KEVOS® MAKEOS · Quality
Grubbs Outlier Check (Suspect Value, G Statistic, Critical Value, Significance)
One of my measurements looks far from the rest: is it a statistical outlier at my significance level, or within what normal scatter could produce?
Grubbs test for a single outlier in up to twelve measurements from a roughly normal population: the mean and standard deviation, the most extreme value (or the largest or smallest, for a one-sided test), the Grubbs statistic G, the critical value from the t distribution for your significance level and sample size, and whether the suspect value is an outlier.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of values used | values | How many of the values below to use (at least 3). |
| Test | choice | Test the most extreme value either way, or only the largest or only the smallest. |
| Significance level | % | Chance of calling a value an outlier when there is none (5 % is common). |
| Values | ||
| Value 1 | Measured value number 1. | |
| Value 2 | Measured value number 2. | |
| Value 3 | Measured value number 3. | |
| Value 4 | Measured value number 4. | |
| Value 5 | Measured value number 5. | |
| Value 6 | Measured value number 6. | |
| Value 7 | Measured value number 7. | |
| Value 8 | Measured value number 8. | |
| Value 9 | Measured value number 9. | |
| Value 10 | Measured value number 10. | |
| Value 11 | Measured value number 11. | |
| Value 12 | Measured value number 12. | |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Number of values used
- What it is
- How many of the values listed below are tested, counting from the first.
- Units and format
- Enter a number in values: values. The form accepts 3 values to 12 values. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 values as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Values beyond this count are ignored; more values raise the critical value slightly.
- Get it right
- The test needs at least three values; with fewer than about seven it rarely finds an outlier.
What this means: Test
- What it is
- Whether to test the value furthest from the mean in either direction, or only the largest or only the smallest value.
- Units and format
- Choose one of 3 options from the list: Two-sided (most extreme value); One-sided: largest value; One-sided: smallest value.
- Example
- The form opens with “Two-sided (most extreme value)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- A one-sided test uses a smaller critical value, so it flags an outlier more readily in that direction.
- Get it right
- Use a one-sided test only if you decided before seeing the data that only high (or low) values matter.
What this means: Significance level
- What it is
- The chance of calling a value an outlier when the data contain none, the significance level of the test.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.1% to 20%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller level raises the critical value, so fewer values are flagged.
- Get it right
- Five per cent is common; use 1 % when wrongly rejecting a good result is costly.
Values
What this means: Value 1
- What it is
- Measured value number 1 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 199.31 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 1 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 2
- What it is
- Measured value number 2 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 199.53 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 2 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 3
- What it is
- Measured value number 3 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200.19 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 3 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 4
- What it is
- Measured value number 4 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200.82 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 4 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 5
- What it is
- Measured value number 5 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 201.92 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 5 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 6
- What it is
- Measured value number 6 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 201.95 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 6 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 7
- What it is
- Measured value number 7 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 202.18 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 7 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 8
- What it is
- Measured value number 8 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 245.57 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 8 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 9
- What it is
- Measured value number 9 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 9 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 10
- What it is
- Measured value number 10 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 10 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 11
- What it is
- Measured value number 11 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 11 as measured, before any rounding or correction you would not apply to the others.
What this means: Value 12
- What it is
- Measured value number 12 of the set being screened for an outlier, such as one replicate of a test result.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mean and standard deviation; an extreme value raises the Grubbs statistic.
- Get it right
- Enter value 12 as measured, before any rounding or correction you would not apply to the others.
Method and formulas
- Two-sided: G = max |Yᵢ − Ȳ| ÷ s; one-sided: G = (Y_max − Ȳ) ÷ s or (Ȳ − Y_min) ÷ s, with s the sample standard deviation (NIST e-Handbook 1.3.5.17).
- Critical value G_crit = (N − 1) ÷ √N × √(t² ÷ (N − 2 + t²)), where t is the upper critical value of the t distribution with N − 2 degrees of freedom at α ÷ (2N) (two-sided) or α ÷ N (one-sided).
- The suspect value is an outlier if G > G_crit.
- Example: G = 2.4688 against a critical value of 2.1266: the suspect value is an outlier.
Limitations
- Tests one outlier only and assumes the rest of the data are roughly normal; for several suspect values NIST points to the generalised ESD or Tietjen–Moore tests.
- An outlier is a reason to investigate, not to delete: find the cause before removing it.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Decide whether to question a stray test result
- Screen calibration or inspection data before analysis
- Check a laboratory result against its replicates
Who it is for
- Quality and laboratory staff
- Test and calibration engineers
- Process engineers
What you get
- Mean and standard deviation
- Suspect value and G statistic
- Critical value of G
- Outlier decision
Interpreting the result
- With few values a single outlier inflates the standard deviation and can hide itself; with three values almost no result can be shown to be an outlier.
References
- NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.5.17 Grubbs’ Test for Outliers — https://www.itl.nist.gov/div898/handbook/eda/section3/eda35h1.htm
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Thresholds, false calls and acceptance decisions
In Eddy-Current Inspection by the Numbers
What it covers: Probability of detection and false calls, guard bands from measurement uncertainty, capability with confidence bounds, lot acceptance, and testing a suspect reading before discarding it.
Useful alongside · Library collection
Screening and cleaning data before analysis: duplicates, gaps, outliers and a clean audit trail
In Research and Evidence for Better Decisions
What it covers: How to screen and clean business and research data before analysis: keep raw data safe, check structure, duplicates, missing values, ranges, units, dates and outliers, and document every change.
Also in Describing data: centre, spread and shape before drawing conclusions
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Grubbs Outlier Check (Suspect Value, G Statistic, Critical Value, Significance) calculator