Detecting Outliers

Outliers are points far from the rest. They can be measurement errors, data entry errors, processing artifacts — or real, important observations that just happen to be extreme. The data alone usually can't tell you which. That's why domain knowledge is the essential second step after detection.

Five sources of outliers to keep in mind:

• Measurement error — faulty or miscalibrated instrument.
• Data entry error — a human typed the wrong thing.
• Experimental error — something went wrong during collection.
• Data processing error — a pipeline bug introduced an artifact.
• True outliers — real, natural observations that just happen to be extreme.

Discovering Outliers

Visual. Scatter plots and box plots. Anything outside the box plot's whiskers is conventionally flagged.

Z-score method. Assumes approximate normality. Compute $z = (x - \mu) / \sigma$ for each point. Flag any point where $|z| > k$. Common choice: $k = 3$. Here $k$ is a threshold multiplier — higher $k$ means only more extreme points are flagged; lower $k$ flags more aggressively. Sensitive to the normality assumption — if your data isn't approximately normal, the z-score method will mis-flag.

IQR method. Does not assume normality. Upper threshold: $Q3 + k \times IQR$; lower threshold: $Q1 - k \times IQR$, where $k = 1.5$ is conventional (Tukey's rule). $k$ controls the fence width: larger $k$ widens the fences and flags fewer points; smaller $k$ narrows them and flags more. Any point outside this range is flagged.

Cook's distance. For regression: measures how much the regression parameters change when a specific point is removed. Useful for identifying influential observations — points that disproportionately steer the model.