Outlier - Revision history

Karl Jones: /* See also */

2016-11-08T17:45:12Z

‎See also

Karl Jones: /* External links */

2016-08-31T17:26:14Z

‎External links

Karl Jones: /* See also */

2016-04-29T13:45:36Z

‎See also

Karl Jones: /* Naive interpretation */

2016-04-29T13:44:25Z

‎Naive interpretation

Karl Jones: Created page with "In statistics, an '''outlier''' is an observation point that is distant from other observations. == Description == An outlier may be due to variability in the measuremen..."

2016-04-29T13:43:08Z

Created page with "In statistics, an '''outlier''' is an observation point that is distant from other observations. == Description == An outlier may be due to variability in the measuremen..."

New page

In [[statistics]], an '''outlier''' is an observation point that is distant from other observations.

== Description ==

An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the [[data set]].

Outliers can occur by chance in any distribution, but they often indicate either [[measurement error]] or that the population has a [[heavy-tailed distribution]]. In the former case one wishes to discard them or use statistics that are robust to outliers, while in the latter case they indicate that the distribution has high [[skewness]] and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two distinct sub-populations, or may indicate 'correct trial' versus 'measurement error'; this is modeled by a [[mixture model]].

In most larger samplings of data, some data points will be further away from the [[sample mean]] than what is deemed reasonable. This can be due to incidental [[systematic error]] or flaws in the theory that generated an assumed family of [[Probability distribution|probability distributions]], or it may be that some observations are far from the center of the data. Outlier points can therefore indicate faulty data, erroneous procedures, or areas where a certain theory might not be valid.

In large samples, a small number of outliers is to be expected (and not due to any anomalous condition).

Outliers, being the most extreme observations, may include the [[sample maximum]] or [[sample minimum]], or both, depending on whether they are extremely high or low. However, the sample maximum and minimum are not always outliers because they may not be unusually far from other observations.

== Naive interpretation ==

Naive interpretation of statistics derived from data sets that include outliers may be misleading.

For example, if one is calculating the [[average]] temperature of 10 objects in a room, and nine of them are between 20 and 25 degrees Celsius, but an oven is at 175 °C, the median of the data will be between 20 and 25 °C but the mean temperature will be between 35.5 and 40 °C.

In this case, the [[median]] better reflects the temperature of a randomly sampled object than the mean; naively interpreting the mean as "a typical sample", equivalent to the median, is incorrect.

As illustrated in this case, outliers may indicate data points that belong to a different population than the rest of the sample set.

== Robustness ==

Estimators capable of coping with outliers are said to be robust: the median is a robust statistic, while the mean is not.

== See also ==

* [[Statistics]]

== External links ==

* [https://en.wikipedia.org/wiki/Outlier Outlier]] @ Wikipedia

[[Category:Data]]
[[Category:Statistics]]

@@ Line 36: / Line 36: @@
 * [[Statistics]]
 * [[Studentized residual]]
 == External links ==

@@ Line 39: / Line 39: @@
 == External links ==
-* [https://en.wikipedia.org/wiki/Outlier Outlier]] @ Wikipedia
+* [https://en.wikipedia.org/wiki/Outlier Outlier] @ Wikipedia
 [[Category:Data]]
 [[Category:Statistics]]

@@ Line 21: / Line 21: @@
 In this case, the [[median]] better reflects the temperature of a randomly sampled object than the mean; naively interpreting the mean as "a typical sample", equivalent to the median, is incorrect.
-As illustrated in this case, outliers may indicate data points that belong to a different population than the rest of the sample set.
+As illustrated in this case, outliers may indicate data points that belong to a different [[statistical population]] than the rest of the [[Sample (staticstics)|sample]] set.
 == Robustness ==