A colleague has a dataset from a before and after study looking at a continuous outcome that was measured in individuals before and after an intervention. An unknown but not insubstantial proportion of the individuals were only measured before or after the intervention.  However, due to an oversight following changes to the study design due to ethics they have only now realised that there is no way to link the before and after measurements that were made to the same individuals, i.e. there is no person ID.  Consequently, the data consists of a mix of paired and independent samples, but can only be treated as independent samples.  Are there any reasonable ways to mitigate this problem or address it, e.g. via some kind of sensitivity analysis?
An investigator wishes to produce a combined analysis of several datasets.  In some datasets there are paired observations for treatment A and B.  In others there are unpaired A and/or B data.  I am looking for a reference for an adaptation of the t-test, or for a likelihood ratio test, for such partially paired data.  I am willing to (for now) to assume normality with equal variance and that the population means for A are the same for each study (and likewise for B).
So I noticed that many cards with tap-effects ship with a clause specifying that they can only be used on untapped permanents, such as  and .  So here's my question:   Doesn't that imply that, given the right situation, one can legally tap an already tapped permanent?   I'll give an example of the kinda scenarios this is relevant for: Can  activate her first ability when no untapped cards are around? Or, thinking untap-effects, could I bounce a forest with  even when there isn't a tapped creature available?  Notice that, unlike the previous batch of examples, the wording on these lacks the clause restricting their use to un/tapped permanents - does that mean that they aren't?  Any kind of clarification would be greatly appreciated here. Solving minimization problem $L_2$ IRLS (Iteration derivation) In the article ''' Chartrand, Rick, and Wotao Yin. "Iteratively reweighted algorithms for compressive sensing." Acoustics, speech and signal processing, 2008. ICASSP 2008. IEEE international conference on. IEEE, 2008. '''  It is given that one iteration of  iterative reweighed least squares problem can be written as $\min \sum_{i=1}^N w_i u_i^2 $ subject to $\Phi u = b  $ which has a closed form solution given as   $u^{(n)} = Q_n \Phi^T (\Phi Q_n \Phi^T)^{-1} b$. where $Q_n$ is the diagonal matrix containing entries $1/(|u_i^{(n-1)}|^2 + \epsilon )^{1/2} $ And the closed form equation can be derived from the Euler Lagrange equation. Can someone please help me to get the derivation of the iteration?\ I understood till $$\min_u u^TWu+λ|| \Phi u−b||_2^2 $$  which can be written as $(\bigtriangledown=0)$ which gives $$ W u + \lambda (\Phi^T \Phi u - \Phi^T b) =0$$ I understand what the game already tells you in the general sense... it changes enemy damage, resistances, and chance of legendary monsters appearing.  But, specifically, how does the difficulty level affect the game? Is going from Normal to Hard a 5% increase in damage? 50%? 200%? Are there any additional things changed that aren't mentioned. Does Survival mode add any extra mechanics, or is it just even bigger numbers than Very Hard? How do I identify which Linux distro is running? We have some new hardware in our office which runs its own customized Linux OS.   How do I go about figuring which distro it's based on? Cheap/free tool to view/convert Canon CR2 RAW format photo files on Windows? As much as I like having the hardcover core rule-books in front of me, usually I read or reference most information for RPGs on my computer.  Unfortunately, my google-fu has failed me at finding places to buy a Player's Handbook PDF, or even whether said PDF exists at all.  My question is this: Is there any place I can go to legally buy a D&amp;D 5e core rulebook PDF?  I'm not looking for the starter set or basic rules, since those are incomplete (and free), I'm just looking for the core books in PDF format. How to use numpad / on a keyboard without a numpad? I've just got into Blender, and I like it a lot. But as I just switched from a stationary computer to a MacBook, I've got some new problems regarding the numpad. I can use 1-9 perfectly, But I have no idea how to emulate buttons like / (used to enter local view). I've searched the web for an answer, but I can't find any. Do photons have acceleration? Photons travel at the fastest speed in our universe, the speed of light.  Do photons have acceleration? Sadly, yesterday I've spilled some water on my MacBook Pro (El Capitan). Before you yell at me - it was closed, turned off and it wasn't a lot of water, the laptop was wet only on the top and under - not inside.  Today I've turned him on. At first battery wasn't recharging for some reason, but SMC reset fixed the problem.  At the first booting speaker was like talking to me, hard to explain but it was weird. Also only right speaker was "talking", despite the fact that only left side of the laptop was watered. Then there was no sound at all, not from the speakers, nor from the headphones. Also microphone's not working. USB ports are okay. The water was spilled from the left side of the laptop. I know this is hardware issue, and something's broken, but I want to be 100% sure. No it's not muted. I've also tried NVRAM reset a few times, but it doesn't fix the problem :(  There might be one factor, before spilling, my laptop "died" for the first time (battery energy ran off), but I doubt it's the case. (but hey, every info matters, right?)  It wouldn't be weird for me, if only left speaker wouldn't work, but built-in microphone not working is kinda weird in this case, isn't it?  I just want to ask you guys, what else can I check, before I'll be 100% sure it's dead inside?  I've plugged in external microphone - it's not working too. How is the no-cloning theorem compatible with the fact that fan-out gates work? I have some difficulty with understanding no-cloning theorem. Simply speaking, according to the theorem, it is not possible to copy a quantum state.  On the other hand, CNOT gate can be used as so-called fan-out gate which purpose is to copy one qubit to another one, previously in state $|0\rangle$.  It seems that these two facts negate each other.   My question: How is no-cloning theorem compatible with the fact that fan-out gate works? So one of this question's  answers got me curious. What is the maximum damage a 20th level character can do with a 9th level Magic Missile by the rules to a single target.  So my best I've been able to find is Aasimar or Goblin WLK 1/WIZ 19   9th Level slot (1D4+1)(11) [keep in mind you only roll once for damage not 11 times]  per  Empowered Evocation (+5)(11) (assuming 20 INT) Hexblade Curse (+6)(11) (Proficiency Bonus +6)    Radiant Soul/Fury of the Small +20 (Level 20 Aasimar/Goblin)   For a total of (D4+12)(11)+20 for (min-max)avg (163-196)179.5  Am I looking at this correctly? Are there other abilities out there that can increase this?  Feel free to include non legendary magic items. NO TOMES PLEASE  Only use things available on D&amp;D Beyond please.  Acceptable books are :   Basic Rules DMG, MM, PHB Sword Coast Adventure's Guide The Tortle Package Volo's Guide to Monsters Xanathar's Guide to Everything and any officially released Adventure Book How can I record sound from the windows command line? Is there an application capable of recording sound that I can run from the command line on XP?  Ideally I'd start it with one command and stop it with another. Or I could specify a duration with the starting command. Check existence of input argument in a Bash shell script Python metaheuristic packages How do I get add-apt-repository to work through a proxy? Does the ANSI standard mandate the logical operators to be short-circuited, in either C or C++?  I'm confused for I recall the K&amp;R book saying your code shouldn't depend on these operations being short circuited, for they may not. Could someone please point out where in the standard it's said logic ops are always short-circuited? I'm mostly interested on C++, an answer also for C would be great.  I also remember reading (can't remember where) that evaluation order isn't strictly defined, so your code shouldn't depend or assume functions within an expression would be executed in a specific order: by the end of a statement all referenced functions will have been called, but the compiler has freedom in selecting the most efficient order.  Does the standard indicate the evaluation order of this expression?  if( functionA() &amp;&amp; functionB() &amp;&amp; functionC() ) cout&lt;&lt;"Hello world"; "Fatal error: Cannot redeclare " Calculus of variations -- how does it make sense to vary the position and the velocity independently? What is a good book to study linear algebra? I'm looking for a book to learn Algebra. The programme is the following. The units marked with a $\star$ are the ones I'm most interested in (in the sense I know nothing about) and those with a $\circ$ are those which I'm mildly comfortable with. The ones that aren't marked shouldn't be of importance. Any important topic inside a unite will be boldfaced.  U1: Vector Algebra. Points in the $n$-dimensional space. Vectors. Scalar product. Norm. Lines and planes. Vectorial product.  $\circ$ U2: Vector Spaces. Definition. Subspaces. Linear independence. Linear combination. Generating systems. Basis. Dimesion. Sum and intersection of subspaces. Direct sum. Spaces with inner products.  $\circ$  U3: Matrices and determinants. Matrix Spaces. Sum and product of matrices. Linear ecuations. Gauss-Jordan elimination. Range. Roché Frobenius Theorem. Determinants. Properties. Determinant of a product. Determinants and inverses.  $\star$ U4: Linear transformations. Definition. Nucleus and image. Monomorphisms, epimorphisms and isomorphisms. Composition of linear transformations. Inverse linear tranforms.  U5: Complex numbers and polynomials. Complex numbers. Operations. Binomial and trigonometric form. De Möivre's Theorem.  Solving equations. Polynomials. Degree. Operations. Roots. Remainder theorem. Factorial decomposition. FTA. Lagrange interpolation.  $\star$ U6: Linear transformations and matrices. Matrix of a linear transformation. Matrix of the composition. Matrix of the inverse. Base changes.   $\star$ U7: Eigen values and eigen vectors Eigen values and eigen vectors. Characteristc polynomial. Aplications. Invariant subspaces. Diagonalization.   To let you know, I own a copy of Apostol's Calculus $\mathrm I $ which has some of those topics, precisely:   Linear Spaces Linear Transformations and Matrices.   I also have a copy of Apostol's second book of Calc $\mathrm II$which continues with   Determinants Eigenvalues and eigenvectors Eigenvalues of operators in Euclidean spaces.   I was reccommended Linear Algebra by Armando Rojo and have Linear Algebra by , which seems quite a good text.   What do you reccomend? Restrict the access to suggested edit reviews on deleted posts on an answer deleted as rude/abusive is visible, even without logging in (and for users with less than 10k reputation). These users can't see the answer , via the , or a direct link to the .    This is a potential avenue for spammers, just like the suggested edit spam used to be, but is ; according to the :     In addition, in order to reduce the incentive for spammers to make spam edits that get rejected, suggested edit spam is hidden from logged-out users, so they can't show their clients public-facing pages with spam (so they won't get paid).   For this to work, the spammer would need two accounts, one to post the spam and a second one to suggest an edit. Even if the spam post is quickly nuked, the review link will be active forever. One could argue that logged-in users without 10k reputation shouldn't be able to see the suggested edits either; I'm partial to that.