Outlier Calculator

Use this Outlier Calculator to find anomalous values in your dataset using multiple detection methods. Paste or type your numbers into the single input box—values can be separated by commas, spaces, or line breaks. Copy and pasting from a spreadsheet column is acceptable. Text is ignored. Click Analyze in the Outlier Calculator to find unusual values and to generate a results printout you can save or share.

The Outlier Calculator performs either the Grubbs Test that can find a single outlier or the Generalized ESD test for multiple outliers. The calculator also performs the nonparametric Tukey method of using fences to find outliers–a quick, robust, assumption-light approach. Finally, it graphs the data and highlights the outliers. The Outlier Calculator also assesses normality and can log transform the data because these hypothesis test methods assume normality. Below the calculator you will find assistance in understanding the methodology choices, setting the options, practical help with interpreting the results, and determining what to do with the outliers. See all my Statistical Calculators!

Outlier Calculator Methods and Options

This Outlier Calculator provides three methods for detecting outliers: Tukey’s method, Grubbs Test, and Generalized ESD. They don’t always agree because each method answers a slightly different question. Importantly, no method can tell you whether a particular value is truly an error that should be removed or a valid but unusual value. Use your judgement throughout this process!

Let’s go through these three detection methods.

Learn more in my article about 5 Ways to Find Outliers.

1) Robust Rule — IQR Fences (Tukey’s method)

This is the boxplot-based rule introduced by John W. Tukey. The outlier calculator labels it “Robust Rule — IQR Fences.” It doesn’t assume normality and holds up well when data are skewed or when more than one point is unusual. The outlier calculator always performs this analysis.

• Compute the first and third quartiles (Q1 and Q3) and the interquartile range IQR = Q3 − Q1.
• Inner fences (1.5×IQR):
  • Lower fence: Q1 − 1.5×IQR
  • Upper fence: Q3 + 1.5×IQR
    Points outside these are called outside values.
• Outer fences (3×IQR):
  • Lower extreme fence: Q1 − 3×IQR
  • Upper extreme fence: Q3 + 3×IQR
    Points beyond these are far out values.

In the plots, the outlier calculator flag points beyond 1.5×IQR (and show the 3×IQR “extreme” fences). This is a rule, not a hypothesis test. There are no p-values and the significance level you choose does not affect it. However, a log-transformation does affect the results. Use this method as a robust first pass and obtain a visual context of your data and potential outliers.

2) Grubbs’ Test (single outlier)

Grubbs’ test checks whether one observation—the most extreme one—is inconsistent with the rest under normality. If you suspect just one outlier, this is a focused test. In the outlier calculator, choose whether to test two-sided (either tail) or one-sided (only high or only low).

• Use Two-sided by default unless your subject-area knowledge tells you to expect only high or low outliers.
• Important: Grubbs is not meant to be run repeatedly to peel off multiple outliers. If you anticipate more than one, use Generalized ESD.

Learn more about the Grubbs Test.

3) Generalized ESD (Rosner)

The Generalized Extreme Studentized Deviate (ESD) procedure (Rosner, 1983) can detect up to R outliers, testing them step-by-step. In the outlier calculator, you supply the maximum number you’re willing to consider (R), and the test reports which steps were significant.

• Pick R as a practical upper bound (the tool suggests ≈10% of the sample size up to 10).
• Assumes data are (approximately) normal after excluding the detected outliers.
• The results table shows the test statistic, critical value, and a p-value for each step so you can see exactly where significance stops.

Choosing the Outlier Detection Method in the Outlier Calculator

• Grubbs’ Test (default): great when you expect a single outlier. Choose Two-sided, Upper, or Lower in the dropdown.
• Generalized ESD: use when you might have more than one outlier. Enter Max Outliers (R). The number of values the test removes depends on statistical significance and can be 0 regardless of R.

Other Outlier Calculator Options

Significance level (α)

Choose 0.01, 0.05 (default), or 0.10.

• Larger α → more sensitive (easier to call something an outlier) but higher false-positive risk.
• Smaller α → more conservative (harder to flag), fewer false positives.
• For ESD, per-step critical values account for the sequential nature of the test; you’ll still see per-step p-values.

Learn more about Understanding and Setting Significance Levels.

Log transform

The parametric tests (Grubbs, ESD) assume data are roughly normal and observations are independent. Real-world data can be skewed (e.g., times, concentrations, physical constraints). A log transform (for positive data) can:

• Reduce skew
• Make the distribution closer to normal, improving test validity

If you check Log transform, the Outlier Calculator analyzes the log values for the outlier and normality tests and in plots.

Normality check (Shapiro-Wilk)

The Outlier Calculator performs the Shapiro-Wilk normality test and reports the W and its p-value:

• If p < 0.05, that’s evidence against normality. In that case, the parametric outlier tests might not be valid as-is.
  • Consider the Log transform option and re-check.
  • Or lean on the Robust Rule — IQR Fences (Tukey) and the plots, which don’t require normality.

Check out my free online Normality Test Calculator, which performs the Shapiro-Wilk test, several other tests, and creates visual diagnostics (QQ Plot and histogram).

Handling the Unusual Data Points the Outlier Calculator Finds

Scan the IQR/boxplot flags and plots first. If they align with Grubbs/ESD and Shapiro-Wilk doesn’t object, you’re on firmer ground. However, outliers aren’t all the same. They typically fall into one of two buckets:

1) A real but rare value from the same process

Sometimes an “outlier” that the calculator detects is just an extreme draw from the natural randomness of your data.

What to do: keep it and analyze it exactly like the other observations. Perhaps you’ll need to use a non-parametric analysis that can handle unusual values.

2) A value caused by a mistake or a protocol problem

Other times an outlier comes from a clear departure from the planned procedure—or from a calculation, entry, or recording error.

What to do: investigate. Track down why the value is off. After that review, you might decide to reject it—but that’s not automatic. Either way, in any follow-up analysis, treat such points as likely coming from a different population than the main sample and make that status clear in your reporting.

Important notes (for both cases):

• The outlier calculator cannot tell you which case you’re in. Statistical tests can flag unusual points but none of them can determine whether a value is a legitimate extreme value or a mistake. That call requires subject-matter knowledge and a little detective work (check units, instrument limits/calibration, timestamps, process conditions, lab notes, data entry steps, etc.).
• Be transparent. If you remove values, state which ones, why, what rule/test you used, and show a sensitivity check (results with and without those points). Transparency lets readers see that your conclusions don’t hinge on a hidden decision.

Learn more in-depth in my article, Guidelines for Removing and Handling Outliers.

References

Grubbs FE (1969) Procedures for detecting outlying observations in samples. Technometrics 11:1-21.
Rosner B (1983) Percentage points for a generalized ESD many-outlier procedure. Technometrics 25:165-172.
Tukey JW (1977) Exploratory data analysis. Reading, Mass: Addison-Wesley Publishing Company.