Carl

This should explain why a lot of parents organize home schooling, and why one room schoolhouses do such a good job. You want a good education? Teach students how and why to learn, and push them to do it. As for curriculum try this 1) Ethics 2) Reading 3) Math. Did you need 300000 bureaucrats to do that?

to teach because they are being told what to do, then the children suffer for it. You either trust the teacher, or send you kid elsewhere.

others, a "core" curriculum is nothing but dead weight, i.e., time wasted on trying to babysit children who would make better decisions than the bureaucrats did. You left out teachers. If teachers do not have permission

@Haridasa I do not agree on several points. First, the concept of a "core" curriculum, winds up being an unachievable goal for some schools, in which, nothing but filtered and unoriginal ideas are badly presented.

That would not be the case for smaller European countries the size of US states. For them, having a Ministry of Education a few hundred miles at most from the classroom does not provide the same deleterious mass dynamic as it would in the US.

For example, if one university has a physics department that concentrates on "string theory," which has little if any practical usage, then all the US dept's want to have large numbers of string theorists writing papers that are only read by string theorists.

And so, I reiterate, there is no role in the US federal system for a Dept of Education precisely because there is a virtual guarantee of heavy handed decisions being made with no feedback or accountability. The US is notorious for "group think."

This resulted in the introduce of eugenics and the sterilization of thousands of low IQ test students, and was cited by Hitler as what convinced him to introduce eugenics to Nazi Germany. Despite that history lesson, some say we should let the Dept of Education set standardized testing of students as a role they couldn't possibly get wrong. In summary, when a role is delegated to people who have "no skin in the game," bad things happen.

@Haridasa I agree with much of your assessment of what should be taught. However, the curriculum should not be set by bureaucrats a thousand miles away from the classroom whose influence cannot be made to have a wholesome effect. Take for example what happened when the Binet IQ test was imported from France to the US.

@Haridasa So why would you dissolve the Dept. of Education? I seem to have multiple reasons why is seems appropriate.

@Haridasa In theory, there is nothing wrong about having "Ministry of Education." However, a US Department of Education is not constitutional because no such power as "education" was delegated from the states to the federal gov't in it. So structurally it should not exist as there is no constitutional amendment delegating that function. In practice, the US Department of Education is ineffectual, obstructive, and opaque, and makes bad decisions beyond the scope of federal constitutional power, so yes, I think it needs to be dissolved.

@Haridasa Which is why one should teach students to survive in their local environment first. It would not be appropriate to teach atheism to uniquely Rosicrucian students, and no central government is so flexible as to adapt to local conditions never mind even trying to teach a gifted, studious child in a decrepit neighborhood among children every other of whom wears gang colors.

@Haridasa Yes, indeed, in the manner of proof we are all limited by its incompleteness see Gödel's incompleteness theorems. However, it would be contrarian to give up and teach nothing. I had a boss who was educated in a one room schoolhouse in rural Saskatchewan. He said that he received a fantastic education, optimal, couldn't be better. That is hardly the case for an over-regulated, inner-city school where students fail to learn to read anything, and never get beyond finger counting. Each student deserves attention.

@Haridasa I do not understand your statement. In what way can any teacher or curriculum planner disabuse themselves from their own biases? For example, do you think that atheism is unbiased? I find that atheists dislike religious beliefs as frequently as religious people dislike atheists. Anti-religiousness is frequently a negative image of religiousness, which, in effect is like the negative of a picture, same information, just backwards.

I gave you a link to Indiana Law, which exhaustively shows how subsidiarity appears in that law. Since subsidiarity arises from Natural Law, which although well presented by Thomas Aquinas, was also espoused by the ancient Greeks. Historically, it was not until Newton's time that the math for min/max problems was established. Its application to game theory is here. Since the topic is as wide as the Amazon River, and as old as time, I do not know what kind of reference you are asking for.

@Haridasa I do not agree. One should be taught various systems of belief, for example Catholicism, Islam, Hinduism, Buddhism, Judaism, Zoroastrianism, etc., etc. Otherwise, the students are just plain uneducated and not prepared for real world interaction with others. What you do not know can get you killed if you say the wrong thing to the wrong person at the wrong time. Having one-dimensional political theorists planning curricula is worse than incompetent, ignorance will get you thrown in jail in the wrong place at the wrong time.

Yes indeed. You are missing the root philosophical argument, which is something obviously embedded in the US Declaration of Independence; "Governments are instituted among Men, deriving their just powers from the consent of the governed". This arises from the principle of subsidiarity, originating from the natural law philosophy of Thomas Aquinas. To wit; there is an optimal organizational size and structure that is ad hoc. Anything else is relatively incompetent.

You mean something like a population average from a group of models fit to multiple curves?

@JimB I understand. Was this related to the question the OP asked or not?

f = ((ssE - ssP)/(dfE - dfP))/(ssP/dfP);

@JimB No, more typically the errors are called between and among. Never heard otherwise. The nomenclature used by the OP and first answer were adequite to identify that.

@JimB Yes, what?

@JimB What is pure error? What do you want? If you want the probability of each parameter of the model contributing significantly to the fit you would use fit["ParameterConfidenceIntervalTable"], and fit["ParameterPValues"].

@JimB What is being done is to read entries from the ANOVATable. What is you question about? Something else perhaps?

An an 5 by 98 row array that has titles in the first row and 98 rows of data. It is just cannon fodder for fitting a polynomial. In other words, it is largely irrelevant and the variable sor is a two dimensional array of x and y values for fitting.

Yes, there is a lot of garbage out there, and yes, I would prefer that people just write tested algorithms, not opinions. Indeed, that is why we are discussing this.

@Glen_b By consistent in my personal context does not include much in the way of cupidity. To do stats properly, necessary but often neglected material includes the analysis and implementation of physical conservation as well as the ability to use math usefully.

What I am trying to do is document what the procedure is, and it does not appear in any one place. For example, some sources document the W-statistic very well, and then completely neglect the calculation of probability, e.g., "Here is the lookup table."

I get your point about normality, but I was quoting someone. Clearly, as I investigate Wilcoxon procedure, normality or its absence seems irrelevant as the probabilities are calculated based on total possible outcomes, at least for small numbers.

One source that I cited is no less than Mathematica documentation, which describe Wilcoxon as a median procedure, so there is no one to look up because it is clearly wrong.

@Glen_b No, I do not look up people, rather I judge what they say on the basis of consistency with other information I gather. This is because one cannot adjudicate content based on credentials. Indeed, I find that stats knowledge alone tends to be insufficient.

@SalMangiafico Would you please put the uses for Wilcoxon into your answer? If there are better indications than use of Wilcoxon in particular circumstances, please document that with more information, e.g., links to papers.

the probability calculation does not appear to be calculated that way, at least for small n. One source I looked at suggested using the mean of w+ and absolute w- to calculate W, and then confidence interval and most suggest the lesser magnitude of w+ and w- for that purpose. What a mess!

@Glen_b One source I looked at stated that Wilcoxon was useful to compare similarly skewed distributions and another than skewness was a "contraindication." One source stated that the sign ranked sum was more normal, but that is likely a red herring since

@antonio It can make sense, but the motive, meaning and method are still context dependent, in that new context.

@Sycorax Some of the comments are useful. Can you leave at least the first few of them?

@Glen_b That would be more normal than the rank observations, not the observations themselves, I would think, but then I could be wrong about that too.

@Glen_b I'm guessing that you have shown that the t-test is more powerful than Wilcoxon. If so, I agree. However, I get messages like this (Mathematica): "TTest::nortst: At least one of the p-values in {0.01190....}, resulting from a test for normality, is below 0.05`. The tests in {T} require that the data is normally distributed." Let's be practical here, when is Wilcoxon useful, how do we best describe what it does?

@ChristianHennig I don't get it. For example, if I compare radioactivity from beta decay of I-131, I can assume "independence" but the events from U-235 that produce I-131 are fission events where the neutrons produced in that decay increase the probability of fission decay of other U-235 nuclei, so you are saying that I cannot use what? I can no longer test which of two U-235 samples is more radioactive? I still don't get how that is. Finally what I want is how to describe Wilcoxon, can you help, please?

@Glen_b Very interesting. I haven't come across a circumstance wherein the Wilcoxon test is less stable than the t-test. However, my question is how to describe Wilcoxon, which is why I wrote a question rather than an answer. Can you answer the question?

@ChristianHennig OK, finally I get it, you mean they are orthogonal: the 2D pairs are at 90 degrees to each other, that's called orthogonal, you are just using jargon I wouldn't use.

@ChristianHennig OK, see how it's calculated in this link. It starts "(make) As many rows as you have pairs of data." These can be called {$X_i,Y_i$} 2D, coordinate pairs. Now, by convention x is called independent, and y, dependent, but for Sperman-rank-correlation (rs) one can write rs$(X_i,Y_i)=\text{rs}(Y_i,X_i)$, which is why I am confused because it doesn't matter which is dependent, or even what that means. For example, in relativity S1 observes S2, or S2 observes S1 are mutually dependent; relative.

@ChristianHennig Humm, I am missing some fine point here, please explain. My problem is, for example, that if the Spearman correlation is very significant, and preformed on paired data, the concept of independence is not apparent to me in the sense that A and B map to C and we examine how A and B map to each other. How can one justify independence if A and B have an rs of 0.99999997 ?

@RichardHardy You do a of what I call service work. Kudos, you are one impressive dude.

@RichardHardy Thanks for the edit, but I found a few more typos to correct as well.

@Glen_b Perhaps one may be assuming independence IFF the result is significant, or am I missing something?

@Glen_b Agreed, but all too commonly: SignedRankTest{{data1,data2}} tests whether the median of data1-data2 is zero. and Analyse-It for Microsoft Excel: Wilcoxon signed ranks test is a non-parametric test for a difference in central location (median) between two paired samples. It's all over the place, so obviously, we have work to do to counteract it. Also, if Spearman rank correlation does not require independent, why should any paired sample comparison assume independence? Habit, perhaps?

OK the y-axis values are from the residuals, which are the from square root of the model minus the square root of the counts. Now, providing that Standardize[residuals] produces standardized residuals (I am taking a guess) then the standardized residuals are as follows: