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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 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.
It is defined as a scaled median difference between the left and right half of a distribution. Its robustness makes it suitable for identifying outliers in adjusted boxplots. [2] [3] Ordinary box plots do not fare well with skew distributions, since they label the longer unsymmetrical tails as outliers. Using the medcouple, the whiskers of a ...
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 ...
Meaning, if a data point is found to be an outlier, it is removed from the data set and the test is applied again with a new average and rejection region. This process is continued until no outliers remain in a data set. Some work has also examined outliers for nominal (or categorical) data.
Due to the local approach, LOF is able to identify outliers in a data set that would not be outliers in another area of the data set. For example, a point at a "small" distance to a very dense cluster is an outlier, while a point within a sparse cluster might exhibit similar distances to its neighbors.
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[7] [8] [9] If the data contains potential outliers, if the population distributions have heavy tails, or if the population distributions are significantly skewed, the Kruskal-Wallis test is more powerful at detecting differences among treatments than ANOVA F-test. On the other hand, if the population distributions are normal or are light ...