Concept Of Standard Error In Statistics
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Dictionary Select a term from the dropdown text box. The online statistics glossary will display a definition, plus links to other related web pages. Select term: Statistics Dictionary Absolute Value Accuracy Addition Rule Alpha Alternative Hypothesis Back-to-Back Stemplots Bar Chart Bayes Rule Bayes Theorem Bias Biased Estimate Bimodal Distribution standard error regression statistics Binomial Distribution Binomial Experiment Binomial Probability Binomial Random Variable Bivariate Data Blinding Boxplot Cartesian Plane Categorical Variable Census Central Limit Theorem Chi-Square Distribution Chi-Square Goodness of Fit Test Chi-Square Statistic Chi-Square Test for Homogeneity Chi-Square Test for Independence Cluster Cluster Sampling Coefficient of Determination Column Vector Combination Complement Completely Randomized Design Conditional Distribution Conditional Frequency Conditional Probability Confidence Interval Confidence Level Confounding Contingency Table Continuous Probability Distribution Continuous Variable Control Group Convenience Sample Correlation Critical Parameter Value Critical Value Cumulative Frequency Cumulative Frequency Plot Cumulative Probability Decision Rule Degrees of Freedom Dependent Variable Determinant Deviation Score Diagonal Matrix Discrete Probability Distribution Discrete Variable Disjoint Disproportionate Stratification Dotplot Double Bar Chart Double Blinding E Notation Echelon Matrix Effect Size Element Elementary Matrix Operations Elementary Operators Empty Set Estimation Estimator Event Event Multiple Expected Value Experiment Experimental Design F Distribution F Statistic Factor Factorial Finite Population Correction Frequency Count Frequency T
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How To Find Standard Error Statistics
that seeks to expand the money supply to encourage economic ... Read More concept sampling error » Latest Videos Why Create a Financial Plan? John McAfee on the IoT & Secure Smartphones concept standard deviation Guides Stock Basics Economics Basics Options Basics Exam Prep Series 7 Exam CFA Level 1 Series 65 Exam Simulator Stock Simulator Trade with a starting balance of $100,000 http://stattrek.com/statistics/dictionary.aspx?definition=standard%20error and zero risk! FX Trader Trade the Forex market risk free using our free Forex trading simulator. Advisor Insights Newsletters Site Log In Advisor Insights Log In Standard Error Loading the player... What is a 'Standard Error' A standard error is the standard deviation of the sampling distribution of a statistic. Standard error is http://www.investopedia.com/terms/s/standard-error.asp a statistical term that measures the accuracy with which a sample represents a population. In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error. BREAKING DOWN 'Standard Error' The term "standard error" is used to refer to the standard deviation of various sample statistics such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population.The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.The standard error is considered part of descriptive statistics. It represents the standard deviation of the mean within a dataset. This serves as a measure of variation for random variables, providing a measurement for the spread. The smaller the spread, the more accurate the dataset is said to be.Standard Error and Population SamplingWhen a population is sampled, the mean, or average, is generally calculated. The standard
Ana-Maria Å imundićEditor-in-ChiefDepartment of Medical Laboratory DiagnosticsUniversity Hospital "Sveti Duh"Sveti Duh 6410 000 Zagreb, CroatiaPhone: +385 1 3712-021e-mail address:editorial_office [at] biochemia-medica [dot] com Useful links Events   Follow us http://www.biochemia-medica.com/content/standard-error-meaning-and-interpretation on Facebook Home Standard error: meaning and interpretation Lessons in biostatistics  http://changingminds.org/explanations/research/statistics/standard_error.htm Mary L. McHugh. Standard error: meaning and interpretation. Biochemia Medica 2008;18(1):7-13. http://dx.doi.org/10.11613/BM.2008.002 School of Nursing, University of Indianapolis, Indianapolis, Indiana, USA  *Corresponding author: Mary [dot] McHugh [at] uchsc [dot] edu  Abstract Standard error statistics are a class of inferential statistics that function somewhat like descriptive statistics in standard error that they permit the researcher to construct confidence intervals about the obtained sample statistic. The confidence interval so constructed provides an estimate of the interval in which the population parameter will fall. The two most commonly used standard error statistics are the standard error of the mean and the standard error of the estimate. The standard error of the mean permits standard error statistics the researcher to construct a confidence interval in which the population mean is likely to fall. The formula, (1-P) (most often P < 0.05) is the probability that the population mean will fall in the calculated interval (usually 95%). The Standard Error of the estimate is the other standard error statistic most commonly used by researchers. This statistic is used with the correlation measure, the Pearson R. It can allow the researcher to construct a confidence interval within which the true population correlation will fall. The computations derived from the r and the standard error of the estimate can be used to determine how precise an estimate of the population correlation is the sample correlation statistic. The standard error is an important indicator of how precise an estimate of the population parameter the sample statistic is. Taken together with such measures as effect size, p-value and sample size, the effect size can be a useful tool to the researcher who seeks to understand the accuracy of statistics calculated on random samples. Key words: statistics, standard error  Received: October 16, 2007               Â
Example | Discussion | See also Description If you measure a sample from a wider population, then the average (or mean) of the sample will be an approximation of the population mean. But how accurate is this? If you measure multiple samples, their means will not all be the same, and will be spread out in a distribution (although not as much as the population). Due to the central limit theorem, the means will be spread in an approximately Normal, bell-shaped distribution. The standard error, or standard error of the mean, of multiple samples is the standard deviation of the sample means, and thus gives a measure of their spread. Thus 68% of all sample means will be within one standard error of the population mean (and 95% within two standard errors). What the standard error gives in particular is an indication of the likely accuracy of the sample mean as compared with the population mean. The smaller the standard error, the less the spread and the more likely it is that any sample mean is close to the population mean. A small standard error is thus a Good Thing. When there are fewer samples, or even one, then the standard error, (typically denoted by SE or SEM) can be estimated as the standard deviation of the sample (a set of measures of x), divided by the square root of the sample size (n): SE = stdev(xi) / sqrt(n) Example This shows four samples of increasing size. Note how the standard error reduces with increasing sample size. Sample 1 Sample 2 Sample 3 Sample 4 9 6 5 8 2 6 3 1 1 8 6 7 8 4 1 3 7 3 8 2 3 6 4 9 7 7 1 1 8 1 9 7 9 3 1 6 8 3 4 Mean: 4.00 6.50 4.83 4.78 Std dev, s: 4.36 1.97 2.62 2.96 Sample size, n: 3 6 12 18 sqrt(n): 1.73 2.45 3.46 4.24 Standard error, s/sqrt(n): 2.52 0.81 0.76 0.70 Discussion The standard error gives a measure of how well a sample represents the population. When the sample is representative, the standard error will be small. The division by the square root of the sample size is a reflection of the speed with which an increasing sample size gives an improved representation of the population, as in the example above. An approximation of confidence intervals can be made using the mean +/- standard errors. Thus, in the above example, in Sample 4 there is a 95% chance that the population mean is within +/- 1.4 (=2*0.70) of the mean (4.78). Graphs that show sample means may have the standard error highlighted by an 'I' bar (sometimes called an error bar) going up and down from the mean, thus indicating the spread, for example as below: See also Central limit theorem Site Menu | Home | Top | Quick Links | Se