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An outlier is an extreme score that falls significantly above or below the rest of the scores within a distribution. While these extreme values can represent genuine cases on the variable being measured—such as a single clinically depressed individual in an otherwise happy sample—they can also result from equipment malfunctions, participant misunderstandings, or researcher errors.

Outlier

When preliminary analyses reveal extreme outliers resulting from data entry errors, misunderstandings, or a lack of participant effort, researchers may justify excluding these anomalous data points. However, strict methodological standards require researchers to apply exclusion criteria consistently, retain the original data without permanently deleting it, and transparently report both the number of exclusions and the specific reasons for their removal.

Excluding Outliers

Extreme outliers may sometimes represent honest and accurate estimates rather than errors. To manage these valid but extreme scores, researchers can either employ resistant statistics like the median, or they can compare analyses conducted both with and without the outliers. If the results differ substantially between the two analyses, best practice dictates reporting both sets of results and thoroughly discussing the discrepancies.

Handling Valid Extreme Outliers

An example of an outlier might involve a single clinically depressed individual whose score on the Beck Depression Inventory falls drastically outside the typical range when measured within a sample of otherwise happy and high-functioning peers.

Example of an Outlier

A key characteristic of the mean is its high sensitivity to extreme scores, or outliers. In highly skewed distributions, the mean is pulled away from the median in the direction of the skew (the longer tail). Because extreme scores heavily influence its value, the mean may cease to be an accurate representation of the typical score in such datasets, leading researchers to often prefer the median for skewed distributions.

Sensitivity of the Mean to Outliers

While outliers are generally understood as extreme values within a dataset, $$z$$ scores provide a formal, quantitative method for identifying them. Commonly, outliers are defined as scores that fall more than three standard deviations away from the mean. In standardized terms, any score with a $$z$$ score strictly less than $$-3.00$$ or strictly greater than $$+3.00$$ is classified as an outlier.

Defining Outliers using z Scores

In a sample composed almost entirely of happy and high-functioning peers, a single clinically depressed person scoring very high on the Beck Depression Inventory would represent an outlier. This occurs because their score represents a truly extreme value relative to the rest of the group.

Outlier in Beck Depression Inventory Scores

An outlier might represent a misunderstanding or lack of effort by a participant. For example, in a task where most participants take only a few seconds to respond, a reaction time of $$3$$ minutes is an outlier. This suggests the participant was not paying attention or did not understand the task.

Reaction Time Outlier Example

An outlier might represent a truly extreme but accurate response rather than an error. For instance, in a university survey where most participants reported having had fewer than $$15$$ sexual partners, a few participants reported extreme scores of $$60$$ or $$70$$. These extreme scores could be honest and accurate estimates rather than intentional exaggerations.

Sexual Partners Survey Outlier Example

Although the range is easy to calculate, it can be highly misleading when outliers are present. A single extreme score can drastically increase the range, creating the false impression that the overall distribution has high variability when most scores are actually grouped closely together.

Impact of Outliers on the Range

$$z$$ scores provide a quantitative method for defining outliers within a distribution. Commonly, an outlier is defined as any score that is more than three standard deviations away from the mean, which corresponds to a $$z$$ score less than $$-3.00$$ or greater than $$+3.00$$.

Identifying Outliers Using z Scores

When handling outliers, researchers must decide how to manage them based on their cause. Data entry errors can be corrected. If an outlier stems from misunderstanding or lack of effort, the response may be excluded using consistent criteria. Importantly, excluded data should not be permanently deleted but set aside for potential future review. When presenting results, researchers must clearly report how many participants or responses were excluded and detail the specific criteria used. For valid extreme responses, researchers can use robust statistics like the median or analyze the data both with and without the outliers.

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