Outliers (Deep) Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A researcher finds that removing one outlier changes the correlation from 0.45 to 0.82. Discuss whether the outlier should be removed and what this dramatic change reveals.

Solution

  1. 1
    The dramatic change (0.45 → 0.82) reveals the outlier is an influential point — it has an outsized effect on the correlation
  2. 2
    Should we remove? Consider: Is it a legitimate observation or a data error? If legitimate, removing it misrepresents the population
  3. 3
    Better approach: report results both with and without the outlier; investigate why that point is extreme
  4. 4
    This reveals: the overall relationship is stronger without the outlier, but the outlier itself is an interesting case worth understanding separately

Answer

Do not remove without investigation. Report both analyses and investigate the outlier's cause.
Outliers that dramatically change results are called influential points. They reveal how sensitive conclusions are to a single observation. The correct response is transparency: report both analyses, investigate the outlier, and never silently delete data without justification.

About Outliers (Deep)

An outlier is a data value that lies unusually far from most other values, potentially indicating measurement error, a rare event, or an important exception.

Learn more about Outliers (Deep) →

More Outliers (Deep) Examples

Example 1 medium

Data: [formula]. Use the [formula] rule to determine if 85 is an outlier, and discuss whether it sho

Example 2 hard

Calculate the effect of an outlier (value 200) on the mean and median for [formula], comparing to th

Example 3 easy

A data set has [formula], [formula]. Determine if each value is an outlier: (a) 85, (b) 15, (c) 105.

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