Probability and Statistics Quick Guide
Calculate basic probability, understand distributions, and interpret statistical significance for everyday decisions.
Key Takeaways
- Statistical thinking helps you make better decisions under uncertainty, evaluate claims backed by data, and avoid common reasoning errors.
- This does NOT mean the result is important, large, or practically meaningful.
- For income data, median is almost always more informative than mean because wealth is heavily right-skewed.
- Always consider effect size alongside significance.
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Probability and Statistics
Statistical thinking helps you make better decisions under uncertainty, evaluate claims backed by data, and avoid common reasoning errors.
Basic Probability
The probability of an event is favorable outcomes divided by total possible outcomes. Rolling a 6 on a fair die: 1/6 ≈ 16.7%. Probability of A AND B (independent): P(A) × P(B). Probability of A OR B (mutually exclusive): P(A) + P(B). The complement: P(not A) = 1 - P(A). Getting at least one 6 in two rolls: 1 - (5/6)² ≈ 30.6%.
Mean, Median, Mode
Mean (average) is sensitive to outliers — a few extreme values can distort it significantly. Median (middle value) is robust to outliers and better represents "typical" values for skewed distributions. Mode (most common value) is useful for categorical data. For income data, median is almost always more informative than mean because wealth is heavily right-skewed.
Standard Deviation
Standard deviation measures spread — how far values typically fall from the mean. In a normal distribution, 68% of values fall within 1 SD, 95% within 2 SD, and 99.7% within 3 SD. If average height is 170cm with SD 10cm, then 95% of people are between 150-190cm. Low SD means values cluster tightly; high SD means wide spread.
Statistical Significance
A result is "statistically significant" (p < 0.05) when there's less than a 5% chance of observing it by random chance alone. This does NOT mean the result is important, large, or practically meaningful. A study with 100,000 participants might find a statistically significant difference that's too small to matter in practice. Always consider effect size alongside significance.
Common Fallacies
The gambler's fallacy: past outcomes don't affect future independent events (a coin doesn't "owe" you heads after a streak of tails). Base rate neglect: a 99% accurate test for a rare disease (0.1% prevalence) still produces mostly false positives. Correlation vs causation: two variables moving together doesn't mean one causes the other.
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