What is a significant outlier?
An outlier is an observation that appears to deviate markedly from other observations in the sample. However, if the data contains significant outliers, we may need to consider the use of robust statistical techniques.
Is the mean robust to outliers?
Robust statistics are resistant to outliers. For example, the mean is very susceptible to outliers (it’s non-robust), while the median is not affected by outliers (it’s robust).
What is the only way to know if you have an outlier?
Multiplying the interquartile range (IQR) by 1.5 will give us a way to determine whether a certain value is an outlier. If we subtract 1.5 x IQR from the first quartile, any data values that are less than this number are considered outliers.
Is the variance robust to outliers in general?
Neither the standard deviation nor the variance is robust to outliers. A data value that is separate from the body of the data can increase the value of the statistics by an arbitrarily large amount. The mean absolute deviation (MAD) is also sensitive to outliers.
What happens when there are too many outliers in a test?
On the other hand, swamping can occur when we specify too many outliers in the test. For example, if we are testing for two or more outliers when there is in fact only a single outlier, both points may be declared outliers (many tests will declare either all or none of the tested points as outliers).
Are there any outliers outside of the IQR?
Although you can have “many” outliers (in a large data set), it is impossible for “most” of the data points to be outside of the IQR. The IQR, or more specifically, the zone between Q1 and Q3, by definition contains the middle 50% of the data. Extending that to 1.5*IQR above and below it is a very generous zone to encompass most of the data.
When to use non-normality assumption to detect outliers?
If the normality assumption for the data being tested is not valid, then a determination that there is an outlier may in fact be due to the non-normality of the data rather than the prescence of an outlier.
Do you generate a normal probability plot before applying an outlier test?
For this reason, it is recommended that you generate a normal probability plotof the data before applying an outlier test.