Real World Analysis

In the final chapter of our Visual Anchors series, we tackle the tools used by Data Scientists every day to make decisions.

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1. Salary Distributions (Box Plot)

Descriptive statistics often mislead. “Average salary” can be skewed by one billionaire. A Box Plot (or Box-and-Whisker) reveals the true spread: the Median, the Interquartile Range (middle 50%), and the outliers.

Scenario: Tech Startup Salaries (in $1000s)

Insight: While the “max” salaries are similar, the Median engineer earns remarkably more ($135k vs$90k). Also, notice the outlier in Engineering (the dot at $250k) — that’s the CTO!

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2. Joint Probability (Heatmap)

In Chapter 3, we discuss Joint Distributions ($P(X=x, Y=y)$). This is effectively a 2D grid of probabilities. A Heatmap allows us to spot the “hot zones” of correlation instantly.

Scenario: Survey of Transport vs Commute Time.

• rows: Car, Bus, Train
• cols: <15m, 15-30m, >30m

Analysis: The dark blue cell (0.25) shows that the most common outcome is Bus + 15-30m. The empty cell (0.0) shows nobody takes a Train for <15m.

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3. A/B Testing Significance (Z-Test)

When a business runs an A/B test, they calculate a Z-Score to see if the new design is truly better. If the score falls into the “critical region” (the tail), the result is Statistically Significant.

Scenario:

• Null Hypothesis: No difference ($Z=0$).
• Observation: We observed a difference of $2.5$ standard errors ($Z=2.5$).

Conclusion: The shading represents the P-value (probability of seeing this result by luck). Since the area is tiny (and $Z > 1.96$), we Reject the Null Hypothesis. The new design worked!