📘 Notes¶

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Structured statistics and probability notes — 30 lessons across 13 chapters, from organizing raw data to multiple regression. Every lesson follows the same shape:

Concept  →  Formula  →  Worked example by hand  →  Excel  →  R  →  Python
         →  Quick Reference table  →  Common Mistakes  →  link to Exercises

Each file links to its matching exercise set at the bottom, and to the previous/next lesson.

01 — Foundations of Data¶

File	Topic
01-01-statistics-basics-and-data-types.md	Population vs. sample, parameter vs. statistic, descriptive vs. inferential, qualitative/quantitative, the four levels of measurement
01-02-data-representation-and-organization.md	Tidy/rectangular layout, wide vs. long, coding & codebooks, sorting, filtering, ranking, data-quality checks

02 — Frequency Distributions¶

File	Topic
02-01-frequency-distributions.md	Categorical and grouped frequency tables, class limits & boundaries, midpoints, width, Sturges' rule, cumulative frequency
02-02-graphical-displays.md	Bar, Pareto, pie, histogram, frequency polygon, ogive, stem-and-leaf, dot plot, boxplot; reading shape and skew; misleading graphs

03 — Central Tendency¶

File	Topic
03-01-mean-median-mode.md	Mean, median, mode, midrange, resistance, choosing the right measure, Pearson's skewness coefficient
03-02-weighted-and-grouped-means.md	Weighted mean, combining group means, mean/variance/median/mode from a frequency table, geometric and harmonic means

04 — Variation & Position¶

File	Topic
04-01-measures-of-variation.md	Range, variance, standard deviation, why `n−1`, coefficient of variation, the empirical rule, Chebyshev's theorem
04-02-measures-of-position-and-outliers.md	Z-scores, percentiles, quartiles, IQR, five-number summary, the 1.5×IQR rule, outlier handling

05 — Probability¶

File	Topic
05-01-probability-basics.md	Sample spaces, events, classical/empirical/subjective probability, the probability rules, complements, odds, simulation
05-02-probability-rules-and-conditional.md	Addition and multiplication rules, independence, conditional probability, contingency tables, tree diagrams, total probability
05-03-bayes-and-counting-rules.md	Bayes' theorem, base-rate neglect, the fundamental counting principle, factorials, permutations, combinations

06 — Discrete Distributions¶

File	Topic
06-01-random-variables-and-expected-value.md	Discrete random variables, probability distributions, expected value, variance, decision problems, rules for `E` and `Var`
06-02-binomial-and-poisson-distributions.md	Binomial, Poisson, geometric, hypergeometric — conditions, formulas, means, and which to choose

07 — Continuous & Normal¶

File	Topic
07-01-continuous-uniform-and-exponential.md	Density vs. cumulative functions, areas as probability, the uniform and exponential distributions, memorylessness
07-02-normal-distribution-and-z-scores.md	The normal curve, standard normal, both directions of every normal problem, the normal approximation to the binomial, assessing normality

08 — Sampling Theory¶

File	Topic
08-01-sampling-methods-and-bias.md	Simple random, systematic, stratified, cluster and multistage sampling; non-probability designs; sampling error vs. bias; experiments
08-02-sampling-distributions-and-clt.md	Sampling distributions, the standard error, the Central Limit Theorem, the sampling distribution of a proportion

09 — Confidence Intervals¶

File	Topic
09-01-confidence-interval-for-a-mean.md	Point vs. interval estimates, z- and t-intervals, interpreting confidence correctly, sample size, CI for a variance
09-02-confidence-interval-for-a-proportion.md	CI for a proportion, margin of error, sample size, Wald vs. Wilson vs. plus-four, difference of two proportions

10 — Hypothesis Testing¶

File	Topic
10-01-hypothesis-testing-fundamentals.md	Null and alternative hypotheses, Type I/II errors, power, the five steps, p-values, statistical vs. practical significance
10-02-one-sample-z-tests.md	Z-test for a mean, z-test for a proportion, one- and two-tailed versions, difference of two proportions

11 — t-Tests¶

File	Topic
11-01-one-sample-t-test.md	The t-distribution, one-sample t-test, reporting format, assumption checks, nonparametric backup
11-02-two-sample-t-test.md	Independent samples: Welch's vs. pooled, equal-variance tests, CI for the difference, Cohen's d
11-03-paired-t-test.md	Dependent samples, collapsing to differences, why pairing is more powerful, matched-pairs design

12 — Chi-Square & ANOVA¶

File	Topic
12-01-chi-square-goodness-of-fit.md	The chi-square statistic, expected counts, goodness-of-fit for uniform and specified distributions, test for a variance
12-02-chi-square-test-of-independence.md	Two-way tables, expected counts under independence, `(r−1)(c−1)` df, Cramér's V, test of homogeneity, Fisher's exact test
12-03-one-way-anova.md	Partitioning variation, the F-statistic, the ANOVA table, post-hoc tests (Tukey, Bonferroni), eta squared

13 — Correlation & Regression¶

File	Topic
13-01-correlation.md	Scatterplots, Pearson's r, the coefficient of determination, testing significance, Spearman and Kendall, correlation vs. causation
13-02-simple-linear-regression.md	The least-squares line, slope and intercept, residuals, `s_e`, prediction vs. confidence intervals, the LINE assumptions
13-03-regression-inference-and-multiple-regression.md	Testing the slope, CI for β₁, the regression ANOVA table, multiple regression, adjusted R², multicollinearity, dummy variables

Notation Used Throughout¶

Symbol	Meaning	Symbol	Meaning
`N`, `n`	Population / sample size	`μ`, `x̄`	Population / sample mean
`σ`, `s`	Population / sample standard deviation	`σ²`, `s²`	Population / sample variance
`p`, `p̂`	Population / sample proportion	`ρ`, `r`	Population / sample correlation
`α`	Significance level	`β`	Type II error rate; also a regression parameter
`df`	Degrees of freedom	`E`	Margin of error, or an expected count
`H₀`, `H₁`	Null / alternative hypothesis	`λ`	Poisson or exponential rate

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