Grubbs’ Outlier G-Statistic & Robust Modified Z-Score (MAD) Outlier Detector Calculator

Detect statistical outliers via Grubbs’ G-test and robust Median Absolute Deviation (MAD) Z-score.

Grubbs’ Outlier Statistic (G)
3.36 G (SDs)
Robust Modified MAD Z-Score 3.957 MAD Z
Theoretical Max G Bound (N−1)/√N 4.007 G_max
Raw Deviation from Mean 42 units
Inputs
⚡ Scenarios:
x_i
Suspected extreme observation x_i.
mean
Sample arithmetic mean x̄.
SD
Sample standard deviation s.
median
Sample median.
MAD
Median Absolute Deviation MAD = median(|x − median|).
N
Sample size N.
Results & Graph
Grubbs’ Outlier Statistic (G)
3.36 G (SDs)
Robust Modified MAD Z-Score
3.957 MAD Z
Theoretical Max G Bound (N−1)/√N
4.007 G_max
Raw Deviation from Mean
42 units

Grubbs’ Outlier Statistic (G)

Graph 1 • Grubbs & MAD Outlier Test • Domain Architecture & Live Telemetry Maps Suspect Outlier Value, Sample Mean, Sample Std Dev through Grubbs & MAD Outlier Test Formula.
Grubbs’ Outlier Statistic (G): 3.36 G (SDs) Grubbs & MAD Outlier Test • Invariants & Metrics Grubbs’ Outlier Statistic (G 3.36 G (SDs) Robust Modified MAD Z-Score 3.957 MAD Z Theoretical Max G Bound (N−1 4.007 G_max Raw Deviation from Mean 42 units
Graph 2 • Grubbs’ Outlier Statistic (G) Across Suspect Outlier Value Sweep (40% → 160%) Evaluates Grubbs G = |x_i − x̄| / s; Modified_Z_MAD = 0.6745 × |x_i − Median| / across 7 operating points (current input highlighted).
0 G (SDs 4.33 G (SDs 8.66 G (SDs 1.15 37.60x_i 0.352 56.40x_i 1.86 75.20x_i 3.36 94x_i 4.86 112.8x_i 6.37 131.6x_i 7.87 150.4x_i
Graph 3 • Joint Sensitivity: Suspect Outlier Value × Sample Mean Compares Grubbs’ Outlier Statistic (G) when Sample Mean is shifted +25% (solid) vs. −25% (dashed).
0 G (SDs 3.66 G (SDs 7.32 G (SDs --- Sample Mean @ 75% 0.0640 -30% 1.19 -15% 2.32 +0% 3.45 +15% 4.58 +30%
Summary: Grubbs’ G statistic is 3.36 (theoretical ceiling 4.01 for N=18) and robust Iglewicz-Hoaglin Modified MAD Z-score is 3.96 (Outlier ≥ 3.5).
Summary: Grubbs’ G statistic is 3.36 (theoretical ceiling 4.01 for N=18) and robust Iglewicz-Hoaglin Modified MAD Z-score is 3.96 (Outlier ≥ 3.5).
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Formula & Mathematical Methodology: Grubbs & MAD Outlier Test Formula

Grubbs G = |xi − x̄| / s
ModifiedZMAD = 0.6745 × |xi − Median| / MAD (Outlier if > 3.5)
Grubbs G = |x_i − x̄| / s; Modified_Z_MAD = 0.6745 × |x_i − Median| / MAD (Outlier if > 3.5)
  • suspectOutlierValue: Suspect Outlier Value (x_i)
  • sampleMean: Sample Mean (mean)
  • sampleStdDev: Sample Std Dev (SD)
  • sampleMedian: Sample Median (median)
  • medianAbsoluteDeviationMad: Median Absolute Deviation Mad (MAD)
  • sampleSizeN: Sample Size N (N)

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Worked Mathematical Example: Grubbs & MAD Outlier Test

Detect statistical outliers via Grubbs’ G-test and robust Median Absolute Deviation (MAD) Z-score.

  1. Specify the function parameters, matrix entries, or confusion matrix counts.
  2. Apply the closed-form or iterative formula: Grubbs G = |x_i − x̄| / s; Modified_Z_MAD = 0.6745 × |x_i − Median| / MAD (Outlier if > 3.5).
  3. Examine the primary result, error bounds, and 3 interactive SVG plots.
Result: Computes Grubbs & MAD Outlier Test via Grubbs G = |x_i − x̄| / s; Modified_Z_MAD = 0.6745 × |x_i − Median| / MAD (Outlier if > 3.5).

Frequently Asked Questions

How does the Grubbs’ Outlier G-Statistic & Robust Modified Z-Score (MAD) Outlier Detector Calculator compute the solution?

It evaluates Grubbs G = |x_i − x̄| / s; Modified_Z_MAD = 0.6745 × |x_i − Median| / MAD (Outlier if > 3.5) directly in your browser and updates three custom SVG visualizations in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this calculator run locally offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Mathematics & Statistics · Non-Parametric & Hypothesis Testing

Grubbs’ Outlier G-Statistic & Robust Modified Z-Score (MAD) Outlier Detector Calculator: inputs, method, and how to read the result

Detect statistical outliers via Grubbs’ G-test and robust Median Absolute Deviation (MAD) Z-score.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Suspect Outlier Value: Suspected extreme observation x_i.
  • Sample Mean: Sample arithmetic mean x̄.
  • Sample Std Dev: Sample standard deviation s.
  • Sample Median: Sample median.

What the calculation includes

With the default values shown, Grubbs’ Outlier Statistic (G) is 3.36 G (SDs). The calculation follows Grubbs & MAD Outlier Test Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Suspect Outlier Value from 94 x_i to 103 x_i changes Grubbs’ Outlier Statistic (G) from 3.36 G (SDs) to 4.08 G (SDs). This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses exact analytical or standard numerical analysis formulations from NIST DLMF.
  • Double-precision floating-point arithmetic has ~15–17 significant decimal digits of precision.

Scope: Global Mathematical & Statistical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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