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May 27

Calculating df for unpooled t-test

I have two samples, same size but unequal variance. I'm trying to find a formula to exactly calculate the df, not just the smaller of the n-1 as df, something as the exact result my TI-83 will give me. I can't find the formula for this anywhere though. I just need to show the formula for a presentation. Is there any sense in caring about the exact formula and if so, any assistance finding it? Thanks 66.133.196.152 (talk) 05:35, 27 May 2010 (UTC)[reply]

You might start by looking at Behrens–Fisher problem. Michael Hardy (talk) 15:08, 27 May 2010 (UTC)[reply]

Gregory-Madhava Series

Can somebody please move this thread here from Science Desk? I don't know how to do it properly. http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Science#Gregory-Madhava_Series --117.204.87.183 (talk) 18:02, 27 May 2010 (UTC)[reply]

(copy & paste? --pm a 18:17, 27 May 2010 (UTC))[reply]

Somebody claims in an article that at Princeton University and some other such institutions Gregory series is now being taught under the name of Gregory-Madhava Series. Leibniz formula for pi#History has a glaring pov sentence. "To give the rightful place to this great mathematician, the series should be named 'mAdhava srENi' or Madhava Series." But that makes things a bit cloudy. What is the actual state of affairs? I don't know mathematics, by the way.--117.204.87.183 (talk) 17:20, 27 May 2010 (UTC)[reply]

I know this formula - and had forgotten it had a name at all - so much for mathematical glory. I doubt many people really care - http://www.google.co.uk/search?hl=en&q=%22Leibniz-Gregory-Madhava%22+formula&aq=f&aqi=&aql=&oq=&gs_rfai= suggests some people are remembering all three. The maths desk might be a better place to ask.77.86.125.207 (talk) 17:27, 27 May 2010 (UTC)[reply]

Considering the OP came from Kerala I guess it is another attempt to rename a series for a local hero. I don't know why people feel this urge to fix attributions and correct all the books. The article Gregory's series should definitely have a better history section and I fullagree with mentioning Madhava in the leader but the bit saying it is also called the Gregory-Madhava or Madhava-Gregory or whatever series would need attribution. It isn't generally called that as far as I'm aware and that's that basically. Perhaps they call it that in India? What's there is wishful thinking as far as I'm concerned. Dmcq (talk) 13:01, 28 May 2010 (UTC)[reply]

By the way Nilakantha Somayaji of the Kerala school is also credited with discovering the series. Dmcq (talk) 13:15, 28 May 2010 (UTC)[reply]

There are primacy claims around these mathematicians. The matter was treated at some length in a popular novel Francis_Ittykkora that came out in 2009 and many people seem to have taken the shabby claims in the novel for truth. (The page asks for a move as the first sentence itself shows in that article.) I would like to know if anybody teaching in Princeton Maths Department would attest to such a renaming:))--117.204.81.28 (talk) 17:33, 28 May 2010 (UTC)[reply]

Keep in mind that who actually discovered/invented it is not the issue for WP. Whatever terminology is being used most often in textbooks is the standard here, right or wrong. It's not out job to figure out what should be named after whom and fix it.--RDBury (talk) 18:34, 28 May 2010 (UTC)[reply]

People, don't you read the posts before you reply them? I was asking about a claim I saw somewhere that a long established formula has recently been renamed to accommodate some not so old discoveries. The claims are suspicious because there is little in the mainstream publications about this school. Primacy or invention is none of my concern and I didn't pose anything here to imply that it is. In my last post I specifically wanted to know if a new appellation has been in vogue at Princeton. I suppose WP couldn't be without some people from Princeton. However, two posters above hint at some nationalistic or primacy claim motive on my part which in fact is not there.--117.204.80.153 (talk) 20:31, 28 May 2010 (UTC)[reply]

Sorry about that. Half the theorems in maths are named after the wrong person and there's always people trying to rename them which as said above isn't Wikipedia's job. If you give a reference to the article about Princeton saying that it could possibly help. I did a quick google and saw a number of references to Leibniz-Gregory-Madhava series which is getting rather overlong! Dmcq (talk) 21:21, 28 May 2010 (UTC)[reply]

Unlike Astronomy where there is a body that has some say over nomenclature, there is no such body in mathematics. I.e. a theorem/series/whatever is called whatever people choose to call it. The usual way in which names change is that someone decides to use a new name in a paper/conference/etc (and makes a point why this name is justified) and others either follow suit or don't. If there are a number of recent papers using eibniz-Gregory-Madhava, than that *is* an alternative name. 213.160.108.26 (talk) 22:48, 28 May 2010 (UTC)[reply]

I edited the Leibniz formula for pi article. Bo Jacoby (talk) 13:03, 30 May 2010 (UTC).[reply]

Newton's Fdt=mdv integral!

Resolved

Will appreciate your control for the following differentials:

Newton's F*dt=m*dv is written as

F*r*dt=m*r*dv (energy conservation equation).That is

1/2*m*Vr^2+m*gr*r+1/2*I*w^2=m*r*dVr (total energy,where g is variable,Vr is the radial velocity and Vp, the perpandicular velocity to Vr, does not affect the total energy)).Then from

Vr^2+2*gr*r+I*w^2/m=2*r*dVr a differential equation is written with (2*gr*r+I*w^2/m=K*dt^2)

dr^2+K*dt^2=2*r*d(dr) and this differential equation is solved as

r=-a*t*(t-tmax)+K where K=-a^2*tmax^2/(4*a+1)

On Cartesian the graph of (r) is a parabola. On Polar, the graph is a cardioidal looking spiral (when on a plane).

The orbit of the planets is this spiral with billions of spires.The amplitude of the spiral's rings are expanding and then after compressing. No sign of ellipse, no focus, no aphelion, no perihelion nor equality of swept out areas in equal interval of time. No Kepler laws according Newton's laws.(??!!).TASDELEN (talk) 19:31, 27 May 2010 (UTC)[reply]

This is not the first time you've asked this or a similar question in the past few weeks. Have you read Kepler's laws of planetary motion#Derivation from Newton's laws as suggested before? Please read through them first and come back here if you still have specific questions that you do not understand about that derivation. Marking as resolved for now. (p.s. This poster's sheer persistence in asking long-winded, borderline nonsensical questions on both Science and Maths RefDesks leads one to assume that either they don't have a grasp of English or that they want to be deliberately difficult. Either way we can;t really help them.) Zunaid 21:00, 27 May 2010 (UTC)[reply]

I've told you before, you need to count the d's: 1/2*m*Vr^2+m*gr*r+1/2*I*w^2=m*r*dVr. That can't be a true statement since one of the four terms has a d and the other three don't. --Tango (talk) 21:16, 27 May 2010 (UTC)[reply]

No Tango.The statement (1/2*m*Vr^2+m*gr*r+1/2*I*w^2=m*r*dVr) is correct as it is the energy conservation expression. With the following correction (K/dt^2=m*gr*r+1/2*I*w^2) we write:

1/2*m*(dr/dt)^2+K/dt^2=m*r*d(dr/dt)/dt which is,after simplification:

r'^2+2*K/m/dt^2=2*r*r" a differential equation (with all the terms of the same size) having the solution:

r=-a*t^2+a*t*tmax+K where K=-a*tmax^2/4=Constant.In fact:

dr/dt=r'=-2*a*t+a*tmax

d(dr/dt)/dt=r"=-2*a

r'^2=4*a^2t^2-4*a^2*t*tmax+a^2*tmax^2

2*r*r"=-4*a*(-a*t^2+a*t*tmax+K)=4*a^2*t^2-4*a^2*t*tmax-4*a*K which is ending by:

4*a^2t^2-4*a^2*t*tmax+a^2*tmax^2+000000=4*a^2*t^2-4*a^2*t*tmax-4*a*K and after simplification

a^2*tmax^2=-4*a*K and K=-a*tmax^2/4 (as I have posed=Constant).

All this has one meaning: [r=-a*t*(t*tmax)+K] and the graph of this equation is a spiral on Polar plane.Not an ellipse.I think Kepler's laws of planetary motion#Derivation from Newton's laws should be revised for (Derivation) and should not be copy-pasted as icon. I insist: either Newton's law indicates my solution or the solution of Zunaid. I need mathematical proofs, confirmations, and not discouraging sentences like they don't have a grasp of English. What about your Turkish? Meanwhile, a difficult question about Kepler's area law: do you believe to the derivations on Wiki? Is Vp perpandicular velocity to Vr (radial velocity) variable or constant? Wiki says: variable. I say constant. Thanks.TASDELEN (talk) 13:10, 28 May 2010 (UTC)[reply]

The article should have a link to where it obtained the derivation from in the References section. Or check out the under-graduate text-book Calculus by James Stewart which actually has a problem exercise on this exact topic. I've done this derivation myself many years ago (I did mathematics as a core course of my degree and took astronomy as an elective) and can confirm that yes, under Newton's laws planetary orbits do come out as ellipses and not spirals. I'll be damned to do that derivation again, it requires a good grasp of vector calculus and a few lemmas regarding the dot product and cross product.

The reason I question your grasp of English is because it makes it difficult to understand your questions. I don't know if you're questioning the derivation of Kepler's Laws (ridiculous) or the accuracy of our article on that topic (entirely plausible). What do you mean "The orbit of the planets is this spiral with billions of spires.The amplitude of the spiral's rings are expanding and then after compressing".

The fact is that Newton's laws do predict Kepler's laws as has been mathematically and experimentally confirmed for the last 300 years. Your claim "No sign of ellipse, no focus, no aphelion, no perihelion nor equality of swept out areas in equal interval of time. No Kepler laws according Newton's laws" means you've made a mistake somewhere. Your derivation/result doesn't suddenly overturns 300 years of actual observations. Zunaid 15:04, 28 May 2010 (UTC)[reply]

Proposals for changing articles should be on the talk page of the article, not on the reference desk. Please note that any change of this magnitude, i.e. saying Newton's derivation is wrong or that we go in a spiral round the sun, would need to be backed up by citations. Wikipedia does not accept WP:Original research in its articles. The reference desk is for asking questions, it is not for proposing your answers in contradiction to Wikipedia articles. If you have an original solution of something that is notable enough to be in Wikipedia it needs to be published in a paper first before the Wikipedia article can be changed to reflect your research. Dmcq (talk) 15:03, 28 May 2010 (UTC)[reply]

NO for.."predict Kepler's laws as has been mathematically and experimentally confirmed for the last 300 years". According my solution, Newton's law of (F*dt=m*dv) resulted in to (r=-a*t*(t-tmax)+K). If this is rigth, Wiki's derivation of Newton's law is wrong. If this is wrong, I have to understand where is the mistake (mathematical lines are there), before saying Wiki's derivation is rigth. I hope you are there to answer similar questions. When commenting r=-a*t*(t-tmax), I think this is a spiral. Canonically, I must comment "this is an ellipse" to have your favour (?!). I am a mechanic, diesel engine repairer, but I am on the field to discuss Wiki's derivation .I do not approve for example Wiki's "Kepler's area law" derivation. And I sincerely asked you if Vperpandicular is constant or variable. Wiki says variable. I say constant. Canonically,I must not ask such (ridiculous) question, otherwise I am wrong, but to be canonic doesn't mean to have rigth. I agree your clause WP:Original research. That was a challenge of discussion before acting for "The reference desk is for asking questions, it is not for proposing your answers in contradiction(!) to Wikipedia articles. If you have an original solution of something that is notable enough to be in Wikipedia it needs to be published in a paper first before the Wikipedia article can be changed to reflect your research", which I agree totally, but peer-reviewers may be old minded canonics,and I prefered to discuss this matter with Wiki's peoples,hoping that they are more democratic.Are you? TASDELEN (talk) 18:49, 28 May 2010 (UTC)[reply]

Seemingly I am an old minded canonical. Dmcq (talk) 20:55, 28 May 2010 (UTC)[reply]

We can't point out precisely what your mistake is - your entire argument is complete nonsense. It is one big mistake. You need to go away and learn the relevant maths before trying to use it. I am going to delete any further questions from you on this topic, you are wasting everybody's time. --Tango (talk) 21:05, 28 May 2010 (UTC)[reply]

As an ordinary (and I hope democratic) Wiki person, I note that you didn't reply to my attempt to be kind to you on the [Science desk]. I agree with Tango, and we could probably find several million other people worldwide who agree with Newton & Kepler (plus a billion who don't know what it is all about). Can you not find a more profitable outlet for your abilities? Dbfirs 15:22, 29 May 2010 (UTC)[reply]

May 27

Calculating df for unpooled t-test

Gregory-Madhava Series

Newton's F*dt=m*dv integral!

Newton's Fdt=mdv integral!