Assumptions Definition and 119 Threads

Statistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions.
Here are some examples of statistical assumptions.

Independence of observations from each other (this assumption is an especially common error).
Independence of observational error from potential confounding effects.
Exact or approximate normality of observations (or errors).
Linearity of graded responses to quantitative stimuli, e.g. in linear regression.

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  1. L

    Measures with Compact Support in Complex Analysis: Finiteness Assumptions

    I was reading in a book, says \mu is a measure with compact support K in C, meaning \mu(U)=0 for U\cap K=0.. Is \mu(K) assumed to be finite in this case? It doesn't say in the book, but they make a statement which is true if that's so. Is there usually some assumption about measures being...
  2. D

    Is there a consensus on the philosophical assumptions of science?

    There are numerous lists online of the basic assumptions of science--too many for me to feel comfortable that there is actually a standardized consensus on this. Here is my question. What are the most generally accepted 'a prioris' of science? And how well do they stand up under careful...
  3. Hydr0matic

    Exploring Bell's Assumptions and Quantum Theory

    The other thread here made me read up a bit on Bell, EPR, Aspect's and so on.. An important part is ofcourse the assumptions discussed intensively in the other thread. vanesch expressed my view about this: Why isn't it obvious here that the mistaken assumption is within quantum theory? Is...
  4. P

    Deriving 3D Wave Eq.: Assumptions & Considerations

    when we derive the wave equation for a an o0ne dimensional wave moving at constant speed we assume that the wave move losslessly that is a plot of \psi(x,t) with x at any time t is same to the extent that one can be obtained from the other by translation. similarly what are the assumptions when...
  5. B

    Can Electrons and Protons Create a Neutral Particle at Rest?

    Homework Statement I'm not going to write the full question as its not neccessary, but this is the gist of it. Electrons are fired at protons and a search is made for a neutral particle created in the impact. Both the electron and proton still exist after the impact, along with this new...
  6. rootX

    Am I correct in my assumptions?

    assume there's a road the cars have length of "d" m, and space btw them is "k", and are moving at "di/dt" and at some time, ahead of them is blocked trafic, and in there the cars moving @ "do/dt" and so i am analyzing portion of the road that has blocked traffic, like how many cars in...
  7. T

    String threory assumptions about spacetime

    I just read that string theory "started out as a generalization of quantum field theory where instead of point particles, string-like objects propagate in a fixed spacetime background". Is this true? And if so, did anyone try to do the same with a curved spacetime? What did they get? Or perhaps...
  8. B

    Doppler shift formula and the assumptions behind it

    Einstein in his "On the electrodynamics of moving bodies" (1905) starts the derivation of the Doppler shift formula by stating: In the system K, very far from the origin of coordinates let there be a sourcce of electromagnetic waves..." . Taking into account his advise "never stop thinking" we...
  9. C

    How Do We Ensure Solutions to Differential Equations Are Unique?

    My question can be most simply put as how can we guarantee that the only solutions of a homogenous linear differential equation are of the form ce^at? or for that matter that the particular solution of a function is given by u(x)f(x) in the variation of parameters method. how can we...
  10. M

    Find Coefficient of Kinetic Friction: Reasonable Assumptions

    ok i have a question about which assumptions which are allowable in this scenario. A sled is being held at rest on a slope that makes an angle theta with the horizontal. After the sled is released, it slides a distance d1 down the slope and then covers the distance d2 along the horizontal...
  11. R

    Star Wars: Assumptions of Outer Space

    This was one of my test questions today. Read it carefully. A viewer knowledgeable in the science of fiction watching Star Wars can safely assume that: A) The rebel heroes can see the light of an explosion in outer space. B) The rebel heroes can hear the sound of an explosion outer...
  12. Z

    Rewrite of my assumptions. Was: Mistakes (again)

    [Moderator's note: no responsibility for the content. LM] This is an attempt to define a bulk which corresponds to both a string cosmological and brane cosmological formalism which disallows other branes that exist outside this universe. Our bulk is homogenous manifold similar to a Joyce...
  13. Z

    Rewrite of my assumptions. Was: Mistakes (again)

    [Moderator's note: no responsibility for the content. LM] This is an attempt to define a bulk which corresponds to both a string cosmological and brane cosmological formalism which disallows other branes that exist outside this universe. Our bulk is homogenous manifold similar to a Joyce...
  14. M

    Solve math equation without assumptions

    One mathematical sum is harassing me since a few days the problem is;:- a^2+b^2=25 and a^3+b^3=91. find the value of a and b. Now here we cannot take that into consoderation that as a^2+b^2=25 , a=3 and b=4. But we have to find the answer without any assumtions.May i please get the...
  15. W

    Designing a Small Ski Lift: Facts and Assumptions

    I'm planning on building a small ski lift for my kids. It's been 20 years since I've taken a physics class so I'm lucky to remember what gravity is. :blushing: Here's a poor image of the hill. I would like to know the following: A) how much lbs of tension is against the lift wire? B)...
  16. D

    Mathematics and unprovable assumptions

    I wasn't quite sure what I should call this, so I hope the tile is OK. Now over the weekend I've on on a general message board where I saw the ideas of mathematics and religion being discussed. The connection with religion is not what I'm interested here, but rather the following sentence...
  17. W

    How do hidden assumptions affect our understanding of mathematics?

    As much as I know (and please correct me if I am wrong) no fundamental mathematical systems like ZF or Peano axioms include an examination of our cognition's ability to count. In my opinion, if we ignore our abilities to count, then there is a reasonable chance that our fundamental axioms...
  18. S

    Trying to learn QED are my assumptions correct?

    When mass is constant, momentum is a function of velocity and velocity is a function of time. So would it be incorrect to say that the more precise your time measurement (or the smaller timeframe you are looking at) the more uncertainty in the position of the particle a la Heisenberg...
  19. T

    Maxwell Equations: What are all the assumptions used in derivation?

    [SOLVED] Maxwell Equations: What are all the assumptions used in derivation? I am trying to refute some of the theories of Tesla which are based on his idea that electromagnetic energy is also transmitted via a longitudinal wave. As far as I know Maxwell's equations do not support a...
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