# Outlier

An outlier is an item that appears to be inconsistent with the other members of an item set.

## References

### 2013

• http://en.wikipedia.org/wiki/Outlier
• In statistics, an outlier[1] is an observation that is numerically distant from the rest of the data. Grubbs[2] defined an outlier as:

An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs.

Outliers can occur by chance in any distribution, but they are often indicative either of 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 kurtosis 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 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. However, 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 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 be indicative of data points that belong to a different population than the rest of the sample set.

Estimators capable of coping with outliers are said to be robust: the median is a robust statistic, while the mean is not.[3]

1. Barnett, V. and Lewis, T.: 1994, Outliers in Statistical Data. John Wiley & Sons., 3rd edition.
2. Grubbs, F. E.: 1969, Procedures for detecting outlying observations in samples. Technometrics 11, 1–21.
3. Ripley, Brian D. 2004. Robust statistics

### 2006

• (Walfish, 2006) ⇒ Steven Walfish. (2006). “A Review of Statistical Outlier Methods.” Pharmaceutical technology 30, no. 11
• ABSTRACT: Statistical outlier detection has become a popular topic as a result of the US Food and Drug Administration's out of specification (OOS) guidance and increasing emphasis on the OOS procedures of pharmaceutical companies. When a test fails to meet its specifications, the initial response is to conduct a laboratory investigation to seek an assignable cause. As part of that investigation, an analyst looks for an observation in the data that could be classified as an outlier. The FDA guidance "Investigating Out of Specification (OOS) Test Results for Pharmaceutical Production" and the US Pharmacopeia are clear that a chemical result cannot be omitted with an outlier test, but that a bioassay can be omitted with an outlier test (1). The two areas specifically prohibited from outlier tests are content uniformity and dissolution testing.

An outlier is defined as an observation that "appears" to be inconsistent with other observations in the data set (2). An outlier has a low probability that it originates from the same statistical distribution as the other observations in the data set. On the other hand, an extreme value is an observation that might have a low probability of occurrence but cannot be statistically shown to originate from a different distribution than the rest of the data.

### 1999

• (Zaiane, 1999) ⇒ Osmar Zaiane. (1999). “Glossary of Data Mining Terms." University of Alberta, Computing Science CMPUT-690: Principles of Knowledge Discovery in Databases.
• QUOTE: Outlier: A data item whose value falls outside the bounds enclosing most of the other corresponding values in the sample. May indicate anomalous data.