the likelihood of $p \ge 0.05$ if the same study was repeated under the exact same condition in the same population?   With a set of possible answers: 5%, 10%, 50%, 95% and 99%.    The most common and most accepted answer seemed to be that you don't have enough information to tell.  However this seems wrong. My reasoning is the following:  0.05 is an arbitrary p-value. So the question really asks - when you obtain a p-value, what's the probability that the second p-value will be greater than the first one? And when rephrased that way 50% looks like an obvious answer.    The question is - what is the correct answer and how to derive it in a more rigorous way?
I have been reading Geoff Cumming's 2008 paper  [~200 citations in Google Scholar] -- and  am confused by one of its central claims. This is one in the series of papers where Cumming argues against $p$-values and in favour of confidence intervals; my question, however, is not about this debate and only concerns one specific claim about $p$-values.   Let me quote from the abstract:     This article shows that, if an initial   experiment results in two-tailed $p= .05$, there is an $80\%$   chance the one-tailed $p$-value from a replication will fall in   the interval $(.00008, .44)$, a $10\%$ chance that $p &lt; .00008$,   and fully a $10\%$ chance that $p &gt; .44$. Remarkably, the   interval—termed a $p$ interval—is this wide however large   the sample size.   Cumming claims that this "$p$ interval", and in fact the whole distribution of $p$-values that one would obtain when replicating the original experiment (with the same fixed sample size), depend only on the original $p$-value $p_\mathrm{obt}$ and do not depend on the true effect size, power, sample size, or anything else:     [...] the probability distribution of $p$ can be derived without   knowing or assuming a value for $\delta$ (or power). [...] We do not assume any prior knowledge   about $\delta$, and we use only the information $M_\mathrm{diff}$ [observed between-group difference] gives about $\delta$ as   the basis for the calculation for a given $p_\mathrm{obt}$ of the distribution of   $p$ and of $p$ intervals.      $\quad\quad\quad$    I am confused by this because to me it seems that the distribution of $p$-values strongly depends on power, whereas the original $p_\mathrm{obt}$ on its own does not give any information about it. It might be that the true effect size is $\delta=0$ and then the distribution is uniform; or maybe the true effect size is huge and then we should expect mostly very small $p$-values. Of course one can start with assuming some prior over possible effect sizes and integrate over it, but Cumming seems to claim that this is not what he is doing.  Question: What exactly is going on here?    Note that this topic is related to this question:  with an excellent answer by @whuber. Cumming has a paper on this topic to:  -- but that one is clear and unproblematic.  I also note that Cumming's claim is repeated several times in the 2015 Nature Methods paper  that some of you might have come across (it already has ~100 citations in Google Scholar):     [...] there will be substantial variation in the $P$ value of repeated experiments. In reality, experiments are rarely repeated; we do not know how different the next $P$ might be. But it is likely that it could be very different. For example, regardless of the statistical power of an experiment, if a single replicate returns a $P$ value of $0.05$, there is an $80\%$ chance that a repeat experiment would return a $P$ value between $0$ and $0.44$ (and a $20\%$ change [sic] that $P$ would be even larger).   (Note, by the way, how, irrespective of whether Cumming's statement is correct or not, Nature Methods paper quotes it inaccurately: according to Cumming, it's only $10\%$ probability above $0.44$. And yes, the paper does say "20% change". Pfff.)
Alien studying human race for mental capacity and ESP How to disable GNOME keyring? I want to disable GNOME keyring globally on my machine. So I deleted the lines  auth    optional        pam_gnome_keyring.so session optional        pam_gnome_keyring.so auto_start   in /etc/pam.d/gdm. It seems to me that this has no effect. When I lock in the syslog writes  Aug 24 18:37:03 foobar gnome-screensaver-dialog: gkr-pam: unlocked login keyring   and another user sees a menu window where he hs to enter his credentials. So what is the correct way to disable keyring for every user on that machine? Short story with space microbes latching onto electromagnetic fields This is a sci-fi story set on Earth. From the depths of space comes these microbes that latch onto electromagnetic fields. Anything electronic is rendered useless. There's the usual stuff where governments try to solve the issue but make it ultimately worse. It's only when they realise that the microbes surround the planet that they realise it is futile. The story closes with people having returned to a simpler life, using medieval farming methods, not using electricity in any form, getting about by horse, etc. I think it was a short story. What does "official Ubuntu flavour" mean? What kind of support do they receive from Canonical or/and Ubuntu community? Who decides a distro should become official flavour? What privileges do "official flavours" have over unofficial derivatives of Ubuntu like Linux Mint, Elementary OS, Deepin OS,etc.? Chapter 5: Are there multiple Endings? I just finished Episode 5 and wondered, if there were alternative endings or game branches. I brought the whole group with me, and am wondering what would have changed if different people accompined me, and if the episode is possible to play out differenly.      On my playthrough, Lee killed the stranger, and on the run back to Christa and Omid, was to weak to continue. Clementine shot him. Kenny died along with Ben after he fell off the building. And Lee was cut off Christa and Omid after they went over the "bridge" first. Derivative of $x^{x^{\cdot^{\cdot}}}$? Which kind of pointer do I use when? How to fix Eclipse with OpenJDK 9 Do not enumerate a section, but add it into table of contents How do I rid of number of a section in the way that it still would be in the table of contents.  If I use   ... \section{SN1} ...   then I see this section name in table of contents as   1 SN1  2 SN2  3 SN3  ...   If I use   \section*{SN}   I don't see it in the content:   1 SN2  2 SN3   How to get in content just   SN1  1 SN2  2 SN3   ? Getting image dimensions without reading the entire file Find a bijection to prove a fact about integer partitions Prove that for fixed positive integers $k$ and $n$, the number of partitions of $n$ is equal to the number of partitions of $2n + k$ into $n + k$ parts.  I tried this with different values of n but can't seem to get a bijection between the two partitions. What should children call a step-grandparent? My mom remarried to a great guy who has been absolutely wonderful to my kids. Ever since my mom and he were dating my kids have called him Mr. Joe. Lately my mom has been bugging me to get the kids to call him Grampa.  I agree that he deserves more respect than Mr.  The problem is that he isn't their real grampa so I don't really want them calling him that. Does anybody have any suggestions on what we should have the kids call him? They are 9 and 12 years old.  EDIT: I appreciate the comments regarding different variations of grampa and hearing how others have no issues with calling their step-granddad grampa. But I was hoping maybe someone has some suggestions for names that show the importance of the step-granddad without calling him some variation of the grampa name but still has a feeling of warmth and family in the name (I hope that makes sense). Can I use a 23 W CFL in a fixture that's rated for a 60 W incandescent? I have a lamp that is rated at 60 Watts for an incandescent bulb with a disclaimer to use a 13 Watt bulb instead when using a CFL replacement. Do I really need to respect that disclaimer? Would not a 23 Watt CFL be just as safe to use? It still draws less power than a 60 Watt incandescent, right? In Nginx, how can I rewrite all http requests to https while maintaining sub-domain? Number Theory: Find all solutions of $\phi(n)=16$ and $\phi(n)=24$ For a simple circuit with a battery supplying a voltage $V$ to a capacitor, let us assume that the charge on the capacitor is $Q$. Now, the work done by the battery or the energy supplied is given by the relation:  $$W=QV$$  But the energy stored in the capacitor is given by:  $$U = \tfrac12 QV$$  The value of $Q$ as well as that of $V$ should be the same in both the equations.  Now my question is, where is the other half of the energy that the battery supplied? Can we use curved spacetime to measure the one-way speed of light? This is related to  and  The idea is to shine a beam of light from a clock towards a heavy mass, like a black hole, in some manner such that the curvature of spacetime around the mass is sufficient to &quot;bend&quot; the light directly back to the clock. That is, to send the light along a self-intersecting geodesic using a sufficiently curved spacetime. Note that in this case the source and the detector are the same object, so no clock synchronization is required. Hypothetically, this should measure the one-way speed of light. None of the given refutations from the similar posts on this site are convincing. Here are some of the main refutations, as I understand them, and my counter to them: (1) In being curved by spacetime, the light is actually changing direction, hence this is not the one-way speed. To my understanding of General Relativity, the light travels along a geodesic; that is, a curve such that, ignoring technicalities of Differential Geometry, its tangent direction is constant. There is no reflection or acceleration. So in this sense, how can the light with a constant tangent direction be said to change direction? One might say that the path deviates from a straight line in Euclidean space, but given that spacetime is not Euclidean, has no , and has no global notion of direction, this is the only definition of straight or &quot;one direction&quot; that makes sense. Thus, either the light does not change direction and is &quot;one-way,&quot; or we need to be clearer about what exactly we mean by &quot;one-way&quot; in the context of General Relativity. (2) Such an experiment would be impossible or impractical. I think some posters were saying this because the original questions implied that the clock would have to be at the event horizon of a black hole, which is of course impossible or impractical; however, I don't think such an extreme closeness to the black hole is required. Given that the  of a black hole, where light orbits in a circle, is outside of the event horizon, shining the light at some distance outside of the photon sphere should be sufficient to curve the light back to the clock, regardless of the distance of the clock from the black hole (see my rough illustration). At the extreme, we could place the clock directly on the photon sphere, which should be theoretically possible. Regardless, the question is not about practicality, but whether the one-way speed is theoretically measurable.  Update: Essentially what this argument boils down to, I think, is that the average speed of light along a single self-intersecting geodesic may differ from the average speed of light along a non-geodesic self-intersecting path, which is always c. Put that way, however, it does seem a little ridiculous. It is hard to see how the anisotropy of the speed could be defined in such a way as to be consistent with this pathological case. Presumably, we could approximate a single self-intersecting geodesic with a non-geodesic path arbitrarily closely, so, logically, the average speeds over each path should be approximately the same, i.e., c. Furthermore, how would the &quot;preferred direction&quot; of the speed of light behave around a black hole, for instance? Regardless, I still think this experiment does actually solve the problem for the given notion of &quot;direction&quot;. Though the problem is usually posed in the flat spacetime of Special Relativity, with a global notion of direction, so the apparent unanswerability of this question should be seen as a limitation of Special Relativity only, which is then solved by General Relativity. What are the costs of books and materials in Harry Potter? In the first book, Harry sees his Gringotts vault for the first time.  (Quotes thanks to Slytherincess!)     Griphook unlocked the door. A lot of green smoke came billowing out, and as it cleared, Harry gasped. Inside were mounds of gold coins. Columns of silver. Heaps of little bronze Knuts.      "All yours," smiled Hagrid.      All Harry's -- it was incredible. The Dursleys couldn't have known about this or they'd have had it from him faster than blinking. How often had they complained how much Harry cost them to keep? And all the time there had been a small fortune belonging to him, buried deep under London.      Hagrid helped Harry pile some of it into a bag. "The gold ones are Galleons," he explained. "Seventeen silver Sickles to a Galleon and twenty-nine Knuts to a Sickle, it's easy enough. Right, that should be enough fer a couple o' terms, we'll keep the rest safe for yeh."      Harry Potter and the Sorcerer's Stone - pages 58-59 - US Hardcover Edition   Jk Rowling posts in the Harry Potter Lexicon      JKR has stated in an interview (Comic Relief 2001) that she estimates the value of one Galleon to be "about five pounds," which works out to around US$9.75 (the exchange rate at the time of the interview was US$7.33). In the introduction to both QA and FB, US$250-million is stated to be the equivelent of 34 million Galleons. That also works out to a value of £5 to the Galleon, at the exchange rate of the time. The price listed on the back of the books, however, is not correct, since US$3.99 would equal less than half a British pound, or 8 sickles and 15 knuts. The book instead incorrectly lists US$3.99 as being equal to 14 sickles and 3 knuts. (Unfortunately, CNN.com uses this incorrect value for their Knuts-to-dollars converter.)      This gives us approximate values as follows:      1 bronze Knut = £0.01 (US about 2 cents)      1 silver Sickle = £0.29 (about US$0.57)      1 Galleon = £5.00 (more or less US$9.75)      These rates vary as the exchange rate fluctuates - see the Wizarding World Currency Converter for the current rate.   Now looking at the quote      Hagrid helped Harry pile some of it into a bag.   and     Right, that should be enough fer a couple o' terms, we'll keep the rest safe for yeh.   Obviously "some" is unspecified, but presuming the costs of ...     Typical elementary-school textbooks cost more than $100 each   He would be carrying at least 10 galleons for each school book, and going by the list of books just for his first year,  (Thanks Ibid!)     COURSE BOOKS      All students should have a copy of each of the following:         The Standard Book of Spells (Grade 1) by Miranda Goshawk   A History of Magic by Bathilda Bagshot   Magical Theory by Adalbert Waffling   A Beginners’ Guide to Transfiguration by Emeric Switch   One Thousand Magical Herbs and Fungi by Phyllida Spore   Magical Drafts and Potions by Arsenius Jigger   Fantastic Beasts and Where to Find Them by Newt Scamander   The Dark Forces: A Guide to Self-Protection by Quentin Trimble         (Harry Potter and Philospher's Stone, Chapter 5)   That's 80 Galleons just for books. This does not include the list of other expenses Harry has for his school years (wand, potion reagents, etc.)  How many Galleons is "some" or is Diagon Alley selling supplies for third world prices?  Sidenote, is this just a case of bad JK maths? I'm reading . Then I'm not able to figure out the difference between hard voting and soft voting in context to ensemble based methods.  I quote descriptions of them from the book. The first two images from the top are description for hard voting, and last one is for soft voting.        In my view hard voting is majority decision, but I don't understand soft voting and the reason why soft voting is better than hard voting. Would anyone teach me these? Writing XML to a file without overwriting previous data