There is a 5% chance that the most extreme value will be identified as an outlier. Assume that you set alpha to 5% and test a data set with 1000 values, all sampled from a Gaussian distribution. Note that alpha applies to the entire experiment, not to each value. If there are no outliers, alpha is the chance of mistakenly identifying an outlier. This has an interpretation familiar from any tests of statistical significance. With the Grubbs' test, you specify alpha. The choice is a bit different depending on which method of outlier detection you choose. You need to decide how aggressively to define outliers. There is always a chance that some true outliers will be missed, and that some "good points" will be falsely identified as outliers. There is no way to cleanly separate outliers from values sampled from a Gaussian distribution. Let us know if you'd like us to include this method of detecting outliers. Some people define these points to be outliers We did not implement this method of outlier detection in Prism (beyond creating box-and-whiskers plots) because it seems to not be widely used, and has no real theoretical basis. When you create a box-and-whiskers plot with Prism, you can choose to show Tukey whiskers, which shows points individually when their distance from the median exceeds 1.5 times the interquartile range (difference between the 75th and 25th percentiles).If you want to allow for the possibility of more than one outlier, choose the ROUT method.If you somehow knew for sure that the data set had either no outliers or one outlier, then choose Grubbs' test.With two outliers, the standard deviation can become large, which reduces that ratio to a value below the critical value used to define outliers. The problem is that the standard deviation is computed from all the values, including the outliers. When that ratio is too large, the value is defined to be an outlier.
Grubbs' method identifies an outlier by calculating the difference between the value and the mean, and then dividing that difference by the standard deviation of all the values. The presence of a second outlier in a small data set can prevent the first one from being detected. While Grubb's test does a good job of finding one outlier in a data set, it does not work so well with multiple outliers.
If that second test finds an outlier, then that value is removed, and the test is run a third time. If an outlier is found, it is removed and the remaining values are tested with Grubbs' test again. While it was designed to detect one outlier, Grubbs' method is often extended to detect multiple outliers. Prism uses the two-sided Grubbs' test, which means it will detect a value much larger than the rest, or a value much smaller than the rest. It can only identify one outlier in each data set. This method is also called the ESD method (Extreme Studentized Deviate).
Grubbs' test is probably the most popular method to identify an outlier. The ROUT method can identify one or more outliers. Prism adapts this method to detecting outliers from a stack of values in a column data table. We developed the ROUT method to detect outliers while fitting a curve with nonlinear regression. Prism offers three methods for identifying outliers: ROUT Prism can also identify outliers during nonlinear regression.
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Note: This page explains how to identify an outlier from a stack of values in a data table formatted for Column data. Prism can perform outlier tests with as few as three values in a data set. Click Analyze from a Column data table, and then choose Identify outliers from the list of analyses for Column data. Identifying outliers in a stack of data is simple.