In contrast, calculating the predicted variation, or standard error—a precursor to the familiar "margin of error" frequently reported alongside poll results—is a bit trickier.
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Looking at standard error rates at the plant, they found statistically significant evidence of higher error rates for workers under 30 but no evidence of more mistakes as workers age into their 60s.
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Ginsburg said, however, that when an IQ score is close to, but above, 70, court precedent requires courts to account for the test's "standard error of measurement" and consider a defendant's adaptive functioning.
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In 2004, for example, the exit polls overestimated John Kerry's share of the vote (by "more than one standard error") in 26 states; it overestimated George W. Bush's share in only four states.
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Though Mr Moore's intelligence was tested repeatedly, Mr Roberts found only two IQ scores worthy of attention: a 78 and a 74, both higher than the 70-point threshold of Atkins and Hall and with a standard error of measurement between 69 and 83.
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" TOM PORCELLI, CHIEF U.S. ECONOMIST, RBC CAPITAL MARKETS, NEW YORK "This report really drives home the rock-solid state of labor in the United States…Given the fact that the standard error in this thing is so significant, (this headline miss is) nothing short of close enough.
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It's also important to realize that, since the points on the graph don't follow any smooth line, there is probably a fair amount of "noise" in the data (for instance, the vertical lines extending from the data points show what statisticians call the standard error of the points).
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The evidence they had on hand was useful but very imprecise: For instance, they found that the eight studies measuring the effect of personal canvassing within two months of election day had an average effect of negative 1.9 percentage points, barely larger than the standard error of 1.7 percent.
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In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean. In regression analysis, the term "standard error" refers either to the square root of the reduced chi-squared statistic, or the standard error for a particular regression coefficient (as used in, say, confidence intervals).
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Each bar represents an average of four animals; error bars, and standard error.
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So, the estimator of Var(∑X) becomes nS2X \+ n'''2 giving : standard error(''''') = √[(S2X \+ '''''2)/n].
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The sampling algorithm used to place mugs favors suggestions that have fewer votes, ensuring that each idea is sufficiently graded. The CRC system tracks the standard error of the grades for each mug, and places each suggestion strategically in an effort to equalize the standard error overall.
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For each industry, we calculate the antilogarithm of the standard error values as the structural uncertainty measure.
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On aggregate, IQ tests exhibit high reliability, although test-takers may have varying scores when taking the same test on differing occasions, and may have varying scores when taking different IQ tests at the same age. Like all statistical quantities, any particular estimate of IQ has an associated standard error that measures uncertainty about the estimate. For modern tests, the confidence interval can be approximately 10 points and reported standard error of measurement can be as low as about three points. Reported standard error may be an underestimate, as it does not account for all sources of error.
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In regression analysis and least squares problems, the standard error of parameter estimates is readily available, which can be expanded into a confidence interval.
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Serum anti-aberrant-lactobacillus antibody titres (geometric mean and standard error) in 97 women vaccinated with SolcoTrichovac (Milovanović 1983). A booster dose was given 12 months after the first injection. Total secretory IgA concentration (arithmetic mean and standard error) of the vaginal secretions of 95 women vaccinated with SolcoTrichovac (Rüttgers 1988). Mucosal surfaces are a major portal of entry for pathogens into the body.
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In scientific and technical literature, experimental data are often summarized either using the mean and standard deviation of the sample data or the mean with the standard error. This often leads to confusion about their interchangeability. However, the mean and standard deviation are descriptive statistics, whereas the standard error of the mean is descriptive of the random sampling process. The standard deviation of the sample data is a description of the variation in measurements, while the standard error of the mean is a probabilistic statement about how the sample size will provide a better bound on estimates of the population mean, in light of the central limit theorem.
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These techniques are derived from statistical measures of spread of data: the standard deviation, the standard error of measurement and the effect size, usually expressed as a standardized mean difference (SMD; also known as Cohen's d in psychology). # Using the one-half standard deviation benchmark of an outcome measure entails that patient improving more than one-half of the outcome score's standard deviation have achieved a minimal clinically important difference. # The standard error of measurement is the variation in scores due to unreliability of the scale or measure used. Thus a change smaller than the standard error of measurement is likely to be the result of measurement error rather than a true observed change.
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In order to determine the statistical significance of the indirect effect, a statistic based on the indirect effect must be compared to its null sampling distribution. The Sobel test uses the magnitude of the indirect effect compared to its estimated standard error of measurement to derive a t statistic OR Where SE is the pooled standard error term and and σ2β is the variance of β and σ2α is the variance of α. This t statistic can then be compared to the normal distribution to determine its significance. Alternative methods of calculating the Sobel test have been proposed that use either the z or t distributions to determine significance, and each estimates the standard error differently.
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The square root of the variance inflation factor indicates how much larger the standard error increases compared to if that variable had 0 correlation to other predictor variables in the model. Example If the variance inflation factor of a predictor variable were 5.27 (√5.27 = 2.3), this means that the standard error for the coefficient of that predictor variable is 2.3 times larger than if that predictor variable had 0 correlation with the other predictor variables.
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In most situations, the problem should be found and fixed. Other types of standard error adjustments, such as clustered standard errors, may be considered as extensions to HC standard errors.
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In the speed-of-light example, removing the two lowest observations causes the mean to change from 26.2 to 27.75, a change of 1.55. The estimate of scale produced by the Qn method is 6.3. We can divide this by the square root of the sample size to get a robust standard error, and we find this quantity to be 0.78. Thus, the change in the mean resulting from removing two outliers is approximately twice the robust standard error.
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Can you inspect the standard output and/or standard error of the executed job on your viewer? Some systems even immediately transfer both to the central scheduler, which might give extra network load.
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Iteman provides an index of decision consistency as well as a classical estimate of the conditional standard error of measurement at the cutscore, which is often requested for accreditation of a testing program.
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He is believed to have a chromosomal translocation of 15/20 and a partial trisomy of 22q12.3. Blood tissue from five other female Syndrome X cases (whose average age was 6.3 years) turned out to be age-appropriate according to a biomarker of aging known as epigenetic clock. The mean epigenetic age of the five pure Syndrome X subjects was 6.7 years (standard error=1.0) which is not significantly different from the mean chronological age of 6.3 years (standard error=1.8).
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Sterne and Egger have compared these with others, and conclude that the standard error is to be recommended. When the standard error is used, straight lines may be drawn to define a region within which 95% of points might lie in the absence of both heterogeneity and publication bias. In common with confidence interval plots, funnel plots are conventionally drawn with the treatment effect measure on the horizontal axis, so that study precision appears on the vertical axis, breaking with the general rule.
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Because the confidence interval termination criterion is centered around the examinees ability estimate, estimate-based item selection is more appropriate. This is because the test will make a classification when the confidence interval is small enough to be completely above or below the cutscore (see below). The confidence interval will be smaller when the standard error of measurement is smaller, and the standard error of measurement will be smaller when there is more information at the theta level of the examinee.
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In the case of a linear model with a working independence variance structure, these are known as "heteroscedasticity consistent standard error" estimators. Indeed, the GEE unified several independent formulations of these standard error estimators in a general framework. GEEs belong to a class of regression techniques that are referred to as semiparametric because they rely on specification of only the first two moments. They are a popular alternative to the likelihood–based generalized linear mixed model which is more sensitive to variance structure specification.
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This forms a distribution of different means, and this distribution has its own mean and variance. Mathematically, the variance of the sampling distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean. Therefore, the relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size.
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Used interactively, this is the terminal display. Used in a batch file, it outputs to the screen (if run interactively) or to the log file when run noninteractively. SYS$ERROR – Standard error. Used interactively, this is the terminal display.
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Patients achieving a difference in outcome score of at least one standard error of measurement would have achieved a minimal clinically important difference. # The effect size is a measure obtained by dividing the difference between the means of the baseline and posttreatment scores by the SD of the baseline scores. An effect size cut off point can be used to define MID in the same way as the one half standard deviation and the standard error of measurement. #Item response theory (IRT) also can create an estimate of MID using judges who respond to clinical vignettes illustrating different scenarios.
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Put simply, the standard error of the sample mean is an estimate of how far the sample mean is likely to be from the population mean, whereas the standard deviation of the sample is the degree to which individuals within the sample differ from the sample mean. If the population standard deviation is finite, the standard error of the mean of the sample will tend to zero with increasing sample size, because the estimate of the population mean will improve, while the standard deviation of the sample will tend to approximate the population standard deviation as the sample size increases.
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The two likely reasons for skin hemorrhaging and necrosis are an inability to effectively neutralize the venom, or unusually potent venom toxicity for that set of stings. In either case, for a small number of victims, these stings lead to multiple organ injury. While not all such victims displayed lesions or necrosis, a strong correlation existed between the number of stings and the severity of injury. Those who died, on average, were stung 59 times (with a standard error of 12), while those who survived suffered, on average, 28 stings (with a standard error of four, and a p=0.01).
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An example funnel plot showing no publication bias. Each dot represents a study (e.g. measuring the effect of a certain drug); the y-axis represents study precision (e.g. standard error or number of experimental subjects) and the x-axis shows the study's result (e.g.
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R package. The package includes marginal and joint maximum likelihood estimation of uni- and multidimensional item response models (Rasch, 2PL, Generalized Partial Credit, Rating Scale, Multi Facets), fit statistics, standard error estimation, as well as plausible value imputation and weighted likelihood estimation of ability.
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In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unknown correlation between outcomes. Parameter estimates from the GEE are consistent even when the covariance structure is misspecified, under mild regularity conditions. The focus of the GEE is on estimating the average response over the population ("population-averaged" effects) rather than the regression parameters that would enable prediction of the effect of changing one or more covariates on a given individual. GEEs are usually used in conjunction with Huber–White standard error estimates, also known as "robust standard error" or "sandwich variance" estimates.
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Yet, there are cases in which the two estimators have the same asymptotic variance. One such case occurs if E[\triangledown\gamma h(W,\gamma)]=0[4]In this special case, inference on the estimated parameter can be conducted with the usual IV standard error estimator.
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Newbury Park, California: Sage Publications, Inc. The problem with this is that there are differing opinions of what parallel tests are. Various reliability coefficients provide either lower bound estimates of reliability or reliability estimates with unknown biases. A third shortcoming involves the standard error of measurement.
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A simple example of MX records that demonstrate the technique: MX 10 dummy.example.com. MX 20 real-primary-mail-server.example.com. This defeats spam programs that only connect to the highest priority (lowest numbered) MX and do not follow the standard error-handling of retrying the next priority MX.
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It uses the `((…))` command and the `$((…))` variable syntax for this purpose. Its syntax simplifies I/O redirection. For example, it can redirect standard output (stdout) and standard error (stderr) at the same time using the `&>` operator. This is simpler to type than the Bourne shell equivalent '`command > file 2>&1`'.
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Several studies have highlighted the consequences of serial correlation and highlighted the small-cluster problem.Bertrand, M., E. Duflo and S. Mullainathan (2004): How Much Should We Trust Differences-in- Differences Estimates? Quarterly Journal of Economics 119(1), pp. 249–275.Kezdi, G. (2004): Robust Standard Error Estimation in Fixed-Effect Panel Models.
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Sending a SIGINFO signal (or a USR1 signal on Linux) to a running process makes it print I/O statistics to standard error once and then continue copying. can read standard input from the keyboard. When end-of-file (EOF) is reached, will exit. Signals and EOF are determined by the software.
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Accuracy is then often measured as the actual standard error (SE), MAPE (Mean absolute percentage error), or mean error between the predicted value and the actual value in the hold-out sample.Mayers, J.H., & Forgy, E.W. (1963). The Development of numerical credit evaluation systems. Journal of the American Statistical Association, 58(303; Sept), 799–806.
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Paper presented at the Annual Meeting of the National Council for Measurement in Education (New Orleans, LA, April 5–7, 1994). Maximizing information at the ability estimate is more appropriate for the confidence interval approach because it minimizes the conditional standard error of measurement, which decreases the width of the confidence interval needed to make a classification.
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In computer programming, standard streams are interconnected input and output communication channelsD. M. Ritchie, "A Stream Input-Output System", AT&T; Bell Laboratories Technical Journal, 68(8), October 1984. between a computer program and its environment when it begins execution. The three input/output (I/O) connections are called standard input (stdin), standard output (stdout) and standard error (stderr).
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These findings are similar to those seen in aged rats, suggesting that increased oxidative stress and inflammation may be responsible for the induction of both radiation and age-related cognitive deficits.” Figure 6-6. Brain-region-specific calcium-dependent protein kinase C expression was assessed in control and irradiated rats using standard Western blotting procedures. Values are means ± SEM (standard error of mean).
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Beta Phoenicis (β Phoenicis, β Phe) is a binary star in the constellation Phoenix. Its apparent magnitude is 3.30, meaning that it can be seen with the naked eye (see Bortle scale). The distance to Beta Phoenicis is poorly known. The original reduction of the Hipparcos satellite's data yielded a parallax value of 16 milliarcseconds, yet its standard error was larger than the parallax value itself.
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In many practical applications, the true value of σ is unknown. As a result, we need to use a distribution that takes into account that spread of possible σ's. When the true underlying distribution is known to be Gaussian, although with unknown σ, then the resulting estimated distribution follows the Student t-distribution. The standard error is the standard deviation of the Student t-distribution.
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The SMOG grade is a measure of readability that estimates the years of education needed to understand a piece of writing. SMOG is an acronym for "Simple Measure of Gobbledygook". SMOG is widely used, particularly for checking health messages. The SMOG grade yields a 0.985 correlation with a standard error of 1.5159 grades with the grades of readers who had 100% comprehension of test materials.
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Mitofsky International, the company responsible for exit polling for the National Election Pool (NEP) and its member news organizations, released a report detailing the 2004 election's exit polling. Alt URL At issue were the early release of some poll information, issues regarding correcting exit poll data using actual voter totals, and differences between exit polls and official results. The NEP report stated that "the size of the average exit poll error ... was higher in 2004 than in previous years for which we have data" and that exit polling estimates overstated Kerry's share of the vote in 26 states by more than one standard error and overestimated Bush's share in four states by more than one standard error. It concluded that these discrepancies between the exit polls and the official results were "most likely due to Kerry voters participating in the exit polls at a higher rate than Bush voters".
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Jacobson-Truax is common method of calculating clinical significance. It involves calculating a Reliability Change Index (RCI). The RCI equals the difference between a participant’s pre-test and post-test scores, divided by the standard error of the difference. Cutoff scores are established for placing participants into one of four categories: recovered, improved, unchanged, or deteriorated, depending on the directionality of the RCI and whether the cutoff score was met.
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Reliability coefficients include Cronbach's alpha, Guttman's lambda, the Feldt-Gilmer Coefficient, the Feldt-Brennan coefficient, decision consistency indices, the conditional standard error of measurement, and reliability if item deleted. The DIF analysis is based on nonparametric item characteristic curves and the Mantel-Haenszel procedure. DIF effect sizes and ETS DIF classifications are included in the output. IRT methods include the Rasch, partial credit, and rating scale models estimated via JMLE.
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"Size Matters: The Standard Error of Regressions in the American Economic Review," Journal of Socio-economics, 33(5), pp. 527-46 (press +). In some cases, economic variables cannot be experimentally manipulated as treatments randomly assigned to subjects. In such cases, economists rely on observational studies, often using data sets with many strongly associated covariates, resulting in enormous numbers of models with similar explanatory ability but different covariates and regression estimates.
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Relying on the sample drawn from these options will yield an unbiased estimator. However, the sample size is no longer fixed upfront. This leads to a more complicated formula for the standard error of the estimator, as well as issues with the optics of the study plan (since the power analysis and the cost estimations often relate to a specific sample size). A third possible solution is to use probability proportionate to size sampling.
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This observed form of the data is important because it causes problems with estimated regression coefficients. Loosely, a parameter in the model "wants" to be infinite, if complete separation is observed. If quasi-complete separation is the case, the likelihood is still maximized at an infinite value for that parameter, but has some restrictions with respect to other parameters. Computer programs will often output an arbitrarily large parameter estimate with a very large standard error.
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Imputation and Variance Estimation Software (IVEware) is a collection of routines written under various platforms and packaged to perform multiple imputations, variance estimation (or standard error) and, in general, draw inferences from incomplete data. It can also be used to perform analysis without any missing data. IVEware defaults to assuming a simple random sample, but uses the Jackknife Repeated Replication or Taylor Series LinearizationKish, Leslie and Martin Richard Frankel (1974). Inference from complex samples.
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Reliability coefficients include Cronbach's alpha, Guttman's lambda, the Feldt-Gilmer Coefficient, the Feldt-Brennan coefficient, decision consistency indices, the conditional standard error of measurement, and reliability if item deleted. The DIF analysis is based on nonparametric item characteristic curves and the Mantel-Haenszel procedure. DIF effect sizes and ETS DIF classifications are included in the output. Confirmatory factor analysis is limited to the common factor model for congeneric, tau-equivalent, and parallel measures.
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Several reliability tests have been performed on the SB5 including split-half reliability, standard error of measurement, plotting of test information curves, test-retest stability, and inter-scorer agreement. On average, IQ scores for this scale have been found quite stable across time (Janzen, Obrzut, & Marusiak, 2003). Internal consistency was tested by split- half reliability and was reported to be substantial and comparable to other cognitive batteries (Bain & Allin, 2005). The median interscorer correlation was .
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HDL levels can be increased by smoking cessation, or mild to moderate alcohol intake. Cannabis in unadjusted analyses, past and current cannabis use was not associated with higher HDL-C levels. A study performed in 4635 patients demonstrated no effect on the HDL-C levels (P=0.78) [the mean (standard error) HDL-C values in control subjects (never used), past users and current users were 53.4 (0.4), 53.9 (0.6) and 53.9 (0.7) mg/dL, respectively].
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Both the Diary and Interview Surveys utilize a representative sample to measure the buying habits of American consumers. Only a small percentage of the U.S. population is surveyed, and therefore the data are subject to sampling errors. The division publishes standard error tables on their website. Non-sampling errors include, but are not limited to, respondents who are either unwilling or unable to provide accurate answers, mistakes made in collecting or recording obtained data, and estimation of missing data.
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Early editions of the WOA additionally included fields such as mixed layer depth and sea surface height. In addition to the averaged fields of ocean properties, the WOA also contains fields of statistical information concerning the constituent data that the averages were produced from. These include fields such as the number of data points the average is derived from, their standard deviation and standard error. A lower horizontal resolution (5°) version of the WOA is also available.
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In statistics, a Galbraith plot (also known as Galbraith's radial plot or just radial plot) is one way of displaying several estimates of the same quantity that have different standard errors. Example for Galbraith's radial plot. It can be used to examine heterogeneity in a meta-analysis, as an alternative or supplement to a forest plot. A Galbraith plot is produced by first calculating the standardized estimates or z-statistics by dividing each estimate by its standard error (SE).
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Iteman is a commercial Windows program specifically designed for classical test analysis, producing rich text (RTF) reports with graphics, narratives, and embedded tables. It calculates the proportion and point biserial of each item, as well as high/low subgroup proportions, and detailed graphics of item performance. It also calculates typical descriptive statistics, including the mean, standard deviation, reliability, and standard error of measurement, for each domain and the overall tests. It is only available from Assessment Systems Corporation.
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It was well known to classical test theorists that measurement precision is not uniform across the scale of measurement. Tests tend to distinguish better for test-takers with moderate trait levels and worse among high- and low- scoring test-takers. Item response theory extends the concept of reliability from a single index to a function called the information function. The IRT information function is the inverse of the conditional observed score standard error at any given test score.
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Location tests are the most familiar Z-tests. Another class of Z-tests arises in maximum likelihood estimation of the parameters in a parametric statistical model. Maximum likelihood estimates are approximately normal under certain conditions, and their asymptotic variance can be calculated in terms of the Fisher information. The maximum likelihood estimate divided by its standard error can be used as a test statistic for the null hypothesis that the population value of the parameter equals zero.
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Otherwise, the null hypothesis of no explanatory power is accepted. Second, for each explanatory variable of interest, one wants to know whether its estimated coefficient differs significantly from zero—that is, whether this particular explanatory variable in fact has explanatory power in predicting the response variable. Here the null hypothesis is that the true coefficient is zero. This hypothesis is tested by computing the coefficient's t-statistic, as the ratio of the coefficient estimate to its standard error.
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On 1 August 2014 the Referendum initiative committee submitted the "Proposal on the holding of a referendum on the Main railway station location" to Brno municipal authority and with 1,531 referendum petition forms containing 21,101 signatures of eligible voters. Fifteen days later, the authority claimed that 5,251 signatures were incorrect (i.e. invalid). The initiative committee considered this statement dubious, arbitrary and obstructive from the side of the public authority. (Standard error rate during signature gathering is around 3%).
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The TL431 is the de facto industry standard error amplifier circuit for switched-mode power supplies with optoelectronic coupling of input and output networks. The TL431 was introduced by Texas Instruments in 1977. In the 21st century the original TL431 remains in production along with a multitude of clones and derivatives (TL432, ATL431, KA431, LM431, TS431, 142ЕН19 and others). These functionally similar circuits may differ considerably in die size and layout, precision and speed characteristics, minimal operating currents and safe operating areas.
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Each ability estimate has an associated standard error of measurement, which quantifies the degree of uncertainty associated with the ability estimate. Item estimates also have standard errors. Generally, the standard errors of item estimates are considerably smaller than the standard errors of person estimates because there are usually more response data for an item than for a person. That is, the number of people attempting a given item is usually greater than the number of items attempted by a given person.
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Gurland and Tripathi (1971) provide a correction and equation for this effect. Sokal and Rohlf (1981) give an equation of the correction factor for small samples of n < 20. See unbiased estimation of standard deviation for further discussion. A practical result: Decreasing the uncertainty in a mean value estimate by a factor of two requires acquiring four times as many observations in the sample; decreasing the standard error by a factor of ten requires a hundred times as many observations.
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In some settings, estimating the variability of a spillover effect creates additional difficulty. When the research study has a fixed unit of clustering, such as a school or household, researchers can use traditional standard error adjustment tools like cluster- robust standard errors, which allow for correlations in error terms within clusters but not across them. In other settings, however, there is no fixed unit of clustering. In order to conduct hypothesis testing in these settings, the use of randomization inference is recommended.
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See below).Linton, L.R., Harder, L.D. (2007) Biology 315 – Quantitative Biology Lecture Notes. University of Calgary, Calgary, AB The Tukey HSD tests should not be confused with the Tukey Mean Difference tests (also known as the Bland–Altman diagram). Tukey's test compares the means of every treatment to the means of every other treatment; that is, it applies simultaneously to the set of all pairwise comparisons :\mu_i-\mu_j \, and identifies any difference between two means that is greater than the expected standard error.
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A bar chart with confidence intervals (shown as red lines) Error bars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement. They give a general idea of how precise a measurement is, or conversely, how far from the reported value the true (error free) value might be. Error bars often represent one standard deviation of uncertainty, one standard error, or a particular confidence interval (e.g., a 95% interval).
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As a result, it is possible to redirect the standard error stream. ( uses temporary files, and runs the two sides serially, one after the other.) Multiple commands can be processed in a single command line using the command separator . For example: C:\>CommandA && CommandB && CommandC On Windows XP or later, the maximum length of the string that can be used at the command prompt is 8191 characters. On earlier versions, such as Windows 2000 or Windows NT 4.0, the maximum length of the string is 2047 characters.
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The proper motion of this star was measured as -4.7 mas/yr in right ascension and +6.4 mas/yr in declination, with a standard error of 4 mas/yr. Examination of the optical spectrum of this nova showed absorption lines of calcium (Ca I), sodium (Na I) and singly ionized iron (Fe II). The initial spectrum was deficient in hydrogen and did not match those typical of other nova types. The infrared spectrum measured on January 31 showed a featureless continuum that decreased with increasing wavelength.
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Thermometer data shown with a dotted line overlapped the reconstruction for a calibration period from 1902 to 1980, then continued sharply up to 1998. A shaded area showed uncertainties to two standard error limits, in medieval times rising almost as high as recent temperatures. When Mann gave a talk about the study to the National Oceanic and Atmospheric Administration's Geophysical Fluid Dynamics Laboratory, Jerry Mahlman nicknamed the graph the "hockey stick", with the slow cooling trend the "stick", and the anomalous 20th century warming the "blade".
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In statistics, the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is used in hypothesis testing via Student's t-test. The T-statistic is used in a T test to determine if you should support or reject the null hypothesis. It is very similar to the Z-score but with the difference that T-statistic is used when the sample size is small or the population standard deviation is unknown.
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An important difference between CTT and IRT is the treatment of measurement error, indexed by the standard error of measurement. All tests, questionnaires, and inventories are imprecise tools; we can never know a person's true score, but rather only have an estimate, the observed score. There is some amount of random error which may push the observed score higher or lower than the true score. CTT assumes that the amount of error is the same for each examinee, but IRT allows it to vary.
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206x206px Users generally know standard streams as input and output channels that handle data coming from an input device, or that write data from the application. The data may be text with any encoding, or binary data. In many modern systems, the standard error stream of a program is redirected into a log file, typically for error analysis purposes. Streams may be used to chain applications, meaning that the output stream of one program can be redirected to be the input stream to another application.
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Jackknifing, which is similar to bootstrapping, is used in statistical inference to estimate the bias and standard error (variance) of a statistic, when a random sample of observations is used to calculate it. Historically, this method preceded the invention of the bootstrap with Quenouille inventing this method in 1949 and Tukey extending it in 1958. This method was foreshadowed by Mahalanobis who in 1946 suggested repeated estimates of the statistic of interest with half the sample chosen at random. He coined the name 'interpenetrating samples' for this method.
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To remedy this problem, researchers may collapse categories in a theoretically meaningful way or may consider adding a constant to all cells.[6] Another numerical problem that may lead to a lack of convergence is complete separation, which refers to the instance in which the predictors perfectly predict the criterion - all cases are accurately classified. In such instances, one should reexamine the data, as there is likely some kind of error. # Wald statistic is defined by, where is the sample estimation of and is the standard error of .
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This dating method works by measuring the ratio of oxidizable carbon to organic carbon. If the sample is freshly burned there will be no oxidizable carbon because it would have all been removed by the combustion process. Over time this will change and the amount of organic carbon will decrease to be replaced by oxidizable carbon. By measuring the ratio of oxidized carbon to organic carbon (the OCR) and applying it to the following equation the age of the sample can be determined with a very low standard error.
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The HP 20b contains functions similar to the HP 10bII, with financial functions including: TVM, IRR, NPV, NUS ("Net Uniform Series"), amortization, depreciation, bonds, yield and accrued interest, interest conversion, list-based cashflow analysis, cashflows, break-even analysis. Math/Statistics functions include: list-base, 1 and 2 variable statistics, mean, standard deviation, population deviation, standard error, forecasting, correlations and covariance, +, -, ×, ÷, %, 1/x, +/-, scientific notation, n!, combinations, permutations, rounding, random numbers, LOG, LN, 10×, PL, square root, trigonometry, probability. For input modes, it supports RPN, Chain and Algebraic input.
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Since only P can be observed or measured directly, heritability must be estimated from the similarities observed in subjects varying in their level of genetic or environmental similarity. The statistical analyses required to estimate the genetic and environmental components of variance depend on the sample characteristics. Briefly, better estimates are obtained using data from individuals with widely varying levels of genetic relationship - such as twins, siblings, parents and offspring, rather than from more distantly related (and therefore less similar) subjects. The standard error for heritability estimates is improved with large sample sizes.
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In computing, Verbose mode is an option available in many computer operating systems and programming languages that provides additional details as to what the computer is doing and what drivers and software it is loading during startup or in programming it would produce detailed output for diagnostic purposes thus makes a program easier to debug. When running programs in the command-line, verbose output is typically outputted in standard output or standard error. Many command line programs can be set to verbose mode by using a flag, such as or . Such a program is cURL.
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Epidemiological analysis: Using commands similar to those in EpiInfo, CIETanalysis produces basic frequencies (like the proportion with a given disease) through to multivariate models of gains (like the proportion that can be "saved" by a given intervention). Users can generate descriptive stats (mean, standard deviation, standard error); odds ratios, risk difference, gains and confidence intervals. An interface with R gives access to most statistical capabilities available in that language; some of these are available through customised drop-down menus. CIETmap can import data in other formats as SPSS, dBase or Excel.
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A negative or positive relation between standard error and effect size would imply that smaller studies that found effects in one direction only were more likely to be published and/or to be submitted for publication. Apart from the visual funnel plot, statistical methods for detecting publication bias have also been proposed. These are controversial because they typically have low power for detection of bias, but also may make false positives under some circumstances. For instance small study effects (biased smaller studies), wherein methodological differences between smaller and larger studies exist, may cause asymmetry in effect sizes that resembles publication bias.
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Guidance for how data should be transformed, or whether a transformation should be applied at all, should come from the particular statistical analysis to be performed. For example, a simple way to construct an approximate 95% confidence interval for the population mean is to take the sample mean plus or minus two standard error units. However, the constant factor 2 used here is particular to the normal distribution, and is only applicable if the sample mean varies approximately normally. The central limit theorem states that in many situations, the sample mean does vary normally if the sample size is reasonably large.
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All inertial navigation systems suffer from integration drift: small errors in the measurement of acceleration and angular velocity are integrated into progressively larger errors in velocity, which are compounded into still greater errors in position.Inertial navigation systems analysis, Kenneth R. Britting, Wiley-Interscience, 1971. Since the new position is calculated from the previous calculated position and the measured acceleration and angular velocity, these errors accumulate roughly proportionally to the time since the initial position was input. Even the best accelerometers, with a standard error of 10 micro-g, would accumulate a 50-meter error within 17 minutes.Calculated from reversing S=1/2.a.
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This result was uncalibrated, as the need for calibration of radiocarbon ages was not yet understood. Further results over the next decade supported an average date of 11,350 BP, with the results thought to be the most accurate averaging 11,600 BP. There was initial resistance to these results on the part of Ernst Antevs, the palaeobotanist who had worked on the Scandinavian varve series, but his objections were eventually discounted by other geologists. In the 1990s samples were tested with AMS, yielding (uncalibrated) dates ranging from 11,640 BP to 11,800 BP, both with a standard error of 160 years.
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Clinical projects include Prostate Specific Antigen volatility or PVI, a method that looks at the variability of PSA levels to determine a person's risk of prostate cancer.Pub Med Reference Number 17895878 The formula for PVI is PVI=[(standard error of PSA values)/(exp^slope of PSA curve)]. Other projects include the usefulness of chromosome analysis in bladder cancerPub Med Reference Number 16831139 and the cost-effectiveness of specialized CT scans for urologic problems. Basic science projects include studies of fibroblast-growth factor III (FGFR-III), an important tyrosine kinase, and using anti-FGFR-III drugs to prevent the growth of bladder cancers.
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The calibration curve itself has an associated error term, which can be seen on the graph labelled "Calibration error and measurement error". This graph shows INTCAL13 data for the calendar years 3100 BP to 3500 BP. The solid line is the INTCAL13 calibration curve, and the dotted lines show the standard error range, as with the sample error, this is one standard deviation. Simply reading off the range of radiocarbon years against the dotted lines, as is shown for sample t2, in red, gives too large a range of calendar years. The error term should be the root of the sum of the squares of the two errors:Aitken (1990), p. 101.
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Ziliak, S. and D. McCloskey (2008), The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives (University of Michigan Press) Gosset acquired that knowledge by study, by trial and error, by cooperating with others, and by spending two terms in 1906–1907 in the Biometrics laboratory of Karl Pearson.h Gosset and Pearson had a good relationship.Stephen T. Ziliak (2019), "How large are your G-values? Try Gosset's Guinnessometrics when a little p is not enough", The American Statistician 73 Pearson helped Gosset with the mathematics of his papers, including the 1908 papers, but had little appreciation of their importance.
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However, when estimating the standard error or confidence interval of her statistical model, she realizes that classical or even heteroscedasticity-robust standard errors are inappropriate because student test scores within each class are not independently distributed. Instead, students in classes with better teachers have especially high test scores (regardless of whether they receive the experimental treatment) while students in classes with worse teachers have especially low test scores. The researcher can cluster her standard errors at the level of a classroom to account for this aspect of her experiment. While this example is very specific, similar issues arise in a wide variety of settings.
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In 1986, Tom Roberts performed a standard error analysis of Miller's "Ether drift" data, using 67 of Miller's original data sheets (obtained from the CWRU archives). This error analysis is related to the averaging Miller performed and is unassailable. The errorbars on the individual data points are nearly 10 times larger than the variation in those points, so Miller's results are not statistically meaningful; not even close. It is also shown why Miller thought his result was valid: the data analysis he used is a comb filter that aliases most of the noise into the same bin where a signal would be, accurately mimicking the signal he sought.
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An asymmetric funnel indicates a relationship between treatment effect estimate and study precision. This suggests the possibility of either publication bias or a systematic difference between studies of higher and lower precision (typically ‘small study effects’). Asymmetry can also arise from use of an inappropriate effect measure. Whatever the cause, an asymmetric funnel plot leads to doubts over the appropriateness of a simple meta-analysis and suggests that there needs to be investigation of possible causes. A variety of choices of measures of ‘study precision’ is available, including total sample size, standard error of the treatment effect, and inverse variance of the treatment effect (weight).
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The CAT algorithm is designed to repeatedly administer items and update the estimate of examinee ability. This will continue until the item pool is exhausted unless a termination criterion is incorporated into the CAT. Often, the test is terminated when the examinee's standard error of measurement falls below a certain user-specified value, hence the statement above that an advantage is that examinee scores will be uniformly precise or "equiprecise." Other termination criteria exist for different purposes of the test, such as if the test is designed only to determine if the examinee should "Pass" or "Fail" the test, rather than obtaining a precise estimate of their ability.
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T-distributions are slightly different from Gaussian, and vary depending on the size of the sample. Small samples are somewhat more likely to underestimate the population standard deviation and have a mean that differs from the true population mean, and the Student t-distribution accounts for the probability of these events with somewhat heavier tails compared to a Gaussian. To estimate the standard error of a Student t-distribution it is sufficient to use the sample standard deviation "s" instead of σ, and we could use this value to calculate confidence intervals. Note: The Student's probability distribution is approximated well by the Gaussian distribution when the sample size is over 100.
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The econometric literature on testing for contagion has focused on increases in the correlation of returns between markets during periods of crisis. Forbes and Rigobon (2002) described the current imprecision and disagreement surrounding the term contagion. It proposes a concrete definition, a significant increase in cross-market linkages after a shock, and suggests using the term "interdependence" in order to differentiate this explicit definition from the existing literature. It shows the elementary weakness of simple correlation tests: with an unchanged regression coefficient, a rise in the variance of the explanatory variable reduces the coefficient standard error, causing a rise in the correlation of a regression.
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Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, and consistency. An estimator is unbiased if its expected value is the true value of the parameter; it is consistent if it converges to the true value as the sample size gets larger, and it is efficient if the estimator has lower standard error than other unbiased estimators for a given sample size. Ordinary least squares (OLS) is often used for estimation since it provides the BLUE or "best linear unbiased estimator" (where "best" means most efficient, unbiased estimator) given the Gauss-Markov assumptions.
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The problem here is that, according to classical test theory, the standard error of measurement is assumed to be the same for all examinees. However, as Hambleton explains in his book, scores on any test are unequally precise measures for examinees of different ability, thus making the assumption of equal errors of measurement for all examinees implausible (Hambleton, Swaminathan, Rogers, 1991, p. 4). A fourth, and final shortcoming of the classical test theory is that it is test oriented, rather than item oriented. In other words, classical test theory cannot help us make predictions of how well an individual or even a group of examinees might do on a test item.
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This is not easily solved, as one cannot know how many studies have gone unreported. This file drawer problem (characterized by negative or non-significant results being tucked away in a cabinet), can result in a biased distribution of effect sizes thus creating a serious base rate fallacy, in which the significance of the published studies is overestimated, as other studies were either not submitted for publication or were rejected. This should be seriously considered when interpreting the outcomes of a meta-analysis. The distribution of effect sizes can be visualized with a funnel plot which (in its most common version) is a scatter plot of standard error versus the effect size.
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Biased standard errors lead to biased inference, so results of hypothesis tests are possibly wrong. For example, if OLS is performed on a heteroscedastic data set, yielding biased standard error estimation, a researcher might fail to reject a null hypothesis at a given significance level, when that null hypothesis was actually uncharacteristic of the actual population (making a type II error). Under certain assumptions, the OLS estimator has a normal asymptotic distribution when properly normalized and centered (even when the data does not come from a normal distribution). This result is used to justify using a normal distribution, or a chi square distribution (depending on how the test statistic is calculated), when conducting a hypothesis test.
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A prediction interval instead gives an interval in which one expects yd to fall; this is not necessary if the actual parameters α and β are known (together with the error term εi), but if one is estimating from a sample, then one may use the standard error of the estimates for the intercept and slope (\hat\alpha and \hat\beta), as well as their correlation, to compute a prediction interval. In regression, makes a distinction between intervals for predictions of the mean response vs. for predictions of observed response—affecting essentially the inclusion or not of the unity term within the square root in the expansion factors above; for details, see .
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In a personnel selection example, test content is based on a defined statement or set of statements of knowledge, skill, ability, or other characteristics obtained from a job analysis. Item response theory models the relationship between latent traits and responses to test items. Among other advantages, IRT provides a basis for obtaining an estimate of the location of a test-taker on a given latent trait as well as the standard error of measurement of that location. For example, a university student's knowledge of history can be deduced from his or her score on a university test and then be compared reliably with a high school student's knowledge deduced from a less difficult test.
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It makes use of the fact that the smaller studies (thus larger standard errors) have more scatter of the magnitude of effect (being less precise) while the larger studies have less scatter and form the tip of the funnel. If many negative studies were not published, the remaining positive studies give rise to a funnel plot in which the base is skewed to one side (asymmetry of the funnel plot). In contrast, when there is no publication bias, the effect of the smaller studies has no reason to be skewed to one side and so a symmetric funnel plot results. This also means that if no publication bias is present, there would be no relationship between standard error and effect size.
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All these standard measures offer a fine granularity or smoothness to the solution space and therefore work very well for most applications. But some problems might require a coarser evolution, such as determining if a prediction is within a certain interval, for instance less than 10% of the actual value. However, even if one is only interested in counting the hits (that is, a prediction that is within the chosen interval), making populations of models evolve based on just the number of hits each program scores is usually not very efficient due to the coarse granularity of the fitness landscape. Thus the solution usually involves combining these coarse measures with some kind of smooth function such as the standard error measures listed above.
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This has to be done by numerical methods rather than by a formula because the calibration curve is not describable as a formula. Programs to perform these calculations include OxCal and CALIB. These can be accessed online; they allow the user to enter a date range at one standard deviation confidence for the radiocarbon ages, select a calibration curve, and produce probabilistic output both as tabular data and in graphical form. In the example CALIB output shown at left, the input data is 1270 BP, with a standard deviation of 10 radiocarbon years. The curve selected is the northern hemisphere INTCAL13 curve, part of which is shown in the output; the vertical width of the curve corresponds to the width of the standard error in the calibration curve at that point.
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An internal compiler error (commonly abbreviated as ICE) is an error that occurs not due to erroneous source code, but rather due to a bug in the compiler itself. They can sometimes be worked around by making small, insignificant changes to the source code around the line indicated by the error (if such a line is indicated at all), but sometimes larger changes must be made, such as refactoring the code, to avoid certain constructs. Using a different compiler or different version of the compiler may solve the issue and be an acceptable solution in some cases. When an internal compiler error is reached many compilers do not output a standard error, but instead output a shortened version, with additional files attached, which are only provided for internal compiler errors.
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The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator (how widely spread the estimates are from one data sample to another) and its bias (how far off the average estimated value is from the true value). For an unbiased estimator, the MSE is the variance of the estimator. Like the variance, MSE has the same units of measurement as the square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root- mean-square error or root-mean-square deviation (RMSE or RMSD), which has the same units as the quantity being estimated; for an unbiased estimator, the RMSE is the square root of the variance, known as the standard error.
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CV measures are often used as quality controls for quantitative laboratory assays. While intra-assay and inter-assay CVs might be assumed to be calculated by simply averaging CV values across CV values for multiple samples within one assay or by averaging multiple inter-assay CV estimates, it has been suggested that these practices are incorrect and that a more complex computational process is required. It has also been noted that CV values are not an ideal index of the certainty of a measurement when the number of replicates varies across samples − in this case standard error in percent is suggested to be superior. If measurements do not have a natural zero point then the CV is not a valid measurement and alternative measures such as the intraclass correlation coefficient are recommended.
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Clustered standard errors are measurements that estimate the standard error of a regression parameter in settings where observations may be subdivided into smaller-sized groups ("clusters") and where the sampling and/or treatment assignment is correlated within each group. Clustered standard errors are widely used in a variety of applied econometric settings, including difference-in-differences or experiments. Analogous to how Huber-White standard errors are consistent in the presence of heteroscedasticity and Newey–West standard errors are consistent in the presence of accurately- modeled autocorrelation, clustered (or "Liang-Zieger") standard errors are consistent in the presence of cluster-based sampling or treatment assignment. Clustered standard errors are often justified by possible correlation in modeling residuals within each cluster; while recent work suggests that this is not the precise justification behind clustering, it may be pedagogically useful.
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The reduction from the baseline in HbA1c was –1.06 (95% CI, –1.28 to –0.85) in the patients who continued to receive gemigliptin 50 mg qd. Add-on to metformin and glimepiride In this multicenter, randomized, blinded, phase III study (study identifier: LG-DPCL010, TROICA study; ClinicalTrials.gov registration number: NCT01990469), eligible patients with inadequate glycemic control (7%≤HbA1c≤11%) were randomized to gemigliptin 50 mg qd (n=109) or placebo (n= 110). The baseline demographics were similar between groups (age, 60.9 years; BMI, 24.9 kg/m2; duration of T2DM, 12.9 years), with mean±standard deviation (SD) baseline HbA1c of 8.12%± 0.82% in the gemigliptin group and 8.15%±0.89% in the placebo group. At week 24, the adjusted mean±standard error change for HbA1c with gemigliptin was –0.88%±0.17% (change with placebo –0.01%±0.18%; difference –0.87%±0.12%; 95% CI, –1.09 to –0.64; P<0.0001).
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In 1998 Michael E. Mann, Raymond S. Bradley and Malcolm K. Hughes developed new statistical techniques to produce (MBH98), the first eigenvector-based climate field reconstruction (CFR). This showed global patterns of annual surface temperature, and included a graph of average hemispheric temperatures back to 1400 with shading emphasising that uncertainties (to two standard error limits) were much greater in earlier centuries. independently produced a CPS reconstruction extending back for a thousand years, and (MBH99) used the MBH98 methodology to extend their study back to 1000. A version of the MBH99 graph was featured prominently in the 2001 IPCC Third Assessment Report (TAR), which also drew on Jones et al. 1998 and three other reconstructions to support the conclusion that, in the Northern Hemisphere, the 1990s was likely to have been the warmest decade and 1998 the warmest year during the past 1,000 years. The graph became a focus of dispute for those opposed to the strengthening scientific consensus that late 20th century warmth was exceptional.
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Bousman & Vierra (2012), p. 4. At Two Creeks, in Wisconsin, a fossil forest was discovered (Two Creeks Buried Forest State Natural Area), and subsequent research determined that the destruction of the forest was caused by the Valders ice readvance, the last southward movement of ice before the end of the Pleistocene in that area. Before the advent of radiocarbon dating, the fossilized trees had been dated by correlating sequences of annually deposited layers of sediment at Two Creeks with sequences in Scandinavia. This led to estimates that the trees were between 24,000 and 19,000 years old, and hence this was taken to be the date of the last advance of the Wisconsin glaciation before its final retreat marked the end of the Pleistocene in North America.Macdougall (2008), pp. 94–95. In 1952 Libby published radiocarbon dates for several samples from the Two Creeks site and two similar sites nearby; the dates were averaged to 11,404 BP with a standard error of 350 years.
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