What is the difference between "resistant to outliers" and "sensitive to outliers"? I can't seem to find these definitions anywhere. Thanks.
Outliers are, supposedly, numbers far from the average value of a set.
The median of a set of numbers is less sensitive to outliers than the mean.
Thanks.
The terms "resistant to outliers" and "sensitive to outliers" are commonly used in statistics to describe how a statistical method or measure is affected by the presence of outliers, which are extreme values that deviate significantly from the majority of the data.
"Resistant to outliers" refers to a statistical method or measure that is not significantly influenced by outliers. It means that even if there are outliers in the dataset, the result or inference obtained from the method or measure will not be greatly affected. In other words, the presence of outliers does not heavily impact the outcome. Measures that are resistant to outliers tend to focus more on the central tendency of the data rather than the extreme values.
On the other hand, "sensitive to outliers" means that a statistical method or measure is greatly influenced by the presence of outliers. Outliers can significantly alter the result or inference obtained from the method or measure. In this case, the presence of outliers can distort the outcome or make it less reliable. Measures that are sensitive to outliers often consider all values, including the extreme ones, when calculating statistical summaries.
To understand which statistical methods or measures are resistant or sensitive to outliers, it is helpful to examine their underlying properties or assumptions. Techniques like robust statistics, which are explicitly designed to handle outliers, are generally more resistant to outliers. Conversely, methods that depend heavily on the raw data, like the arithmetic mean, tend to be sensitive to outliers.
In order to determine whether a specific method or measure is resistant or sensitive to outliers, you may refer to textbooks, academic papers, or statistical software documentation that discuss the properties and assumptions of the method or measure in question. Additionally, you can experiment with different datasets, including outliers, to observe how the method or measure responds to their presence.