Outlier Detection

Q: Should I use z-scores or the IQR rule?

The IQR rule is more robust because the quartiles are not pulled by the outliers themselves, whereas extreme values inflate the SD used in z-scores. For roughly normal data with large n, |z| > 3.29 (p < .001) is a common alternative.

Identify extreme or unusual values that may distort your statistical analyses and require investigation.

Outlier Detection identifies observations that are unusually far from the rest of the data. Outliers can be legitimate extreme values, data entry errors, or cases from a different population. They can severely distort means, inflate variances, and bias regression coefficients — making their detection an essential data quality step.

StatRyx applies multiple detection methods: Z-score method (|z| > 3), modified Z-score using the median absolute deviation (more robust), IQR fence method (< Q1 − 1.5×IQR or > Q3 + 1.5×IQR), and for multivariate data, Mahalanobis distance with chi-square significance testing.

StatRyx reports each flagged observation with its detection method, provides summary statistics with and without the outliers, and makes recommendations about whether to investigate, transform, or retain each outlier.

Univariate outliers are extreme on a single variable, usually flagged with the IQR rule (beyond 1.5 × IQR from the quartiles) or |z| > 3. Multivariate outliers are unusual combinations of values, such as a young age with a very high income, and are flagged with Mahalanobis distance against a chi-square cutoff (usually p < .001). An outlier is a reason to investigate, not automatically to delete: check for data entry errors first.

When to use the Outlier Detection

During data cleaning before running any analysis to check data quality
When your results seem implausible and you suspect a data entry error
When reporting that you checked for and addressed outliers in your methods section
Before regression or SEM, where a handful of multivariate outliers can change the coefficients
You see an implausible value (e.g., an age of 250) and want to find every similar case

When not to use it

You want to remove any case that disagrees with your hypothesis — use Never remove outliers without a substantive justification — report the analysis both with and without them instead
The variable is naturally skewed (e.g., income, reaction time) — use Transform the variable or use a robust or nonparametric method instead of deleting extreme values instead
You want to know how much a few cases change your conclusion — use Sensitivity Analysis instead

Worked example

Case	Variable	Value	z-score	Method	Recommendation
ID 47	Depression	89	3.8	Z-score & IQR	Investigate
ID 112	Anxiety	−2	−3.1	IQR fence	Check data entry

How to report it (APA 7)

Outliers were identified using the IQR fence method and Mahalanobis distance (p < .001). Three cases were flagged as univariate outliers on the depression scale (z > 3.3) and two multivariate outliers were detected (Mahalanobis D² > 18.47). Analyses were conducted with and without these cases; results did not differ substantively.

Frequently asked questions

Is outlier detection free on StatRyx?

Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.

Should I always remove outliers?

No. Outliers should only be removed if there is a documented reason (e.g., data entry error, equipment malfunction, ineligible participant). Otherwise, report results with and without outliers and note that they do not change the conclusions.

What is Mahalanobis distance?

Mahalanobis distance measures how far an observation is from the multivariate centroid, accounting for correlations among variables. It detects cases that are unusual in combination — even if each variable looks normal on its own.

How do I report outliers in APA 7?

Say which method and cutoff you used, how many cases were flagged, what you did with them and why: "Three cases exceeded the Mahalanobis distance criterion (p < .001). Results were unchanged when they were excluded, so all cases were retained."

Should I use z-scores or the IQR rule?