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.

View More On Wikipedia.org
Recent contents Top users
  1. A

    Simplification assumptions in physics problems

    Hello, Recently, I had been looking at Physics problems, and Physics word problems to be more specific. My question is, are simplifying assumptions required in physics-math-related problems? Like, you must neglect air resistance because it is a simplifying assumption right? Is this true...
  2. kq6up

    Assumptions in Newton's Second Law

    With my understanding of Newton's second -- if I am going to use it to solve a problem, I would need to write ALL velocities in the system with respect to the lab frame (inertial rest frame) -- correct? Thanks, Chris
  3. DiracPool

    What Are the Doppler Effects Experienced by Alice and Bob?

    Thought experiment: Alice, Bob, and the planet Zolan. Alice is floating in space 10 light seconds from the planet Zolan (Z) with a radio emitter and detector. She and planet Z are in the same rest frame. Bob has the same devices as Alice but is on planet Z. Bob then accelerates from...
  4. Q

    Assumptions Built in to Solving Titration Equilibria?

    I'm trying to reach a more thorough understanding of what's going on when we calculate equilibrium concentrations and was wanting to understand more what assumptions we make in order to follow through with the calculations. Let me ask off of an example: Consider mixing equal amounts of NH3...
  5. A

    Assumptions in Mathematical Word Problems

    Hi there, Consider a related rates problem, Gas is being added into a balloon at a rate of dE/dt = x ft^3/sec Find the rate at which the radius is changing at time h. This is a completely false problem; I am just giving an example. My question is, How would you know if there is a...
  6. M

    Nonparametric bootstrap: Assumptions and number of bootstrap samples?

    I've been figuring out the use of the nonparametric bootstrap and if I understand correctly, this is the procedure: 1. Take an original sample, a vector x = (x1, ..., xn) 2. Generate k vectors, each called a 'bootstrap sample', of the same length as x by random sampling (with replacement)...
  7. J

    MHB Explaining Dimensions of Tanagrams Without Midpoint Assumptions

    I am currently working on an assignment using Tanagrams. I have the information that I have: • 2 large, and congruent, isosceles right triangles • 1 medium isosceles right triangle • 2 small, and congruent, isosceles right triangles • 1 square • 1 parallelogram The pieces can be...
  8. A

    Why Should You Avoid Assumptions in Math?

    So I started my first ever university course, at U of T. (It's a summer course.) The class textbook, which is called "An Introduction to Proofs and Problem Solving", should give you an idea of what the class is about. Anyway, the first thing that my Professor taught us is that you should never...
  9. S

    Explanation of Axioms, First Principles, and Assumptions

    College sophomore here and just wanted to ask for an explanation of terms that I have come across in my math and philosophy courses thus far, but without direct teaching of them. I've seen these terms used in forum discussions and mentioned off-handedly by profs., but don't have a specific...
  10. S

    Want to understand ke formula without having to accept any assumptions

    To prepare for a future physics course, I googled Newton’s Laws and then found about the Work Energy Theorem. I can see how Newton’s Laws makes sense but I don’t get why the kinetic energy formula is correct. The only experiment for the Work Energy Theorem I can find does not meet the...
  11. D

    Verify Is Math Correct? Assumptions Correct?

    Can someone please tell me if I have solved the problem? Is the math correct? Were the assumptions correct? Thank you in advance Homework Statement Show that: I(B) = 44 uA I(C) = 4.4 mA V(CE) = 1.2 V...
  12. S

    Least squares assumptions: finite and nonzero 4th moments

    This isn't a homework problem - I'm just confused by something in a textbook that I'm reading (not for a class, either). I'd appreciate an intuitive clarification, or a link to a good explanation (can't seem to find anything useful on Google or in my textbook). My book states that one of the...
  13. B

    Kinetics Assumptions: Approximations & Equilibria

    I would like to understand under what circumstances rate laws can leave out rate terms from certain reactions, in general, as a process of approximation. I am familiar with the basic method regarding the steady-state approximation already. Any books, websites or articles which are good or...
  14. bohm2

    Questioning assumptions behind Bell's and related theorems

    I have trouble understanding the mathematical arguments behind this view but I thought I would post it, in case anybody has any information/understanding/insights. The basic idea is that the mathematical assumptions on which the validity of Bell's inequality depends are that all the random...
  15. L

    Assumptions about particular solutions

    Hello, Working through some reduction of order problems. I'm not sure about why the structure of a particular solution is assumed. Here's what I mean: Given y"-4y = 2 and a known solution is e^-2x, use reduction of order to find a second solution and a particular solution. Using a...
  16. S

    Analyzing Assumptions for Neutron Flux: Fast & Thermal Groups

    Assumptions 1) a=absorption 2) f=fission 3) ∅=neutron flux 4) time independent 5) group 1, fast neutrons 6) group 2, thermal neutrons 7) All fission neutron are boring in fast group 8) All neutrons created by thermal group, thus vƩf2 exists vƩf2 does not 9) Down scattering occurs but up...
  17. Philosophaie

    Metrics for the Sun & Earth: Rs & Assumptions

    Is there a Metric for the Sun and Earth other than the Schwarzschild Metric who has the Schwarzschild Radius on the interior of the body? What are the assumptions that turn that from GR to Newtonian? Rs(Earth)=8.87*10^-3m Rs(Sun)=2954m
  18. W

    Assumptions of Griffith's fracture theory

    Any experts on Griffith's fracture theory? I am studying the subject and I am having hard time finding out if the theory is valid for all possible initial crack lengths. I have heard from pretty reliable source that we must assume small crack length compared to the macroscopic length of the...
  19. F

    What Are the Fundamental Assumptions of Modern Physics?

    It seems to me that classically physics is based upon the idea of measurement, that the length of a meter, the duration of a second, and the mass of an object is the same for one person as it is for another. Wheeler in his Geometrodynamics further was able to express mass and time in terms of...
  20. J

    Exploring Infinity: The Proof and Assumptions

    The proof that 1/2+1/4+1/8+...=1 goes like this: X=1/2+1/4+1/8+... 2X=2/2+2/4+1/8+... 2X=1+1/2+1/4+... 2X-X=1+(1/2-1/2)+(1/4-1/4)+... X=1 The assumption that goes with this is that we can pair up the first term of X with the second term of 2X and so on without having the smallest term of...
  21. N

    Question on assumptions made during variation of parameters

    I was recently trying to prove the variation of parameters formula for an nth degree equation, and I have come up with a question about the assumptions made during the derivation. During the derivation we assume that: u1'y1(k) + u2'y2(k) + . . . + un'yn(k) = 0 for k < n-1. It leads to the...
  22. N

    FreeFall motion Assumptions in proving

    Homework Statement a stone is thrown vertically upwards with a speed of u metres per second. a second stone is thrown vertically uppwards from the same point with the same initial speed but T seconds later than the first. prove that they collide at a distance (4u^2-g^2T^2)/(8g) metres above...
  23. P

    Clarifying the Redundancy of Assumptions in Theorem 4.12

    I attached the problem and its solution. I was looking at this solution and got a little confused. Why did they say that "Assume that S = {v1, v2, · · · , vn} is a basis for V and c is a nonzero scalar. Let S1 = {cv1, cv2, · · · , cvn}. Since S is a basis for V , V has dimension n. Since S1...
  24. M

    Why are the coefficients of the Landau theory Taylor expansion even?

    Assume that we can expand the Helmholtz potential about T=T_c, M=0 in a standard Taylor series form of functions of the variables, A(T,M)=\sum^{\infty}_{j=0}L_j(T)M^j=L_0(T)+L_2(T)M^2+L_4(T)M^4+... Why A(T,M) must be even function of M? Coefficients can be expanded about T=T_c...
  25. M

    Assumptions about arrival independence

    Hi How to be mathematically correct about assumption of independence about arrivals of clients at a bank? Physically I understand that there is no possible dependence between2 sequent arrivals of clients but anyway when I make this assumption I want to be correct according literature...
  26. M

    Newton's Second Law assumptions

    Hi people Newton's Second Law a=F/m assumes that either a body is pointlike or that force is transmitted instantaneously across it. Special relativity which applies to Newton's First Law and which was developed from the assumption of a finite velocity of energy transmission, has enjoyed...
  27. C

    Radiation Assumptions: Understanding Multipole Moments & λ

    Hey I'm taking a course which involves electrodynamics and i am currently reading about radiation. By expanding the relative distance between the current distribution r' and the point we're looking at r in a powerseries and assume that r' << r for all r' and r we obtain the vector potential...
  28. I

    Enthelpy equations with pressure/volume assumptions

    I'm trying to learn the various equations of enthalpy with certain assumptions, but I couldn't understand where they came from. So, I tried to derive them myself, but now I'm lost beyond reason. I'm getting confused between the various forms of the enthalpy equation, depending on constant...
  29. B

    Dimensional Analysis justifying assumptions and force dependent on angle

    Homework Statement i have attached a copy of the full question and my answer to part a (i'm stuck on part b which i have written below. The diagram is a bit too complicated to describe in words) In an examination of this problem Edge (1968) assumed one-dimensional inviscid, incompressible...
  30. E

    Mathematica Mathematica Assumptions for integration [pertaining to loop corrections]

    Long story short I have an integral which is something like this: (in Mathematica code) Integrate[1/{(1 - b^2)*{((1 - y)*z + y)^2 + (1 - y)^2*(1 - z)^2} + 2*(b^2 + 1)*{(1 - y)*(1 - z)*((1 - y)*z + y)}}, {y, 0, 1} ] Written without assumptions. b is actually only in [0,1] and I think I...
  31. tom.stoer

    Assumptions for derivation of Plancks' law

    What are the most general assumoptions for the derivation of Planck's law in quantum statistical mechanics: - thermodynamical equilibrium - non-interacting bose gas (photons) Do I miss anything?
  32. M

    Is Constant Velocity Assumed in Work-Energy Problems?

    It's been a while since I've done any work-energy questions, and I just noticed how vague some questions could be (or maybe I don't understand it that well). Anyway, suppose I have a box moving down an incline where the only forces acting on it are its weight, the normal force, and friction...
  33. N

    Martingale problem: help writing and equation using the martingale assumptions

    Hi, I have been given this problem and the solution however, neither make sense to me. x_t=\int exp(t-s)E(k_s|F_t)ds (the integral is from t to infinity) where k_u=m^d_u-(m^d_u)^*-α(y_u-y_u^*) for all u>0 suppose (m_t, t>0) is a martingale, what is an equation for x_t using...
  34. Y

    Debye's Assumptions For Heat Capacity

    What are the Debye model`s assumptions for heat capacity or density of states? According to the einstein model we assume that N oscillators of the same frequency [ω][/o] and in one dimention. In three dimention N is replaced by 3N, there being three modes per oscillator.
  35. P

    Binomial Distribution - Assumptions

    Hi, An airline knows from past experience that the probability of a person booking a seat and then not turning up is 0.04. A small plane has 50 seats and 55 bookings are made. a) A binomial distribution is used to model this situation. What assumption must be made? Comment on how...
  36. C

    K system proof - writing proof for p and q without assumptions

    Homework Statement I'm having some issues coming up with a proof for |- (Box(P) ^ Box(Q)) -> Box(P ^ Q). Box is the unary operator for "necessary for". Homework Equations Axiom 1 A -> (B -> A) Axiom 2 (A -> (B -> C)) -> ((A->B) -> (A -> C)) Axiom 3 (~a -> B) -> ((~A -> ~B) -> A)...
  37. S

    How to set assumptions in matlab

    Homework Statement I want to know how to set assumptions in Matlab. i want to integrate 3*a*x/b but i want to tell MATLAB that b is less than a. Homework Equations The Attempt at a Solution I know how to set assumptions that a variable is real/nonreal/positive/negative. eg...
  38. T

    Falsity of assumptions question.

    In the course of proving that \sqrt{3} is irrational, I had another question pop up. To prove that \sqrt{3} is irrational, I first assumed 2 things: \sqrt{3} is rational, and the rational form of \sqrt{3} is in it's lowest form. I then broke the proof up into cases and showed that none...
  39. R

    Can Realistic Assumptions Help Design an Efficient Air Acceleration System?

    I came up with my own design problem, after completing a refrigeration design problem on the completion of my thermo I class. My design problem is this: I want to accelerate air to 56m/s via a compressor and then a nozzle. I'm trying to do a cost analysis of how much power I would save if the...
  40. B

    Birthday Problem with Realistic Assumptions

    Hi, All: The standard way of approaching the birthday problem, i.e., the problem of determining the number of people needed to have a certain probability that two of them have the same birthday, is based on the assumption that birthdays are uniformly-distributed, i.e...
  41. N

    Exploring Griffiths' Assumptions on Current & Charge Distribution

    I will refer to Griffiths' textbook Introduction to Electrodynamics, Third Edition. On page 70 he calculates divergence of E and implicitely assumes that divergence of rho is 0, where rho is charge density distribution. On page 223 he calculates rotB and says that rotJ = 0, where J is current...
  42. G

    Find dF/ds in Terms of u, v & w - Conditions and Assumptions

    Hi! As a part of a mathematical construction I used the rate of change of F(s) with s, i.e. dF/ds. F and s are smooth functions. The problem is that s(u,v,w) is a function of u, v & w and actually I need to find the rate of change of F with respect to u, v & w. The question is: what does...
  43. S

    Exploring Black Body Assumptions for Deriving Spectrums

    To derive the blackbody spectrum, we set up the situation by assuming that a cavity is in thermodynamic equilibrium with a heat bath. My questions are: 1) Is the heat bath the black body? 2) Why is it called a blackbody? 3) Why does the cavity have to be in thermal equilibrium with...
  44. R

    Levi-civita connection assumptions

    In a lot of textbooks on relativity the Levi-Civita connection is derived like this: V=V^ie_i dV=dV^ie_i+V^ide_i dV=\partial_jV^ie_idx^j+V^i \Gamma^{j}_{ir}e_j dx^r which after relabeling indices: dV=(\partial_jV^i+V^k \Gamma^{i}_{kj})e_i dx^j so that the covariant derivative is...
  45. G

    Linear Elastic Analysis w/ Abaqus CAE: Truss Structure Assumptions

    In a linear elastic analysis using Abaqus CAE what assumptions does abaqus make of a simple truss structure. Cheers Gordon
  46. P

    Solving Homework Equations with Air Standard Assumptions

    I usually try to avoid asking how to do entire question sets, but I'm officially at loss at the moment. I need a point in the right direction. Homework Statement I have a ramjet that has a velocity of 2500 km/h, pressure is 40 kPa, and temperature is 240K Head addition is 1080 kJ/kG Velocity...
  47. G

    Ideal Gas Assumptions: Can it Turn into a Liquid?

    I was wondering if it assumed the gas could not turn into a liquid?
  48. D

    Exploring Math and Assumptions in Our World

    So lately I've been digging into geometry and I always seem to come back to the same question, how can we really test to make sure our math values can correctly apply to world that we live in? First, let's assume that we live way back in time and our scale of measurements where limited (for...
  49. M

    Assumptions behind the OLS regression model?

    Hi, In many statistics textbooks I read the following text: “A models based on ordinary linear regression equation models Y, the dependent variable, as a normal random variable, whose mean is linear function of the predictors, b0 + b1*X1 + ... , and whose variance is constant. While...
  50. D

    What Are Bohr's Major Assumptions for Hydrogen Atomic Spectra?

    What are the major assumptions made by Bohr to explain atomic spectra from hydrogen? I had this on a test last week and was just wanting to know the answers. I was not required to answer it but am worried I will see it again. I looked through the book and can't find anything that is...
Back
Top