What is Statistical: Definition and 655 Discussions
Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.
Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.
A standard statistical procedure involves the collection of data leading to test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual relationship between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.
Homework Statement
We know that after long run of simple mass-spring system, there should be a probability of finding the mass at certain points between -A and A.. Obviously in probability of finding the particle near A or -A is higher than finding the particle at 0, because the speed is the...
I was looking at a research paper the other day. In the paper they described some of the results from an experiment. They looked at two of the variables recorded in the experiment, mass and velocity. They looked at mass independently. First, they took the median of the mass. They then had two...
Hi, I need assistance in performing statistical checks in MCNP5 i.e print table 160. I am not sure where the PRINT card should be placed and the format of it. I am using F4mesh tallies
Is it accurate to say that interference cannot happen in Statistical Mechanics? I know it is considered a wave mechanics phenomenon but aren't waves just highly statistical ensembles, like anything else?
I always thought that Fourier says periodic spectra could be summed to create any signal...
Can someone recommend me some good textbooks or articles that contain or focus on statistical thermodynamics and/or oscillatory motion (preferably with advanced math, not just stories)?
I want to find photon energy distribution, let's say in a closed cube box,there are 100 photons(suppose 1 photon contains 1 Joule),and there's a mirror on left side and then there's a glass in between and the right side is completely black. I want to find photon energy distribution(like how much...
Hello everybody.
I've recently finished work through Weinberg's course in QFT which made my understanding of theoretical physics quite peculiar. For example, I can't understand statistical physics from Landau&Lifshitz book at all as there are a lot of unfounded arguments. I wonder firstly is it...
Consider the quote ''The macrostate which corresponds to the highest number of microstates which result in that macrostate, is the state which will be observed.''
Can someone specify in which context this is correct because I'm quite confused by it. If I have an isolated box with N particles in...
My job requires me to update excel reports and also send out analysis and summaries. My concern is, I don't really have a lot of experience with statistics, numbers analysis, or have enough background to know what type of tools are available for me.
For example, let's say I send out a weekly...
Hello!
I am a master student, and I am about to start working on my master thesis, which, in my counrty, is a substantial work of 6 months which usually involves original research.
I will be supervised by two professors of Statistical Mechanics, who have many research interest. In these days...
There are some applications of thermodynamics in engineering which I don't bother to talk about. What I want to ask is, are there any problems in engineering for which thermodynamics is not enough and people have to use statistical mechanics?
Thanks
When dealing with cosmological perturbations, there are a lot of different notions that are thrown around in the literature like statistical homogeneity and isotropy. However, these terms are often not motivated and clearly defined.
Could anyone recommend any good references where these notions...
So I have just been reading up on statistical thermodynamics and have no idea why the bose-einstein, fermi dirac and maxwell boltzman are all integers, that makes sense, but then when you make the degenerate correction to the maxwell Boltzmann by dividing by N! we get decimal answers. Why is...
Homework Statement
A simple model for liquid crystals confined to 2 dimensions is o assume each molecule can only align in one of 2 perpendicular directions. To construct a landau model its convenient to define order parameter, s :
s = 2 ( Np - 0.5Nt ) / Nt
Np - number molecules...
I'm enjoying Lennard Susskind's lectures on Statistical mechanics. I've briefly studied this material before, but I've learned a lot about more practical calculations from these lectures: he's used the partition function to derive all sorts of fun expressions, and to analyse the ideal gas and a...
Hey guys,
I've never studied this subject before (except basic thermal physics in high school), and I have a course on it this semester. I'm in a semi international program, and this course isn't taught in English (but the tutorials are, thankfully), so I will need to study on my own.
In...
Hey guys, I've been looking up on the web and couldn't find prerequisites for graduate level statistical mechanics. What would be the mathematics/physics background needed for the course? Would I need undergraduate statistical physics first?
As always, thanks in advance!
Homework Statement
A mixture of two substances exists on a cubic lattice of N sites, each of which is occupied by either an A molecule or a B molecule. The number of A molecules is NA and the number of B molecules is NB, such that NA + NB = N. The energy of interaction is k_BT\chi_{AA} between...
I should have studies statistics in school.
I have been collecting some trip data from you commute to and from work, and I want to determine what factors are influencing trip duration. There are multiple factors, which I cannot easily isolate.
The factors I'm most interested in are:
- duration...
Hello all!
I'm hoping you will be able to direct me to sources of raw income1 / employment data. Hopefully this thread can be a help to others who have similar needs in the future, as well.
(I did a quick search for a similar thread and didn't find anything - please correct me if I'm wrong.)...
Fundamental assumtption:
"a closed system is equally likely to be in any of its g accessible micro- states, and all accessible micro- states are assumed to be equally probable."
There's just a few things I don't understand about this,
1. Isn't saying that a closed system is equally likely to...
Hello, I am wondering if anyone would be able to guide me through a practice question for an upcoming test. I am not feeling very confident at this point and would very much appreciate some help!
The question is as follows;
Let {X}_{1},{X}_{2}…, {X}_{n}and {Y}_{1},{Y}_{2}…,{Y}_{m} be two...
I don't think I've fully grasped the underlying ideas of this class, so at the moment I'm just sort of flailing for equations to plug stuff into...
Homework Statement
Show that in the mean field model, M is proportional to H1/3 at T=Tc and that at H=0, M is proportional to (Tc - T)1/2...
Homework Statement
Show that the number of photons in equlibrium at tempertaure t in a cavity of volume V is,
N=[2.404 V (t/ħc^3]/Pi^2
The total number of photons is the sum of the average number of photons over all modes n->∑<s>
Homework Equations
n=Sqrt[nx^2+ny^2+nz^2]
ωn=(n Pi c)/L...
I have access to this book at my uni's library. I'm considering to learn from it as my main source.
Is it severely outdated?
How good is it for learning statistical mechanics?
Homework Statement
1.) For N particles in a gravity field, the Hamiltonian has a contribution of external potential only (-mgh). Show that the particle density follows the barometric height equation (1).
2.) For N particles in a open system at constant pressure p and temperature T, let there...
It is well known that quantum mechanics in the path-integral form is formally very similar to equilibrium statistical mechanics formulated in terms of a partition function. In a relatively recent, very readable and straightforward paper
http://lanl.arxiv.org/abs/1311.0813
John Baez (a well known...
Hello,
This is more a question about history of science in general.
During my lectures on statistical physics, I noticed that some of the problems that Bolztmann faced lead to the introduction of:
##h/2\pi## (to introduce the unit of an action leading to a "unitless" partition function) which...
Hello everyone! :)
I am studying for an honours course in Statistical Physics. I have stumbled upon the book "Statistical Mechanics of Phase Transitions" by J.M. Yeomans. The layout of the book, as well as information, is exactly what I need. I want to work through the problems and was...
I am planning to take a course on Statistical Physics in my university. The main text to be followed is Statistical Physics by F. Reif. As of now, I have completed university level courses on Calculus, Differential Equations, Linear Algebra. What other knowledge would be required to help me get...
It seems like two main applications of statistical mechanics in academia research include the application to solid mechanics/materials and the application to heat transfer. How do statistical mechanics and thermodynamics differ in these two aspects? Is it basically the same theory applied to...
Dear Physics Forum personnel,
I am a undergraduate sophomore with double majors in microbiology and chemistry. I have been involving in two research laboratories: theoretical physical chemistry (focused on inorganic chemistry & solid-state physics) and pathogenic bacteriology. I actually...
Hi,
I need to calculate the ratio of statistical weights of the final state to the initial state of Cl2
Is there any formulas or tabulated data?
Thank you in advance
See image.
I have to present this on Monday and don't really know what I'm doing having missed a couple of lectures through illness. Any help or hints would be very much appreciated.
Thanks,
TM
Homework Statement
Consider a chain with N >> 1 segments of length 1. One end of the chain is at the origin, the other at a point R. In this onedimensional model the segments may face left or right. The number of segments facing right is n.
1: What is the number of possible configurations in...
This is an exercise from an old examination that I am trying to understand by following the given solution to this problem. The exercise is about to calculate the four spin average <SiSjSkSl> and the indices i,j,k and l, given a Hamiltonian H.
Solution:
The problem is that i can't follow the...
Suppose we have a random service time ##T## with residual service time ##R## observed at some point along the way.
What is the correct way to call ##T## (in 1-2 words, without having to introduce ##R##) if:
1) For any observation time, ##\mathbb{E}R\leq\mathbb{E}T##?
2) For any observation...
Homework Statement
Hello, I tried to solve a problem on my own and then I looked up a solution on the web, and I realize that it seems that I goofed. The problem statement can be found at http://www.hep.fsu.edu/~reina/courses/2012-2013/phy5524/homework/solutions/hw5_sol.pdf (Problem 1, part...
Homework Statement
I am trying to solve a problem but I am confused on what's going on with an approximation.
I have to find the pressure in function of V, T and N of an ideal gas using the partition function, then obtain the chemical potential in function of T, p and N and I must graph it in...
Good day,
I'm starting my master in physics, and it's time for me to choose my courses. I've decided that I probably want to pursue the direction of quantum information processing, and I'm trying to pick my courses with that in mind. For my first semester I'll be taking four courses: Quantum...
Hello,
I am having trouble understanding collision frequency in following discussion from Kubo,
$$collision\ frequency = \frac{1}{\frac{l}{v_{x}}}=\frac{p_{x}}{ml}$$
What am I missing ?
I'm currently in a physics grad program and am interested in doing research where statistical analysis is involved by using R or SAS. What fields of physics research relies on this the most? Should I look into theory, computational, or experimental groups? Or perhaps observational astronomy?
I want to know which statistical method to use for the below problem.
Suppose I have the revenue data of 5 companies in the same industry. And, also the market share of the industry. I calculated the ratio of all against each other. Now, with the above calculation, i want to find out which among...
hi pf!
so i am going to take the skewness and kurtosis of a sample. however, if i already have a pdf, is there really any reason for doing this?
thanks!
josh
Consider the following problem: A spring with spring constant ##k## is suspended vertically from a fixed support and the spring is in equilibrium with a heat bath of temperature ##T## and resides in a gravitational field ##g##. A mass ##m## is hung from the other end of the spring. Find the...
Hi, I'm a rising senior and interested in developing nano-sensors/imaging, and I'm also thinking of going into industry after grad school.
I'm debating on whether to take Data mining or Statistical Physics/Thermodynamics and wasn't sure which will be more suited for my needs.
Both courses are...