Statistics Study Library.

Categorical vs. quantitative variables · Frequency tables and relative frequency tables · Dotplots, stemplots, histograms, and boxplots · SOCS framework: shape, outliers, center, spread · Mean, median, IQR, standard deviation · Identifying and computing outliers using 1.5 × IQR rule · z-scores and standardization · Normal distribution: proportions and percentiles · Empirical rule (68–95–99.7)

Scatterplots: construction and interpretation · DUFS framework: direction, unusual features, form, strength · Correlation coefficient r: meaning and properties · Least-squares regression line (LSRL): equation ŷ = a + bx · Slope and y-intercept interpretation in context · Residuals: definition and computation (residual = observed − predicted) · Residual plots: checking for linearity · Coefficient of determination r²: interpretation · Transformations for nonlinear data: logarithmic and power models

Population vs. sample; census vs. sample survey · Sampling methods: simple random sample (SRS), stratified random, cluster, systematic · Sources of bias: undercoverage, nonresponse bias, response bias, wording bias · Observational studies vs. experiments · Confounding variables and lurking variables · Principles of experimental design: control, randomization, replication, blinding · Placebo effect and control groups · Completely randomized designs · Randomized block designs · Matched pairs designs

Basic probability rules: complement, addition, multiplication · Conditional probability: P(A|B) = P(A ∩ B) / P(B) · Independence of events · Two-way tables and Venn diagrams for probability calculations · Tree diagrams for multi-stage probability · Discrete random variables: probability distributions, expected value E(X), variance Var(X) · Linear transformations of random variables · Combining independent random variables: means add, variances add (not standard deviations) · Binomial distribution: BINS conditions, mean, standard deviation, probability calculations · Geometric distribution: mean and probability calculations · Normal distribution: z-scores and probability calculations using tables or calculator

Concept of a sampling distribution of a sample statistic · Sampling distribution of the sample mean x̄: mean = μ, SD = σ/√n · Sampling distribution of the sample proportion p̂: mean = p, SD = √(p(1−p)/n) · Central Limit Theorem (CLT): shape of sampling distributions for large n · Conditions for approximately normal sampling distribution of x̄ (n ≥ 30 or population normal) · Conditions for approximately normal sampling distribution of p̂ (Large Counts: np ≥ 10 and n(1−p) ≥ 10) · 10% condition: sample size ≤ 10% of population (for independence) · Standard error vs. standard deviation distinction · Simulation as a method for building empirical sampling distributions

One-sample z-interval for a population proportion p · One-sample z-test for a population proportion p · Two-sample z-interval for a difference in proportions p₁ − p₂ · Two-sample z-test for a difference in proportions p₁ − p₂ · Conditions for inference: Random, 10%, Large Counts (np̂ ≥ 10 and n(1−p̂) ≥ 10) · Four-step inference procedure: State, Plan, Do, Conclude · Interpreting confidence levels and confidence intervals in context · Interpreting p-values in context · Type I error (false positive) and Type II error (false negative) · Power of a test: definition and factors that affect it · Factors affecting width of confidence intervals

One-sample t-interval for a population mean μ · One-sample t-test for a population mean μ · Paired t-procedures: t-interval and t-test for paired differences μ_d · Two-sample t-interval for a difference in means μ₁ − μ₂ · Two-sample t-test for a difference in means μ₁ − μ₂ · Conditions for inference on means: Random, 10%, Normality/CLT · Assessing normality condition from data (small n: inspect plot; large n: CLT applies) · Degrees of freedom for t-procedures · Using t-table and calculator for t-probabilities and critical values · Interpreting results of t-procedures in context

Chi-square goodness-of-fit test: one sample, one categorical variable vs. a claimed distribution · Chi-square test for homogeneity: multiple populations, one categorical variable · Chi-square test for independence: one population, two categorical variables · Expected counts formula: (row total × column total) / table total · Conditions for chi-square inference: Random, 10%, all expected counts ≥ 5 · Degrees of freedom: df = k − 1 (GOF); df = (r−1)(c−1) (homogeneity/independence) · Chi-square statistic: χ² = Σ((O − E)² / E) · Interpreting chi-square test results in context

Inference for regression slope β: conceptual framework · t-test for slope: hypotheses H₀: β = 0 vs. Hₐ: β ≠ 0 (or one-sided) · t-interval for slope b · Conditions for regression inference: Linear, Independent, Normal, Equal variance, Random (LINE + R) · Reading and interpreting computer regression output (coefficient table, SE, t-statistic, p-value) · Standard error of the slope SE_b · Degrees of freedom for regression t-procedures: df = n − 2