Ancova for unequal variances What is the best way to compare two non-homogeinous populations (Levene's) with covariates (e.g. age). I know ancova assumes homogeneity. Is there a way around this? Many thanks
Alternatives to one-way ANOVA for heteroskedastic data I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.  One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a  ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.   I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.  Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?  P.S.: my raw data are below:   A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36  0.363 0.371 0.398 0.407 0.409 0.432     0.494 0.719 B: 0.11  0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19  1.233 1.505 1.897 C: 0.106 0.114 0.143 0.435 0.448 0.51  0.576 0.588 0.608 0.64  0.658 0.788 0.958
How to search text throughout entire file system? Is there a quasistatic process that is not reversible? I have seen several questions and good answers on the link between reversible and quasistatic processes, such as  or . However, these questions only adress one side of the problem : a reversible process is necessarily quasistatic.  I am interested in the other side of the equivalence : is there a process that is quasistatic, yet not reversible ? It looks to me that an irreversible process cannot be made perfectly quasistatic.  The  article about quasistatic processes takes as an example the very slow compression of a gas with friction. As the compression occurs very slowly, the transformation is quasistatic, and the friction makes it irreversible. I am not convinced by this example : if you press on the piston with a vanishingly small force you will have to reach the threshold of the Coulomb law for solid friction before moving the piston anyway. It makes the process non-quasi-static, however small the Coulomb threshold might be.  Another example I've heard of is the reaction between a strong acid and a strong base. It is always an irreversible process, and you could make it quasistatic by adding very small drops of base into acid at a time. But by trying to do that, you would inevitably reach a limit to the size of the drop imposed by surface tension.  Even if "reversible" and "quasistatic" mean very different things, is it true to consider that in practice, a reversible process and a quasistatic process is essentially the same thing ? Z-axis issue with the floating review info panel, permits various elements to flow over it Is there a general method (which can be implemented by hand) to finding the $n$-th roots of $2 \times 2$ matrices? Is there a similar method for a general $m \times m$ matrix? (for $n &gt; 1$ and $n\in\mathbb{Z}$) Let $P$ be a probability measure on $(\Omega, \mathscr{F})$, If $a,b,\in\mathscr{F}$ and $A\subset B$, then $P(B)-P(A)=P(B\setminus A)\ge 0$.  So far I have:  $A\subset B \implies B\setminus A = B\cap A^c = \emptyset$ as $A$ and $B^c$ are disjoint. Since $A\cup (B\setminus A)=A\cup (B\cap A^c)=(A\cup B)\cap (A\cup A^c)=B\cap\Omega = B$  Then for $A,B\in \mathscr{F}\implies P(A\cup (B\setminus A))=P(A)+P(B\setminus A) = P(B)$ by countable additivity.  Rearranging, $P(B)-P(A)=P(B\setminus A) \ge 0$. Is torque as fundamental a concept as force? I used to think that torque and force were equally “fundamental”. In other words, my understanding was that we usually use Cartesian coordinates in many common problems because it is a convenient system, so as a result instantaneous forces which act in straight lines seem “easier” mathematically but torques require some extra “baggage”. This baggage includes typically teaching that torque is defined in terms of force.  But if say we happened to choose polar coordinates for the problem the situation would appear the other way around. So it would be arbitrary if we chose to define forces in terms of torques instead.  But later on I learned that angular momentum is conserved independently of regular linear momentum (IIRC). Given the definitions of force &amp; torque as derivatives of momentum, this makes it seem much less certain that one should define either torque in terms of force or vice versa — it gives the impression they are more distinct than it first seemed.  That said, as far as I know a lot of physics is about defining &amp; describing “fundamental forces” — not “fundamental torques”.   So is choosing to use either force or torque as the basis of laws &amp; problems arbitrary? Or is there an actual fundamental rationale to when one or the other should be used? How to calculate a confidence interval for estimating a proportion when the population is very small? I plan to execute a little study on whether dentists tend to grant privately insured patients (PRIV) a sooner appointment compared with publicly insured patients (PUB). I want to restrict this study to the dentists of a single town in Germany.  In this town there are about 500 dental practices and I am willing to call maximum 100 practices (twice, once as a PUB and once as PRIV). (A sample without replacement of size up to 100)  So the result of this examination would be a list of up to 100 practices with an associated value of 1 - if the appointment for the PRIV was more than two days sooner - and a 0 - if not. The proportion of 1s is what I want to estimate.  Now the sources I have been reading always assumed a much larger population with a finite population correction close to 1. This is why I doubt that blindly using a conservative or approximate confidence interval would lead to a statistically meaningful result.   So my first question is, of course, whether it is reasonable at all trying to estimate the proportion using a confidence interval in this case? And if yes, then what statistical technology/method (leading to a CI) would be a good choice for this use case?   One idea that comes to mind is using a sample size of 25 f.x., in that case the FPC would be 0.95 - "close enough" to 1. But it seems stupid trying to improve the quality of an estimation by reducing the information used for the estimation. I'm interested: What is C#'s analog of std::pair in C++? I found System.Web.UI.Pair class, but I'd prefer something template-based.  Thank you! Currently using ubuntu 15.10 on azure and installed the gnome and vnc4server latest version on ubuntu. Please find log file below:  Current VNC client screen:    $ cat .vnc/myhost1\:1.log    --cut-- VNCSConnST:  Server default pixel format depth 16 (16bpp) little-endian rgb565 VNCSConnST:  Client pixel format depth 8 (8bpp) colour-map Window manager warning: Invalid WM_TRANSIENT_FOR window 0x20000c specified for    0x20000b (I        nitialization error). Error org.freedesktop.DBus.Error.NameHasNoOwner: Could not get owner of name    'org.gnome.ze        itgeist.Engine': no such name amdxdg-su: no graphical method available for invoking '/usr/bin/amdcccle' as 'root'  $ cat .vnc/xstartup unset SESSION_MANAGER  [ -x /etc/vnc/xstartup ] &amp;&amp; exec /etc/vnc/xstartup [ -r $HOME/.Xresources ] &amp;&amp; xrdb $HOME/.Xresources  vncconfig -iconic &amp;  gnome-panel &amp; gnome-settings-daemon &amp; metacity &amp; nautilus -n &amp; gnome-terminal &amp;   How to get 24bit color with wide screen (Now I getting square screen in vnc client) Traditionally  at the end of a filename after uploading it via the image uploader. That doesn't seem to work any more. I've tested it on Q&amp;A as well as chat.        (Yes, I know big M doesn't work)  Could we have this fixed please? With the new permission model for Marketing Cloud Installed Packages, there is a problem with the "Read"-Scope for Data Extensions.  If an installed package is granted the permission/scope "Data Extensions - Read" the API-Call fails with HTTP 403 "Forbidden".  How to provide read access to Data Extensions?  Related documentation: How to add an edge ring around a hole What is the easiest way to add/extrude an edge loop around the hole in the first image to make it like the second image? Find the area of largest rectangle that can be inscribed in an ellipse The actual problem reads:      Find the area of the largest rectangle that can be inscribed in the ellipse    $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.$$   I got as far as coming up with the equation for the area to be $A=4xy$ but then when trying to find the derivative I don't think I'm doing it right. A recent quandary came up with some friends in a game of Ticket to Ride.  If, in the last turn, you have the cards to play a route longer than the number of trains that you have left, can you do so?  Or are you limited by your number of trains? What is the location of lock screen images on Windows 10? Where, or what format, are the images used by Windows 10 when logged out or in lock-screen?  I searched the entire drive for *.jpg, *.bmp, *.png, and *.tif but the one I was looking for did not appear.  At first glance, , although not exactly a duplicate, appeared to have the path I wanted.  But when I went there, the pre-login image was there, but the lock-screen image was not.  (And contrary to the claim in that answer, the files there did have extensions.)  UPDATE: I just did a lockscreen, and got an image that IS in that directory, but earlier today, it was consistently an image of an interesting footbridge that is not in that directory. Can I exclude spam domains from my search results? Sometimes when I search for something, there are plenty of links to sites with no content (those who only have the premade templates which the search terms), spammers, and leechers (as in copying content from other sites, like B r o t h e r s o f t who leeches on SoftPedia.com).  How come they have such a high ranking without any original content (furthermore, why are they not simply banned from the results)?  And also, is there some way of filtering them out? Like for example completely exclude a domain from search results? When to use 'by' instead of 'at' or 'on' to specify time/date? series of young adult science fiction books from early 1980s about last of a race of martial experts that sees the destruction of his home planet I remember that the main character is trying to find the group that destroyed his home planet while he was on a mission. His planet was very difficult to live on and the people became expert in martial arts and were the best soldiers in the galaxy. They were mercenaries and often helped against tyrants. There was a very memorable section in at least one book about an initiation task that the main character had to do in that he had to survive in their wilderness for days. He was at some point surrounded in a old building by thousands of poisonous worm/snake creatures that he managed to survive until rescued by the leaders. How do I find my follower if and when they leave me? Evaluating $\int_0^{\large\frac{\pi}{4}} \log\left( \cos x\right) \, \mathrm{d}x $