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Z-Test Statistic

← hover each part to see what it means

zz-score: how many std deviations from the mean=(x̄ - μ)sample mean minus population mean/(σ/√n)standard error — shrinks as sample grows

📝 Margin note: When |z| > 1.96, your p-value is under 0.05 — reject H₀ at 95% confidence. That's it. That's the whole test.

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Probability & Distributions

Dr. Priya Nair

PhD Biostatistics, Johns Hopkins

"I write every explanation assuming the reader is brilliant but has never seen this before. That's how I wish someone had taught me."

Foundationfrom Probability & Distributions

Why the Normal Distribution is Everywhere

The Central Limit Theorem is the reason stats works at all. It says: add enough random things together and you get a bell curve. Every time.

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Dr. Priya Nair
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Hypothesis Testing

Marcus Webb

Former student, now stats tutor

"I failed stats twice. Then I rewrote every chapter until my roommate — a history major — could explain p-values back to me."

Common Mistakefrom Hypothesis Testing

The p-value is NOT the probability your hypothesis is true

This is the most misunderstood sentence in all of statistics. Your p-value is the probability of your data given H₀ is true — not the other way around.

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Marcus Webb
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Regression & Prediction

Yuki Tanaka

Senior Data Scientist, ex-Netflix

"I contributed the real-world examples because textbooks always use toy datasets. Your future boss will hand you messy, real data."

Real Worldfrom Regression & Prediction

Reading a Regression Table from Python Output

The coef column tells you: if X goes up by 1, Y changes by this much. That's 80% of what your manager actually cares about.

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Yuki Tanaka
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📝Core Feature

Margin Notes on Every Formula

Hover any variable to get a plain-English explanation. No more symbol-hunting in the index.

z =(x̄ - μ)/(σ/√n)
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Adaptive Practice Problems

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🧠Core Feature

Concept Maps

See how p-values, z-scores, and confidence intervals connect — the picture your professor never drew.

Population μ
Sample x̄
Standard Error
z-score
p-value
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Python Output Decoder

Paste your statsmodels or scipy output. Get a line-by-line explanation.

coef std err t P>|t| const 12.4 1.2 10.3 0.000 ✓
🔖Core Feature

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Hypothesis Testing
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Ananya Krishnan

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Tobias Reinholt

Self-taught Data Analyst, Copenhagen

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