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Grubbs's Test For Outliers
In statistics, Grubbs's test or the Grubbs test (named after Frank E. Grubbs, who published the test in 1950), also known as the maximum normalized residual test or extreme studentized deviate test, is a test used to detect outliers in a univariate data set assumed to come from a normally distributed population. Definition Grubbs's test is based on the assumption of normality. That is, one should first verify that the data can be reasonably approximated by a normal distribution before applying the Grubbs test. Grubbs's test detects one outlier at a time. This outlier is expunged from the dataset and the test is iterated until no outliers are detected. However, multiple iterations change the probabilities of detection, and the test should not be used for sample sizes of six or fewer since it frequently tags most of the points as outliers. Grubbs's test is defined for the hypothesis: :H0: There are no outliers in the data set :Ha: There is exactly one outlier in the data set Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank E
Frank or Franks may refer to: People * Frank (given name) * Frank (surname) * Franks (surname) * Franks, a medieval Germanic people * Frank, a term in the Muslim world for all western Europeans, particularly during the Crusades - see Farang Currency * Liechtenstein franc or frank, the currency of Liechtenstein since 1920 * Swiss franc or frank, the currency of Switzerland since 1850 * Westphalian frank, currency of the Kingdom of Westphalia between 1808 and 1813 * The currencies of the German-speaking cantons of Switzerland (1803–1814): ** Appenzell frank ** Argovia frank ** Basel frank ** Berne frank ** Fribourg frank ** Glarus frank ** Graubünden frank ** Luzern frank ** Schaffhausen frank ** Schwyz frank ** Solothurn frank ** St. Gallen frank ** Thurgau frank ** Unterwalden frank ** Uri frank ** Zürich frank Places * Frank, Alberta, Canada, an urban community, formerly a village * Franks, Illinois, United States, an unincorporated community * Franks, Missouri, Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degrees Of Freedom (statistics)
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom. In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself. For example, if the variance is to be estimated from a random sample of ''N'' independent scores, then the degrees of freedom is equal to the number of independent scores (''N'') minus the number of parameters estimated as intermediate steps (one, namely, the sample mean) and is therefore equal to ''N'' − 1. Mathematically, degrees of freedom is the number of dimensions of the domain o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tau Distribution
In statistics, a studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation. It is a form of a Student's ''t''-statistic, with the estimate of error varying between points. This is an important technique in the detection of outliers. It is among several named in honor of William Sealey Gosset, who wrote under the pseudonym ''Student''. Dividing a statistic by a sample standard deviation is called studentizing, in analogy with standardizing and normalizing. Motivation The key reason for studentizing is that, in regression analysis of a multivariate distribution, the variances of the ''residuals'' at different input variable values may differ, even if the variances of the ''errors'' at these different input variable values are equal. The issue is the difference between errors and residuals in statistics, particularly the behavior of residuals in regressions. Consider the simple linear regression model : Y = \alp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Studentized Residual
In statistics, a studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation. It is a form of a Student's ''t''-statistic, with the estimate of error varying between points. This is an important technique in the detection of outliers. It is among several named in honor of William Sealey Gosset, who wrote under the pseudonym ''Student''. Dividing a statistic by a sample standard deviation is called studentizing, in analogy with standardizing and normalizing. Motivation The key reason for studentizing is that, in regression analysis of a multivariate distribution, the variances of the ''residuals'' at different input variable values may differ, even if the variances of the ''errors'' at these different input variable values are equal. The issue is the difference between errors and residuals in statistics, particularly the behavior of residuals in regressions. Consider the simple linear regression model : Y = \a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Q Test
In statistics, Dixon's ''Q'' test, or simply the ''Q'' test, is used for identification and rejection of outliers. This assumes normal distribution and per Robert Dean and Wilfrid Dixon, and others, this test should be used sparingly and never more than once in a data set. To apply a ''Q'' test for bad data, arrange the data in order of increasing values and calculate ''Q'' as defined: : Q = \frac Where ''gap'' is the absolute difference between the outlier in question and the closest number to it. If ''Q'' > ''Q''table, where ''Q''table is a reference value corresponding to the sample size and confidence level, then reject the questionable point. Note that only one point may be rejected from a data set using a ''Q'' test. Example Consider the data set: :0.189,\ 0.167,\ 0.187,\ 0.183,\ 0.186,\ 0.182,\ 0.181,\ 0.184,\ 0.181,\ 0.177 \, Now rearrange in increasing order: :0.167,\ 0.177,\ 0.181,\ 0.181,\ 0.182,\ 0.183,\ 0.184,\ 0.186,\ 0.187,\ 0.189 \, We hypothe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peirce's Criterion
In robust statistics, Peirce's criterion is a rule for eliminating outliers from data sets, which was devised by Benjamin Peirce. Outliers removed by Peirce's criterion The problem of outliers In data sets containing real-numbered measurements, the suspected outliers are the measured values that appear to lie outside the cluster of most of the other data values. The outliers would greatly change the estimate of location if the arithmetic average were to be used as a summary statistic of location. The problem is that the arithmetic mean is very sensitive to the inclusion of any outliers; in statistical terminology, the arithmetic mean is not robust. In the presence of outliers, the statistician has two options. First, the statistician may remove the suspected outliers from the data set and then use the arithmetic mean to estimate the location parameter. Second, the statistician may use a robust statistic, such as the median statistic. Peirce's criterion is a statistical procedur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chauvenet's Criterion
In statistical theory, Chauvenet's criterion (named for William Chauvenet) is a means of assessing whether one piece of experimental data — an outlier — from a set of observations, is likely to be spurious. Derivation The idea behind Chauvenet's criterion is to find a probability band, centered on the mean of a normal distribution, that should reasonably contain all n samples of a data set. By doing this, any data points from the n samples that lie outside this probability band can be considered to be outliers, removed from the data set, and a new mean and standard deviation based on the remaining values and new sample size can be calculated. This identification of the outliers will be achieved by finding the number of standard deviations that correspond to the bounds of the probability band around the mean (D_) and comparing that value to the absolute value of the difference between the suspected outliers and the mean divided by the sample standard deviation (Eq.1). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Probability Plot
The normal probability plot is a graphical technique to identify substantive departures from normality. This includes identifying outliers, skewness, kurtosis, a need for transformations, and mixtures. Normal probability plots are made of raw data, residuals from model fits, and estimated parameters. In a normal probability plot (also called a "normal plot"), the sorted data are plotted vs. values selected to make the resulting image look close to a straight line if the data are approximately normally distributed. Deviations from a straight line suggest departures from normality. The plotting can be manually performed by using a special graph paper, called ''normal probability paper''. With modern computers normal plots are commonly made with software. The normal probability plot is a special case of the Q–Q probability plot for a normal distribution. The theoretical quantiles are generally chosen to approximate either the mean or the median of the corresponding or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Histogram
A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to " bin" (or "bucket") the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent and are often (but not required to be) of equal size. If the bins are of equal size, a bar is drawn over the bin with height proportional to the frequency—the number of cases in each bin. A histogram may also be normalized to display "relative" frequencies showing the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1. However, bins need not be of equal width; in that case, the erected rectangle is defined to have its ''area'' proportional to the frequency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Box Plot
In descriptive statistics, a box plot or boxplot is a method for graphically demonstrating the locality, spread and skewness groups of numerical data through their quartiles. In addition to the box on a box plot, there can be lines (which are called ''whiskers'') extending from the box indicating variability outside the upper and lower quartiles, thus, the plot is also termed as the box-and-whisker plot and the box-and-whisker diagram. Outliers that differ significantly from the rest of the dataset may be plotted as individual points beyond the whiskers on the box-plot. Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution (though Tukey's boxplot assumes symmetry for the whiskers and normality for their length). The spacings in each subsection of the box-plot indicate the degree of dispersion (spread) and skewness of the data, which are usually described using the five ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Run Sequence Plot
A run chart, also known as a run-sequence plot is a graph that displays observed data in a time sequence. Often, the data displayed represent some aspect of the output or performance of a manufacturing or other business process. It is therefore a form of line chart. Overview Run sequence plots are an easy way to graphically summarize a univariate data set. A common assumption of univariate data sets is that they behave like:NIST/SEMATECH (2003)"Run-Sequence Plot"In: ''e-Handbook of Statistical Methods'' 6/01/2003 (Date created). * random drawings; * from a fixed distribution; * with a common location; and * with a common scale. With run sequence plots, shifts in location and scale are typically quite evident. Also, outliers can easily be detected. Examples could include measurements of the fill level of bottles filled at a bottling plant or the water temperature of a dish-washing machine each time it is run. Time is generally represented on the horizontal (x) axis and the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphical Technique
Statistical graphics, also known as statistical graphical techniques, are graphics used in the field of statistics for data visualization. Overview Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial form. They include plots such as scatter plots, histograms, probability plots, spaghetti plots, residual plots, box plots, block plots and biplots. Exploratory data analysis (EDA) relies heavily on such techniques. They can also provide insight into a data set to help with testing assumptions, model selection and regression model validation, estimator selection, relationship identification, factor effect determination, and outlier detection. In addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others. Graphical statistical methods h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
