What is Statistics: Definition and 997 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.

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  1. Artemisa

    Error floors in this Bayesian analysis

    In this article((https://arxiv.org/pdf/2001.04581.pdf)), the authors use a Bayesian analysis based on the positions of astrophysical bodies and their errors in the medians. This statistical analysis uses the markov chain monte carlo chains. The uncertainties in the positions are large, so what...
  2. hagopbul

    About meta trader platform

    TL;DR Summary: Asking about meta trader platform and what mathematical theories should i read about Hello : Recently got my attention a claim about meta trader platform and how you can use it as supportive income source What is this platform exactly ? What should I read to be able to use...
  3. Graham87

    I Basic standard deviation calculation

    I don’t get how they got the equation for the standard deviation. Why do they only square with the time in the denominator? Thanks!
  4. H

    Good introductory book on statistical/data analysis?

    TL;DR Summary: I'm looking for a book on statistical/data analysis. Hey all. I've been doing statistical analysis in my research (such as using PCA and LDA), but I have never received a formal education on statistical analysis or data mining, and what I know about analysis is quite scattered...
  5. P

    Understanding the meaning of "expected fraction" (Statistics)

    The first part of the question asked me to calculate the mean and standard deviation for the number of remain votes in the simple binomial model consisting of total sample size of 2091 people. I believe this is fairly straightforward, it was simply ##E(X) = \mu = 2091(0.5) = 1045.5## votes and...
  6. S

    Probability of Hypokalemia w/ 1 or Multiple Measurements

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  7. A

    Break a Stick Example: Random Variables

    Hello, I would like to confirm my answers to the following random variables question. Would anyone be willing to provide feedback and see if I'm on the right track? Thank you in advance. My attempt:
  8. shahbaznihal

    A Computing the Fisher Matrix numerically

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  9. P

    I Are Boltzman's statistics compatible with a deterministic universe?

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  10. A

    A How to derive the sampling distribution of some statistics

    Assume that ##T## has an Erlang distribution: $$\displaystyle f \left(t \, | \, k \right)=\frac{\lambda ^{k }~t ^{k -1}~e^{-\lambda ~t }}{\left(k -1\right)!}$$ and ##K## has a geometric distribution $$\displaystyle P \left( K=k \right) \, = \, \left( 1-p \right) ^{k-1}p$$ Then the compound...
  11. WMDhamnekar

    MHB Probability, Expected value, joint P.D.F. and order statistics

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  12. L

    [Statistics] Calculate the percentage

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  13. A

    I Modeling the concentration of gas constituents in a Force Field

    Say there is a gas made up of two gas molecules: Molecule A and Molecule B. Molecule A has a mass: ma and mole fraction: na. Molecule B has a mass: mb and mole fraction: nb. The gas is at thermal equilibrium and has a constant temperature throughout itself (T) everywhere. It is placed in a...
    • Anon42
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    • Concentration Diffusion Equilibrium Field Force Gas Modeling Statistics
    • Replies: 6
    • Forum: Thermodynamics
  14. D

    Ancillary statistics

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  15. A

    Calculus Advanced Calculus with Applications in Statistics

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  16. S

    I Bayesian statistics in science

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  17. chwala

    Solve the variance problem below - statistics

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  18. tixi

    Labwork Statistics help: Average of averages

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  19. Amitkumarr

    I Finding bias of the coin from noise corrupted signals

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  20. V

    B Convince Covid-19 Vaccine Efficiency Through Statistics

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  21. ohwilleke

    I Why Do Physicists Use Gaussian Error Distributions?

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    • ohwilleke
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    • Distributions Error Experimental error Experimental physics Gaussian Physicists Statistics
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  22. S

    Stock trading volume statistics

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  23. W

    A Using Statistics to Test for Normality of Pi

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  24. Falgun

    Prob/Stats Looking for a probability and statistics textbook

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  25. shahbaznihal

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  26. chwala

    Discrete data vs continous data in statistics

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  27. W

    I Bias in Linear Regression (x-intercept) vs Statistics

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  28. L

    Statistics: Verifying a Probability Proof

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  30. V

    MHB Creating An Awesome Statistics Course For Students

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  31. S

    Question about hint given by the problem related to statistics

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  32. S

    MHB Statistics and probability

    The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds...
  33. Athenian

    Finding the Relative Uncertainty for the Standard Error of the Mean

    While I will not be showing the graph here, I am trying to dissect what the question even means. While I do understand that relative uncertainty can be found via the equation ##\frac{\sigma_A}{A}##, I do not understand how I can find the "relative uncertainty of SEM". Does anybody here have any...
  34. CPW

    Encouraging fact from cancer statistics

    We study cancer to get better at killing it. And here is an enouraging detail: Since 1975, the cancer death rate in the United States has decreased by 21.9% with a 15% decrease from 2007 to 2017. (https://seer.cancer.gov/csr/1975_2017)
  35. Dale

    Insights Posterior Predictive Distributions in Bayesian Statistics

    Continue reading...
  36. C

    I Large Q^2 statistics at different colliders

    How tractable is it experimentally to measure deeply virtual compton scattering in bins of large Q^2, where Q^2 is the virtuality of the incoming photon, at e.g. Jefferson Lab which collides electron and proton? I know at LHC, colliding proton-proton, such processes would instead be statistics...
  37. dx

    A Photon Statistics

    In a given mode with an average number of photons ``##\bar{n}##, the photons are distributed around their average according to the formula $$p_n = e^{-\bar{n}} \frac{\bar{n}^n}{n!}$$ The justification of this formula in quantum field theory involves considering field operators acting on a...
  38. D

    Rotational partition function for CO2 molecule

    Hello fellow physicists, I need to calculate the rotational partition function for a CO2 molecule. I'm running into problems because I've found examples were they say this rotational partition function is: ##\zeta^r= \frac T {\sigma \theta_r} = \frac {2IkT} {\sigma \hbar^3}## Where...
  39. iVenky

    I What are the statistics of probability of dying today vs age?

    I don't intend to sound macabre, but I was having this thought if I have to quantify the probability of someone dying given his age (in days) how would I go about quantifying that with a minimal accuracy (ok if it's not accurate but I just need some number with days). Has anyone ever worked out...
  40. Dale

    Insights How to Get Started with Bayesian Statistics

    Continue reading...
  41. R

    What statistics services/platforms do you use that help you in life?

    I encountered a website with statistics for a large number of video games, specifically regarding their availability across various platforms, their sales over time and some other things and methods to visualize them I found this really helpful. Might there be other services like this that...
  42. E

    Online course for probability and statistics with emphasis on python

    I have been looking for a way to learn probability and statistics online and have searched but found nothing yet. I am looking for a course on probability and statistics that will not only teach me the basics but all there is to know about the subject. I would love it if the visualizations are...
  43. I

    B Different sample methods in statistics

    What is the difference between stratified and quota sampling of a population? For example, you can choose 200 males and 200 females from a state by quota sampling; or collect raw data first, stratify it, and then choose 200 males from one subsample and 200 females from the other subsample...
  44. G

    Confidence Interval Question help please

    Here is the question I'm struggling with (Q1) : I just... I just don't understand what my first step is. Whats my barx1 and barx2? (bar x = mean, x1 = subscript 1) My thoughts on approaching this question : barX1 - barX2 `~ N(u1-u2, sd1^2/n1 + sd2^2/n2) Find Z value when p = 0.975, z = + or...
  45. G

    B Statistics Help : Hypothesis Testing

    Answer : I understnad why x(< or = ) 2 but I do not understand why we use 16 instead of 17 for the second range? When P(X>=16) > 0.005(which is the level of significance). Thank you for all the help given :)
  46. archaic

    Prob/Stats Introductory textbook for Probability and Statistics

    Hello! I'll be taking a probability and statistics course this semester. Does anyone know of any good textbook? I have access to an extensive catalogue of books on springer, so it would be extremely preferable for me if you could recommend something from there. Thanks.
  47. T

    Exploring the Grand Partition Function for an Einstein Solid

    $$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3.127)$$ Where ##Q## is the grand partition function, ##Z_N## is the canonical partition function and: $$\beta = \frac{1}{kT} \hspace{1cm} \alpha = \frac{\mu}{kT} \hspace{1cm} (3.128)$$ In the case of an...
  48. Schwann

    I 'Conservative' p-values adjusted

    Hello everyone! Could anybody recommend some strategy of p-values adjustment, as the distribution of my p-values indicates the presence of a big number of false negatives? Usually p-values are adjusted in order to overcome Type 1 errors (e. g. FDR or FWER estimation), but what I need to do is...
  49. SamRoss

    I Seeking better explanation of some quantum stats formulae

    In "Introduction to Quantum Mechanics", Griffiths derives the following formulae for counting the number of configurations for N particles. Distinguishable particles... $$ N!\prod_{n=1}^\infty \frac {d^{N_n}_n} {N_n !} $$ Fermions... $$ \prod_{n=1}^\infty \frac {d_n!} {N_n!(d_n-N_n)!}$$...
    • SamRoss
    • Thread
    • Configuration Explanation Formulae Griffiths Particles Quantum Statistics Stats
    • Replies: 3
    • Forum: Quantum Physics
  50. michaelwright

    B Fun with (im)probabilities

    Hi folks - I need some help with a tricky probability. Here's the situation: Let's say there are 4M internet users in Age Group A. (The total set) Of those 4M, there are 1,000 users who play a specific sport. Those 1,000 are spread evenly over 125 teams, so 8 players each. 1. What's the...
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