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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 Related:  Statistics

Second team does not see Tevatron's mystery signal - physics-math - 10 June 2011 Read full article Continue reading page |1|2 Is particle physics, like beauty, in the eye of the beholder? A task force is being formed to figure out the discrepancy, but the final arbiter may be the Large Hadron Collider in Switzerland, which will ultimately collect more data than the Tevatron. In April, members of the Tevatron's CDF experiment reported finding a curious signal in the debris from eight years' worth of collisions between protons and antiprotons. Last week, evidence for the signal, or "bump" in the data, seemed to get even stronger. But now, a rival team performing an independent analysis of Tevatron data has turned up no sign of the bump. "Nope, nothing here – sorry," says Dmitri Denisov, a spokesman for DZero. Different detectors When the CDF collaboration came out with its result in April, DZero researchers spent a couple of days doing a quick check of their data and saw no bump. Today, they are reporting that their analysis shows no bump. Modelling issue? Task force

Statistics Notes: Standard deviations and standard errors Inner Product An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. More precisely, for a real vector space, an inner product satisfies the following four properties. Let , and be vectors and be a scalar, then: and equal if and only if A vector space together with an inner product on it is called an inner product space. Examples of inner product spaces include: 1. , where the inner product is given by 2. , where the inner product is given by the dot product 3. with inner product When given a complex vector space, the third property above is usually replaced by where refers to complex conjugation. Every inner product space is a metric space. If this process results in a complete metric space, it is called a Hilbert space.

Tutorials, Calculators, Consulting and Statistics Help List of unsolved problems in physics Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail. Unsolved problems by subfield[edit] The following is a list of unsolved problems grouped into broad area of physics.[1] Cosmology, and general relativity[edit] Cosmic inflation Is the theory of cosmic inflation correct, and if so, what are the details of this epoch? Horizon problem Electroweak Horizon Problem Why aren't there obvious large-scale discontinuities in the electroweak vacuum, if distant parts of the observable universe were causally separate when the electroweak epoch ended? Future of the universe Is the universe heading towards a Big Freeze, a Big Rip, a Big Crunch or a Big Bounce? Gravitational wave Can gravitational waves be directly detected? .

Statistical significance of correlations Statistical significance of correlations The chart below shows how large a correlation coefficient must be to be statistically significant. The chart shows one-tailed probabilities, so multiply the probabilities along the top row of the chart by 2 to get 2-tailed probabilities. In other words, the columns labeled .05, .025, .01, .005, .0005 (for one-tailed probabilities) should be changed to .10, .05, .02, .01, and .001 (for two-tailed probabilities). For our purposes, we will always be using two-tailed probabilities. Here is an example of how to read the chart. After finding that row, look across the table. Reading this way you will see that your correlation of .44 is significant at the .025 (one-tailed) level, which is .05 two-tailed. If you had 20 participants and a correlation of -0.53, what could you say? If you had 14 participants and a correlation of .49, what could you say?

Pioneering Ants Challenge Self-Organization Assumptions | Wired Science Some worker ants are more equal than others. As with other social insects, it was once thought that workers were essentially equivalent in ant colony hierarchies. But it appears that a few well-informed individuals shape group decisions by leading nestmates to new homes. The findings could add a new dimension to ant-derived models of self-organization. “Although self-organized systems appear very effective under the assumption that all individuals follow the same simple set of rules, the presence of key, well-informed individuals altering their behavior according to their prior experience might generally enhance performance even further,” wrote biologists from the University of Bristol and the University of Toulouse in an Aug. 24 Journal of Experimental Biology paper. To study nest-hunting, Nathalie Stroeymeyt and colleagues Nigel Franks and Martin Giurfa collected “house-hunting” ants, or Temnothorax albipennis, from the southern coast of the United Kingdom.

Applets This page contains applets from McClelland's Seeing Statistics, which have been integrated with material in Fundamental Statistics for the Behavioral Sciences, (5th edition) by David C. Howell. You merely need to click on the appropriate link to open the applet, and then follow the directions on the page. These applets will run best if you have Sun's Java Virtual Machine installed on your computer. Chapter 4: Brightness Matching Experiment Chapter 5: Why Divide by N-1? Chapter 6: Normal Distribution and z- Scores Chapter 8: Testing a Simple Null Hypothesis Chapter 9: Correlation Construction of scatter diagrams: CorrelationPoints allows user to click on a scatter diagram to add data points with the correlation coefficient automatically updated with each new point. Chapter 17: Factorial Analysis of Variance Graphing interactions illustrates main effects and interactions, and shows how one can change without the other. Comments to: Return to index

Scientists say its high NOON for microwave photons An important milestone toward the realization of a large-scale quantum computer, and further demonstration of a new level of the quantum control of light, were accomplished by a team of scientists at UC Santa Barbara and in China and Japan. The study, published in the Feb. 7 issue of the journal Physical Review Letters, involved scientists from Zhejiang University, China, and NEC Corporation, Japan. The experimental effort was pursued in the research groups of UC Santa Barbara physics professors Andrew Cleland and John Martinis. The team described how they used a superconducting quantum integrated circuit to generate unique quantum states of light known as "NOON" states. These states, generated from microwave frequency photons, the quantum unit of light, were created and stored in two physically-separated microwave storage cavities, explained first author Haohua Wang, postdoctoral fellow in physics at UC Santa Barbara. Explore further: A quantum logic gate between light and matter

Statistics Tutorial - Choosing a T-Test Explanation Paired or Independent t-test?There are two types of t-test, the paired t-test and the independent t-test. This page tells you how to pick the right one for your data. We have already seen that when comparing two samples, it is important to know whether or not the samples are paired. With paired (dependent) samples, it is possible to take each measurement in one sample and pair it sensibly with one measurement in the other sample. One of the reasons that you need to identify the type of experimental design that you are dealing with is that you need to use the right t-test for the right design: The paired t-test is used when you have a paired designThe independent t-test is used when you have an independent designThat's easy enough. The other thing you need to decide at this point is easy to decide, but can be slightly harder to understand. Level 3 of this topic explains why you need to make this choice.