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Standard error of the mean

Standard error of the mean
When you take a sample of observations from a population, the mean of the sample is an estimate of the parametric mean, or mean of all of the observations in the population. If your sample size is small, your estimate of the mean won't be as good as an estimate based on a larger sample size. Here are 10 random samples from a simulated data set with a true (parametric) mean of 5. The X's represent the individual observations, the red circles are the sample means, and the blue line is the parametric mean. As you can see, with a sample size of only 3, some of the sample means aren't very close to the parametric mean. You'd often like to give some indication of how close your sample mean is likely to be to the parametric mean. Here's a figure illustrating this. Usually you won't have multiple samples to use in making multiple estimates of the mean. This figure is the same as the one above, only this time I've added error bars indicating ±1 standard error. Similar statistics Example Web pages

Particles found to break speed of light Audit Sampling Requires Auditor Judgment December 1994 The goal of an agency audit is to insure compliance with the client's work standards, evaluate performance and maximize profits. Obviously, no matter how competent the auditor or how sophisticated the collection software, reviewing each account is a physical impossibility. Even if 100 percent of the information could be tested, the cost of testing would likely exceed the expected benefits (the assurance that accompanies examining 100 percent of the total) to be derived. What is required is a sampling of the accounts. To accomplish this, the auditor needs to examine a representative sample or cross-section of the various type of accounts (e.g., legal, good telephone, skip, payment arrangements, settled, closed) as well a review of the remittance history. How the sample should be selected and how large the sample should be are critical issues for researchers as well as auditors. According to researchers M. Simple Random Sampling Systematic (Interval) Sampling Haphazard Selection

Living Earth Simulator will simulate the entire world Described as a “knowledge collider,” and now with a pledge of one billion euros from the European Union, the Living Earth Simulator is a new big data and supercomputing project that will attempt to uncover the underlying sociological and psychological laws that underpin human civilization. In the same way that CERN’s Large Hadron Collider smashes together protons to see what happens, the Living Earth Simulator (LES) will gather knowledge from a Planetary Nervous System (PNS — yes, really) to try to predict societal fluctuations such as political unrest, economic bubbles, disease epidemics, and so on. The scale of the LES, when it’s complete, will be huge. It is hoped that supercomputing centers all over the world will chip in with CPU time, and data will be corralled from existing projects and a new Global Participatory Platform, which is basically open data on a worldwide scale. The timing of EU’s billion-euro grant is telling, too. Read more at FuturICT

Introduction to Sampling Distributions Introduction to Sampling Distributions Prerequisites Distributions, Inferential Statistics Learning Objectives Define inferential statistics Graph a probability distribution for the mean of a discrete variable Describe a sampling distribution in terms of "all possible outcomes." Suppose you randomly sampled 10 people from the population of women in Houston Texas between the ages of 21 and 35 years and computed the mean height of your sample. Discrete Distributions We will illustrate the concept of sampling distributions with a simple example. All possible outcomes are shown below in Table 1. Notice that all the means are either 1.0, 1.5, 2.0, 2.5, or 3.0. The distribution shown in Figure 2 is called the sampling distribution of the mean. There is an alternative way of conceptualizing a sampling distribution that will be useful for more complex distributions. It is important to keep in mind that every statistic, not just the mean has a sampling distribution. Continuous Distributions

SpaceX Craft Docks With Space Station; Commercial Era Begins : The Two-Way The historic first docking of a commercial spacecraft at the International Space Station orbiting above Earth happened without a hitch today, as SpaceX's Dragon capsule arrived with supplies for the crew orbiting high above Earth. Just before 10 a.m. ET, astronauts aboard the space station successfully grabbed the capsule with a robotic arm. A little after noon ET, the pulled the Dragon into its docking space. NASA was webcasting, and we have embedded its feed in this post (our apologies if you're on a device that doesn't support the player). Earlier this week on All Things Considered, NPR's Nell Greenfieldboyce reported about the historic mission. Update at 12:10 p.m. Dragon has finished docking with the International Space Station. That happened at exactly 12:02 p.m. Update at 10:40 a.m. Capturing Dragon "was a big moment for SpaceX and a big moment for NASA too," NPR's Nell Greenfieldboyce said on Morning Edition a short time ago. Update at 10:15 a.m. Update at 9:56 a.m.

Glossary You can use the "find" (find in frame, find in page) feature of your browser to search the glossary. 0-1 box A box of numbered tickets, in which each ticket is numbered either 0 or 1. Affine transformation. See transformation. Affirming the antecedent. A valid logical argument that concludes from the premise A → B and the premise A that therefore, B is true. Affirming the consequent. A logical fallacy that argues from the premise A → B and the premise B that therefore, A is true. Alternative Hypothesis. In hypothesis testing, a null hypothesis (typically that there is no effect) is compared with an alternative hypothesis (typically that there is an effect, or that there is an effect of a particular sign). and, &, conjunction, logical conjunction, ∧. An operation on two logical propositions. Ante. The up-front cost of a bet: the money you must pay to play the game. Antecedent. In a conditional p → q, the antecedent is p. Appeal to Ignorance. Applet. Association. Average. A sometimes vague term. Bias.

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