1.21:
Quantifying and Rejecting Outliers: The Grubbs Test
Grubbs' test, like Dixon's Q-test, is a statistical test to identify the outliers in data with a normal distribution. Here, the number of observations should equal or exceed seven.
For a given data set, this test involves calculating the Grubbs' statistic G, which is the ratio of the absolute difference between the questionable value and the mean value to the standard deviation of the sample.
The calculated G value is then compared with the tabulated critical value of G for a given confidence level and the number of observations.
If the calculated G value exceeds the critical value of G, the questionable observation is considered an outlier of the data and rejected.
Alternatively, if the calculated G value is smaller than the critical value of G, the data retains the questionable observation.
1.21:
Quantifying and Rejecting Outliers: The Grubbs Test
Sometimes, a data set can have a recorded numerical observation that greatly deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier. To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is known as the Grubbs statistic, 'G.' When the calculated G value exceeds the G critical value for a given confidence level and the number of observations, the questionable observation is considered an outlier and removed from the data set. On the contrary, if the calculated G value is smaller than the critical G value, the questionable observation is not considered an outlier and therefore retained in the data set.