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The fences are obtained by inflating the envelope of the 50% central region by 1.5 times the height of the 50% central region. Any observations outside the fences are flagged as potential outliers. When each observation is simply a point, the functional boxplot degenerates to a classical boxplot, and it is different from the pointwise boxplots.
Figure 2. Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value. A boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles.
In statistics, Grubbs's test or the Grubbs test (named after Frank E. Grubbs, who published the test in 1950 [1]), 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.
Boxplot (with an interquartile range) and a probability density function (pdf) of a Normal N(0,σ 2) Population. In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. [1] The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread.
It is possible to quickly compare several sets of observations by comparing their five-number summaries, which can be represented graphically using a boxplot. In addition to the points themselves, many L-estimators can be computed from the five-number summary, including interquartile range , midhinge , range , mid-range , and trimean .
= + Boxplot Diagram with Outliers The lower fence is the "lower limit" and the upper fence is the "upper limit" of data, and any data lying outside these defined bounds can be considered an outlier. The fences provide a guideline by which to define an outlier , which may be defined in other ways.
To construct a contour boxplot, data ordering is the first step. In functional data analysis, each observation is a real function, therefore data ordering is different from the classical boxplot where scalar data are simply ordered from the smallest sample value to the largest. More generally, data depth, gives a center-outward ordering of data ...
The presence of outliers can severely bias the correlation coefficient. Large sample sizes can result in statistically significant correlations that may have little or no practical significance. It is not possible to draw conclusions about causality based on correlation analyses alone.