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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 ...
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
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 ...
The four datasets composing Anscombe's quartet. All four sets have identical statistical parameters, but the graphs show them to be considerably different. Anscombe's quartet comprises four datasets that have nearly identical simple descriptive statistics, yet have very different distributions and appear very different when graphed.
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.
However, the studentized range distribution used to determine the level of significance of the differences considered in Tukey's test has vastly broader application: It is useful for researchers who have searched their collected data for remarkable differences between groups, but then cannot validly determine how significant their discovered ...
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.
The modified Thompson Tau test is used to find one outlier at a time (largest value of δ is removed if it is an outlier). 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.