Z-Score Range Test

A simple outlier detection method that uses standardized scores to identify data points that fall outside expected ranges, helping assess normality assumptions.

Z-Score Range Test Overview & Outlier Detection

What it measures:

Converts data points to standardized scores (z-scores) and identifies values that fall outside typical ranges expected in a normal distribution.

Strengths:

• • Simple to calculate and understand
• • No special software required
• • Works with any sample size
• • Identifies specific outliers

Limitations:

• • Not a formal normality test
• • Doesn't test overall distribution shape
• • Limited to outlier detection
• • Assumes normality to interpret z-scores

Z-Score & Standardization Formula

Standardized z-score for an individual data point

= individual data point

= population (or sample) mean

= population (or sample) standard deviation

A z-score expresses how many standard deviations a data point is from the mean, enabling comparison of outlier candidates across differently-scaled distributions.

Reading the Standardized Z-Score Plot

Example Z-Scores & Signal Interpretation

Normal Distribution Expectations:

±1 Standard Deviation

~68% of data should fall within |z| ≤ 1

±2 Standard Deviations

~95% of data should fall within |z| ≤ 2

±3 Standard Deviations

~99.7% of data should fall within |z| ≤ 3

sixsigmacenter.com Implementation Guide

Preparing Your Data for Upload

• • One column of the measured characteristic, one row per unit. The platform computes the mean, standard deviation, and every z-score for you.
• • Do not pre-compute a z-score column. A z-score built on a contaminated mean hides the very outlier you are hunting.
• • Add an identifier column (serial, lot, timestamp) so a flagged point traces back to a physical part and a containment action.
• • Group-level comparisons need a grouping column; stacking groups into one column inflates the standard deviation and masks outliers.

Z-scores assume approximate normality. On visibly skewed data, characterize the distribution first — a z of 3 means something different under a lognormal fit.

Interpretation Guidelines & Best Practices

Outlier Thresholds:

• • |z| > 2: Potential outlier (~5% expected)
• • |z| > 2.5: Probable outlier (~1% expected)
• • |z| > 3: Extreme outlier (~0.3% expected)

Normality Indicators:

• • Most values within ±2 standard deviations
• • Few or no extreme outliers (|z| > 3)
• • Outliers roughly balanced on both sides

Best Practices:

• • Use with other normality tests for complete assessment
• • Investigate identified outliers for data quality issues
• • Consider sample size when evaluating outlier frequency
• • Document and justify outlier treatment decisions

Example Data Layout for Z-Score Range Test

Data with calculated Z-scores and outlier flags for standardized outlier detection. Sample Size Recommendation: Minimum 15-25 observations for meaningful Z-score analysis - larger samples provide more reliable estimates of mean and standard deviation for outlier detection.

This is how your spreadsheet or CSV file should be structured before you upload it. Match the column names, keep one row per observation, and leave the analysis to the platform.