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. S

    Use of calculus in a launch of a rocket - Relevant Assumptions

    I know that we have to assume certain things for the math to be achievable (at my level). for instance, I assumed that the rocket goes in a straight line instead of orbiting around the earth at an angle. but I can't develop any further assumptions as the task is so generalised and open-ended...
  2. M

    Assumptions for string vibrator system

    For this, Is it possible to calculate the time it takes for the initial antinode at the string vibrator to become a node in the transient phase of the system? Also do we assume that once the system has reached steady state, that the mass has such a large inertia that it is stationary so acts as...
  3. Jarvis323

    A Hidden Assumptions in Bell's Theorem?

    There has been a lot of discussion on Bell's theorem here lately. Superdeterminism as a Bell's theorem loophole has been discussed extensively. But I have not seen discussion about Karl Hess, Hans De Raedt, and Kristel Michielsen's ideas, which essentially suggest that there are several hidden...
  4. Arne

    I Assumptions about the convex hull of a closed path in a 4D space

    Hello everyone, I am struggling to get insight into a certain set in 4D space. Given is a closed path in 4D-space with constant Euclidean norm $$\vec{\gamma} (\theta):[0,2\pi]\to\mathbb{R}^4, \ \ \vec{\gamma}(0)=\vec{\gamma}(2\pi), \ \ ||\vec{\gamma}(\theta)||_2 = \mathrm{const.}$$ I am looking...
  5. B

    Checking assumptions in boundary conditions of double well system

    The idea here (as I'm told) is to use the boundary conditions to get a transcendental equation, and then that transcendental equation can be solved numerically. So I'm making a few assumptions in this problem: 1. The potential ##V(x)## is even, so the wavefunction ##\psi(x)## is either even or...
  6. A

    A What assumptions underly the Lorentz transformation?

    The Lorentz transform for velocities is as follows: $$u=\frac{v+w}{1+\frac{vw}{c^{2}}}$$ But which assumption exactly underlies this so that you get exactly this formula and not any other formula with approximately the same properties?
  7. gentzen

    A Dieter Zeh's MWI as Schrödinger equation + further assumptions

    Sorry for derailing that discussion even further. My reference to Dieter Zeh's German book was unlucky, not just because it is not a peer reviewed paper, but also because I did not remember the exact place with the remark. Since this has bothered me since a long time anyway, I now searched the...
  8. G

    A What assumptions underlie the proof that singularities are inevitable?

    Poking around on the internet has not helped me. Penrose references Hawking and his 1996 book and I have ordered that, but I suspect my progress through that book will be slow. I have read that the assumptions include an energy condition, which I assume is expressed as a restriction on the...
  9. Killtech

    I About non-observable assumptions

    From a discussion about completeness of QM i picked up some people having the weird idea that theories shouldn't model things that are not observable. This is bewildering as this is a very common practice in physics and the opposite can be extremely tricky to achieve. But it made me contemplate...
  10. C

    I Assumptions for blackbody spectra vs. emission spectra vs. absorption spectra

    Hi there, I am a physical oceanographer teaching an introductory undergraduate Earth science class that has a unit on astronomy. I have a physics undergraduate background, took a few astronomy classes at the undergraduate level back in the day, and did a bit of undergraduate research in...
  11. C

    Chemistry Assumptions made when doing calorimetry / errors that occur

    I just know that one assumption is that the specific heat capacity of water (as the surrounding) stays the same (or the change in its heat capacity is negligible). Please Help me with the rest.
  12. Demystifier

    A Assumptions of the Bell theorem

    Loosely speaking, the Bell theorem says that any theory making the same measurable predictions as QM must necessarily be "nonlocal" in the Bell sense. (Here Bell locality is different from other notions of locality such as signal locality or locality of the Lagrangian. By the Bell theorem, I...
  13. T

    I Differentiability assumptions of Wirtinger derivatives

    In defining the Wirtinger (aka Cauchy-Riemann) linear operators, often used in signal analysis and in proofs of complex derivatives and the Cauchy-Riemann equations, one assumes differentiability in the real sense. This assumption is usually seen as obvious in the complex analysis setting...
  14. E

    Modelling assumptions when friction is involved

    Whenever friction exists within a mechanics problem, there must be some dissipation of mechanical energy into thermal energy. However, I'm not sure how we determine which bodies can or cannot possesses thermal energy. Suppose we consider the case of a block sliding down a rough wedge, which is...
  15. NTL2009

    Electrical Please double-check my thermal dissipation assumptions

    BACKGROUND, skip if you want: I'm repairing the amps (2) and power supply for a 1970's era Rhodes Electric Piano (for my local HS music depart). Since this is a classic instrument, I found plenty of info, so the rebuild went well, but I'm curious about one thing, and want to check my...
  16. Pencilvester

    I Lorentz Transformation Derivation: Assumptions Req'd?

    In deriving the Lorentz transformation, is it required to assume that the transformation to get from coordinate system ##\bf {x}## to ##\bf {x’}## should be the same as that to get from ##\bf {x’}## to ##\bf {x}## (with the simple correction of flipping the velocity)? If no, could someone...
  17. Clara Chung

    Question about hydraulic jump assumptions

    Sorry for the poor image... A better picture can be viewed here https://www.dropbox.com/s/uyi01l27vu2fwyw/96.png?dl=0 I don't understand the assumption in the red box... If I don't ignore the atmospheric pressure, F_1 = integrate from 0 to h_1 (ρg(h_1-z)+p_a)dz = 1/2 ρgh_1^2 + p_a*h_1, similarly...
  18. W

    I Assumptions made in stationary-state scattering

    Hi all, I recently started learning about quantum scattering in school and came across a few things I find confusing. Thanks in advance for any assistance! 1. Plane wave approximation to incident waves. In past QM courses, I kept reading that plane waves were not "physical" since they do not...
  19. M

    Assumptions in the derivation of the kinetic theory of gases

    When deriving the kinetic theory of gases, we take the change in momentum of a particle as it hits one side of a box and divide it by the time over which the collision takes place. The time is derived by taking the total distance the particle traveled in the box (i.e. from one end, off the side...
  20. P

    Assumptions made when deriving the speed of light

    Homework Statement The problem I have been working with recently has been deriving the speed of light using maxwells equations, however in order to do this I must make two assumptions; there is no net charge or displacement currents in the space in which I am attemptin to derive the speed of...
  21. Dadface

    I QM Assumptions Regarding Entanglement Properties

    In a nutshell I think that in local realistic theories it is assumed that: Each entangled object has definite properties at all times, even when not observed. I know the assumption is proved to be incorrect but is that an assumption actually made in such theories?But what assumptions about...
  22. anorlunda

    Insights The What and Why of Circuit Analysis Assumptions - Comments

    Greg Bernhardt submitted a new PF Insights post The What and Why of Circuit Analysis Assumptions Continue reading the Original PF Insights Post.
  23. M

    I Panel study, multiple linear regression, assumptions

    Hey. I am doing a project where I am studying a set of companies over a 7-year period. I am doing a multiple linear regression analysis either with fixed or random effects (so, it's a panel study). What I am wondering is if the general assumptions/requirements apply when using the fixed/random...
  24. T

    Did i calculate the V/A/R of a plasma arc properly?

    Hello there! So i am currently sitting in my EME class and have nothing to do, so i decided to try spit-balling the V/A/R of the plasma arc my Tesla Lighter produces. note that i did not physically take it apart, and my goal was just to get a rough estimate for the arc itself or at least get a...
  25. F

    I A question about assumptions made in derivation of LSZ formula

    I've been reading through a derivation of the LSZ reduction formula and I'm slightly confused about the arguments made about the assumptions: $$\langle\Omega\vert\phi(x)\vert\Omega\rangle =0\\ \langle\mathbf{k}\vert\phi(x)\vert\Omega\rangle =e^{ik\cdot x}$$ For both assumptions the author first...
  26. Cocoleia

    Why is it not possible for D2 to be off in this diode problem?

    Homework Statement I am working on this problem, where I need to find I and V Homework EquationsThe Attempt at a Solution I know the right answer will be when D1(left) is off and D2(right) is on, we went over the solution in class. I wanted to do the 4 assumptions just to try to understand. I...
  27. G

    A Assumptions behind Maxwell's equations for constant speed

    I need some help in defining what are the assumptions needed to derive a constant speed of light from Maxwell equations. Is it correct to say that this result applies to a sinusoidal wave as an assumption? In my understanding that is (more or less) equivalent to planar waves in vacuum: is it...
  28. Mayan Fung

    Fundamental assumptions of statistical mechanics

    The assumption states that all states (or I shall say micro-states) are equally probable. This is the foundation where we construct our theories on entropy, different kind of distributions, etc. Is there any explanation for this assumption? Or why did the scientists that time take this...
  29. S

    Turbine Work - Can I assume ideal gas?

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  30. C

    What is wrong with our assumptions?

    [Moderator note: Thread moved from technical forum so no template shown] I am trying to do a simple experiment that estimates the mass of an object based on how an Atwood machine reacts when it is added to one side. For this experiment we have a pulley with 200-gram masses on either side of...
  31. J

    Solving Unsteady Problems in Mechanical Engineering

    Hello all, I am recently graduated in mechanial engineering and started working and so I don't have much experience yet. I have to deal with an unsteady problem. Now in the textbooks a lot steady assumptions are made and so these relations are not really valid for my problem. This is maybe a...
  32. A

    I Can MANOVA still be used with violated assumptions?

    For my bachelor thesis I need to perform a MANOVA to compare two groups (N of group 1 is 80 and N of group 2 is 68) on 16 dependent variables. I checked the different assumptions and two of them were violated. The first one being the Univariate Normality for almost all dependent variables. Also...
  33. O

    The conditions and assumptions for the Antoine equation?

    Homework Statement Derive the basic relationship that the Antoine equation represents. Most importantly, explain the underlying condition when the Antoine equation applies and the underlying assumptions for the Antoine equation to be valid. Homework Equations Clausius-Clapeyron Equation...
  34. R

    I Relativity: Coming to Terms 1: Starting Assumptions

    Coming to terms with the theory of relativity is a long and difficult process that requires shedding all the popular misconceptions and hype surrounding the subject matter. Science doesn't sell but throw in carefully worded claims of time travel, matter materialization, shape shifting and...
  35. DavideGenoa

    I Differentiating twice under the integral (with assumptions)

    Let ##k:\mathcal{O}\times\mathbb{R}^n\to\mathbb{R}##, with ##\mathcal{O}\subset\mathbb{R}^m## open, be such that ##\forall x\in\mathcal{O}\quad k(x,\cdot)\in L^1(\mathbb{R}^n) ##, i.e. the function ##y\mapsto k(x,y)## is Lebesgue summable on ##\mathbb{R}^n##, according to the usual...
  36. jdawg

    Thermodynamics: Dead state assumptions

    Homework Statement Im having a little trouble with knowing what to assume for the dead state! In the question that I posted, I don't understand how they knew to assume that the water in the system is a super heated vapor? Or how they knew that the dead state is a compressed liquid? Homework...
  37. redtree

    A Assumptions of the Schwarzschild solution to the EFE

    Given that no assumption is of a point energy is necessary to derive the vacuum (Schwarzschild) solution to the EFE, why is the solution assumed to apply to spacetime surrounding a point energy?
  38. zonde

    Eberhard assumptions and FTL communication

    In this paper http://dx.doi.org/10.1103/PhysRevA.47.R747 Eberhard derives Bell type inequality from these assumptions: A theory is defined as being "local" if it predicts that, among these possible sequences of events [with the same number of events N], one can find four sequences (one for each...
  39. Lagraaaange

    Assumptions of Kinetic Theory: How big should a cubical element be?

    Homework Statement Assuming uniform distribution. What must be the size of a cubical element of volume in the container so that the number of particles in each volume element may vary by 0.1% when the gas is as standard conditions. Probable deviation is given by N^(1/2) where N is the number of...
  40. Math Amateur

    Mathematica Mathematical Logic - Dandah symbol for discharging assumptions ....

    I am reading the book Mathematical Logic by Ian Chiswell and Wilfred Hodges (C&H) ... and am currently focused on Chapter 2: Informal Natural Deduction ... I need help with what C&H call the 'dandah' or more specifically symbols with a dandah through them ... The relevant text in C&H...
  41. L

    Constant and variable specific heat assumptions

    1. Homework Statement A gas (treated as air) powered turbine provides power to a compressor which then sends the compressed air through an intercooler (heat exchanger). Turbine: Gas enters @ 0.03kg/s, 370 degrees Celsius Gas leaves @ 300 degrees Celsius and a "lower pressure" Compressor...
  42. F

    Finding lens diameter - German physics task

    Hey everybody, I'm right now trying to solve a question I found in a German physics competition 2006 concerning the diameter of a thin camera lens. I'm not able to find a solution, since there is basically nothing given. Here the task (I underlined phrases which might be important): A ruler...
  43. Derek Potter

    The Assumptions of MWI Everett's Relative State Formulation

    Everett created the Relative State Formulation in order to resolve the contradictions, as he saw it, of QM. He introduced his doctoral thesis by stating that conventional QM works perfectly well - it predicts quantum statistics. However, interpreting conventional QM realistically leads to...
  44. H

    Approximating Magnetic Field for Spinning Disk with Large Distance from Center

    Homework Statement I am asked to show that B = \frac{\mu_0Q\omega}{2\pi R^2}[\frac{R^2+2x^2}{(R^2+x^2)^{1/2}}-2x] simplifies to this B \approx \frac{\mu_0}{2\pi}\frac{\mu}{x^3} if x>>R where \mu is the magnetic dipole moment for a disk spinning with angular velocity \omega, which is \mu...
  45. D

    Assumptions of exponential smoothing

    What are the assumptions of exponential smoothing? For example, should autocorrelation of the data be low in order for the exponential smoothing model to be valid, should the process be stationary, etc?
  46. M

    Kochen-Specker Theorem Assumptions

    I read over a high-lever description of this theorem (http://en.wikipedia.org/wiki/Kochen%E2%80%93Specker_theorem) and was wondering how reasonable the assumptions are. Specifically, is it reasonable to assume that the value of a sum of observables is the same as the sum of the values of the...
  47. A

    Assumption on central forces between two particles

    Homework Statement Consider Newton’s force law for two particles interact through a central force F12(r1',r2',u1,u2), where by Newton’s third law F12 = -F21. m1(d^2r1/dt^2) = F12(r1,r2,u1,u2) m2(d^2r2/dt^2) = F21(r1,r2,u1,u2) A. Show that Newtonian mechanics is form invariant with respect...
  48. C

    Assumptions in dark-energy density parameter measurement

    I've understood that the main evidence for a non-zero ##\Omega_\Lambda## comes from supernova 1a measurements where one measures the redshifts along with the luminosity distances (equivalently magnitude) of the supernovae and, plots them against each other, then compares the result with...
  49. C

    Calculating Gravity of a New Planet with a Gas Atmosphere - Homework Solution"

    Homework Statement A space-probe discovers a planet with a gas atmosphere, detects a non-zero value for speed of sound 60km relative to the surface of the planet. It measures a surface temperature of -5 degrees C and an average atmospheric molecular mass of 38 x 10 ^ -27kg. Find G_p the...
  50. T

    Clarification of Onderdonk's Fuse Equation Assumptions

    Hi all, I am trying to get an understanding of Onderdonk's Fuse Equation: ##I_{fuse}=Area*\frac{\sqrt{log\left(\frac{T_{melt-T_{ambient}}}{234-T_{ambient}}+1\right)}}{33*Time}## Empirically I do not see that this function accurately depicts the behavior of the wires I am using. For example, I...
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