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The idea behind Chauvenet's criterion finds a probability band that reasonably contains all n samples of a data set, centred on the mean of a normal distribution.By doing this, any data point from the n samples that lies outside this probability band can be considered an outlier, removed from the data set, and a new mean and standard deviation based on the remaining values and new sample size ...
To apply a Q test for bad data, arrange the data in order of increasing values and calculate Q as defined: = 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 ...
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. [3] Grubbs's test is defined for the following hypotheses: H 0: There are no outliers in the data set H a: There is exactly one outlier in the data set
The strength of this method lies in the fact that it takes into account a data set's standard deviation, average and provides a statistically determined rejection zone; thus providing an objective method to determine if a data point is an outlier. [citation needed] [23] How it works: First, a data set's average is determined. Next the absolute ...
The normal probability plot is formed by plotting the sorted data vs. an approximation to the means or medians of the corresponding order statistics; see rankit. Some plot the data on the vertical axis; [1] others plot the data on the horizontal axis. [2] [3] Different sources use slightly different approximations for rankits.
Moreover, the MAD is a robust statistic, being more resilient to outliers in a data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it. In the MAD, the deviations of a small number of outliers are irrelevant.
A simple example is fitting a line in two dimensions to a set of observations. Assuming that this set contains both inliers, i.e., points which approximately can be fitted to a line, and outliers, points which cannot be fitted to this line, a simple least squares method for line fitting will generally produce a line with a bad fit to the data including inliers and outliers.
Since when stand-out data is compared it was by definition not selected at random, but rather specifically chosen because it was extreme, it needs a different, stricter interpretation provided by the likely frequency and size of the studentized range; the modern practice of "data mining" is an example where it is used.