Statistics
Review Statistics study guides, quizzes, and flashcards covering probability, hypothesis testing, and regression.
Topics
ANOVA Foundations
Break down ANOVA from the ground up — covering between- and within-groups variance, the F-statistic ratio, degrees of freedom, and why a significant result still requires post-hoc tests to pinpoint which group means differ.
Binomial Distributions
Master the binomial distribution from the ground up — covering the four conditions for a binomial setting, the probability formula P(X = k) = C(n, k) · pᵏ · (1 - p)ⁿ⁻ᵏ, and how to find mean and standard deviation using np and √(np(1 - p)).
Central Limit Theorem
Unpack the Central Limit Theorem and see why sample means form a normal distribution as n grows — even when the population isn't normal. Master key mechanics like standard error (σ/√n), the n ≥ 30 rule, and applying z-scores to sample mean problems.
Confidence Level and Margin of Error
Unpack the mechanics of confidence intervals and margin of error, from how critical values (z* and t*) are chosen to how sample size affects interval width. Master the distinction between z- and t-distributions and what confidence level actually means across repeated samples.
Data Visualization and Distribution Shapes
Visualize how raw data takes shape through histograms, dot plots, and box plots while mastering symmetric, skewed, and uniform distributions — and learn why skewness shifts the mean toward the tail but leaves the median largely unaffected.
Experimental Design and Bias
Unpack the core principles of experimental design — from random assignment and confounding variables to single- and double-blind procedures, placebo controls, and bias types — so you can confidently distinguish true experiments from flawed ones.
Hypothesis Testing Logic
Unpack the logic behind hypothesis testing, from null and alternative hypotheses to p-values, significance levels, and Type I and II errors. This pack clarifies how test statistics and tail direction shape your reject-or-fail-to-reject decision.
Measures of the Center of the Data
Master the three measures of center — mean, median, and mode — and learn how each responds to outliers, skewness, and weighted values. Understand when to use the median over the mean for skewed data like income, and how symmetric vs. skewed distributions shift these measures apart.
Measures of Variability
Unpack the core measures of spread — range, standard deviation, variance, and IQR — and learn when to use each based on data shape and outliers. Covers Chebyshev's theorem and the n − 1 correction for unbiased sample estimates.
Percentiles and Z-Scores
Unpack the relationship between percentiles, z-scores, and the standard normal distribution — covering the z = (x − μ) / σ formula, IQR-based outlier detection, and how standardized scores translate raw data into comparable percentile ranks.
Prediction
Master the mechanics of simple linear regression, from calculating slope and y-intercept using ŷ = a + bx to interpreting r² and avoiding extrapolation pitfalls. Covers when correlation is significant enough to predict and why the point (x̄, ȳ) always anchors the line.
Probability Rules
Master the core rules that govern probability calculations, including the Addition and Multiplication Rules, conditional probability, and the complement rule. Covers independent vs. mutually exclusive events so you can confidently solve problems involving P(A or B), P(A and B), and P(A′).
Rare Events the Sample Decision and Conclusion
Unpack the logic behind rare events in hypothesis testing, from formalizing "unlikely" with the significance level α to applying the p-value decision rule. Clarify why failing to reject H₀ isn't proof of its truth and how to state conclusions in context.
Sampling Methods
Break down the core sampling methods — simple random, stratified, cluster, and systematic — alongside non-probability approaches, sampling bias, and coverage error, so you can evaluate which methods support valid statistical inference and which don't.
Simple Linear Regression Model
Break down simple linear regression from the equation ŷ = b₀ + b₁x to least squares estimation, residual analysis, r², and hypothesis testing on the slope — everything you need to model, validate, and interpret a linear relationship between two variables.
Standard Normal Distribution
Master z-scores, standardization, and the standard normal curve — covering how to convert raw scores using z = (x − μ) / σ, read cumulative probabilities from a z-table, apply the empirical rule, and use symmetry to handle negative z-scores.
Statistics, Data, and Variables
Break down the core building blocks of introductory statistics — from descriptive vs. inferential methods and population vs. sample to variable types, levels of measurement, and sampling techniques — so you know exactly which concepts and tests apply to your data.
T Distribution
Master the t distribution — from degrees of freedom and heavier tails to t-tests and confidence intervals for unknown population standard deviations. See how the t and z distributions converge as sample size grows.
The Exponential Distribution
Master the exponential distribution, from its PDF and CDF to its unique memoryless property and link to the Poisson process. This pack covers rate parameter λ, mean and standard deviation of 1/λ, and right-skewed waiting time behavior.