Statistical Definition and 659 Threads

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. T

    Statistical Physics: Discovering Condensed Matter & Solid State

    Lately I've been reading a lot of statistical physics and I really enjoy it. I was curious what sorts of physics more study in this area would lead me to. Condensded matter? Solid state?
  2. Monique

    Statistical flaws revealed in top journals' papers

    http://www.newscientist.com/news/news.jsp?id=ns99995051" Rounding numbers seems to be a difficult task for some..
  3. S

    Chaos Theory & Statistical Anentropy: Intro for 15yo HS Student

    I would just like to know what exactly is the basis of the Chaos Theory; has it anything to do with the idea of statistical anentropy? Could someone give me an introduction to these topics? (I am a 15 year old going into a Honors Physics course in high school, thinking maybe I would like to...
  4. wolram

    What Role Does Statistics Play in Modern Astrophysics?

    http://nedwww.ipac.caltech.edu/level5/Sept03/Feigelson/paper.pdf PhyStat 2003: Statistical Problems in Particle Physics, Astrophysics, and Cosmology Statistical Challenges in Modern Astronomy E. D. Feigelson Department of Astronomy & Astrophysics, Penn State University, University...
  5. G

    Is Spearman's Rank Coefficient Applicable to Multiple Sets of Results?

    I have got a bit of problem here. I have got 4 sets of results for a biology experiment, and I want to find the correlation between them. So I read about Spearman's rank coefficient but it only works for two sets of results. Can somebody help please?
  6. J

    Solving Statistical Problems Without Population Data

    need some help with statistics! My problem is this: I am given a set of data for a group of individuals and from that data I am supposed to infer the moments of that data as compared to the population as a whole. The problem is, I do not have the relevant data pertaining to the entire...
  7. A

    How Can I Calculate Probabilities for Event Success Rates?

    I have near to no knowledge of statistics, and I want to build a statistical model that can help me calculate %chance of an event happening in situations of type: every try has 25% success rate after 6 tries, what are the probabilities of having succeeded at least 5times? After 12tries...
  8. A

    Recomendations for the best Statistical Mechanics books

    I'm planing on learning Statistical Mechanics by myself. I would like to hear recomendations on what you think are the best Statistical Mechanics books. My interest right now would be books that are on a undergraduate level, with detailed explanation, examples and problems, but you could also...
  9. kat

    News Statistical Analysis of Casualties in the Palestinian - Israeli Conflict,

    I find the analysis of the deaths of children about 3/4's of the way down, interesting, as well as tragic. http://www.ict.org.il/articles/articledet.cfm?articleid=439 More on the deaths of children http://www.camera.org/index.asp?x_context=7&x_issue=16&x_article=346
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