Statistics
Review Statistics study guides, quizzes, and flashcards covering probability, hypothesis testing, and regression.
Topics
ANOVA Foundations
Break down the logic of ANOVA by examining how total variability is partitioned into between-group and within-group variance, how the F-statistic is calculated from MSB and MSW, and what a significant result actually tells you. This pack also covers one-way ANOVA assumptions, interpreting the null hypothesis, and when to apply post-hoc tests like Tukey's HSD to pinpoint which group means truly differ.
Binomial Distributions
Master the mechanics of binomial distributions by working through the four required conditions, the probability formula P(X = k) = C(n,k) · p^k · (1−p)^(n−k), and the binomial coefficient. This pack covers how to calculate mean and standard deviation using np and √(np(1−p)), and explains why large samples push the distribution toward a normal shape.
Central Limit Theorem
Unpack the Central Limit Theorem and see why it sits at the heart of inferential statistics. This pack covers how sampling distributions of sample means become normal as n increases, why the standard error shrinks with larger samples, and how the n ≥ 30 rule of thumb applies in practice — giving you the foundation to interpret z-scores, confidence intervals, and hypothesis tests with confidence.
Confidence Level and Margin of Error
Unpack the relationship between confidence levels, margin of error, and interval width by working through the mechanics of z* and t* critical values, standard error, and sample size effects. This pack clarifies the most commonly misunderstood concept — what a 95% confidence level actually means across repeated sampling — and covers when to apply the z-distribution versus the t-distribution.
Data Visualization and Distribution Shapes
Visualize your way through the core tools of introductory statistics by examining histograms, dot plots, stem-and-leaf plots, and box plots alongside the distribution shapes they reveal — symmetric, skewed, and uniform. Understand how skewness shifts the mean toward the tail while the median holds steady, and see how outliers affect measures of center and spread differently. Perfect for students mastering the five-number summary and choosing the right graph for any dataset.
Experimental Design and Bias
Unpack the core principles that separate well-designed experiments from flawed ones, including control groups, random assignment, replication, and blinding techniques like single- and double-blind procedures. Examine how systematic biases — sampling bias, placebo effect, and response bias — distort results, and why observational studies can reveal correlation but never causation. Ideal for students preparing for exams on experimental design fundamentals.
Hypothesis Testing Logic
Unpack the core logic behind hypothesis testing, from setting up the null and alternative hypotheses to interpreting p-values and applying the significance level α. This pack walks you through Type I and Type II errors, one- and two-tailed tests, and statistical power, giving you a clear framework for understanding how statisticians use sample data to make confident decisions about population claims.
Measures of the Center of the Data
Master the three primary measures of center — mean, median, and mode — and learn when to use each one. This pack covers how outliers affect the mean, why the median is preferred for skewed distributions, and how the relationship between mean and median reveals distribution shape, including how to estimate the mean from grouped frequency data.
Measures of Variability
Break down the key measures of spread in introductory statistics, including range, variance, standard deviation, and IQR. Understand why Bessel's correction adjusts sample standard deviation, when to use IQR over standard deviation for skewed data, and how the coefficient of variation lets you compare variability across datasets with different units or scales.
Percentiles and Z-Scores
Master the two core tools for measuring relative standing in a distribution: percentiles and z-scores. Work through the z = (x − μ) / σ formula, learn how negative and positive z-scores locate values around the mean, and see how cumulative probabilities connect to the standard normal curve. The IQR and quartile relationships are covered too.
Prediction
Master the mechanics of simple linear regression and prediction by working through the least-squares equation ŷ = a + bx, the role of Pearson's r in calculating slope, and the coefficient of determination r². This pack also clarifies the critical distinction between valid interpolation and unreliable extrapolation, helping you know exactly when a regression line can and cannot be trusted for prediction.
Probability Rules
Master the core rules that govern how probabilities combine and interact. This pack covers the Addition and Multiplication Rules, conditional probability, mutually exclusive and independent events, and complement shortcuts — giving you the tools to calculate P(A or B), P(A and B), and P(B|A) with confidence across any introductory statistics problem.
Rare Events the Sample Decision and Conclusion
Unpack the logic behind rare events in hypothesis testing, from interpreting p-values relative to significance level α to applying the reject-or-fail-to-reject decision rule. This pack clarifies what it truly means when p ≤ α, why failing to reject H₀ is not proof of its truth, and how to write conclusions grounded in real-world context.
Sampling Methods
Break down the core sampling methods used in introductory statistics, from simple random and stratified sampling to cluster and systematic approaches. Compare probability and non-probability methods, understand how sampling bias — including undercoverage and self-selection — distorts results, and learn how sample size and randomization determine how well your sample represents the population.
Simple Linear Regression Model
Build a solid foundation in simple linear regression by mastering the equation ŷ = a + bx, the least squares method, and how to interpret slope and y-intercept. This pack covers residual analysis, correlation, r², hypothesis testing on the slope, and the risks of extrapolation — everything you need to apply and evaluate linear regression models with confidence.
Standard Normal Distribution
Master the standard normal distribution by working through z-score conversions using z = (x − μ) / σ, interpreting cumulative areas under the bell curve, and reading z-tables accurately. This pack covers how symmetry around z = 0 simplifies probability calculations and how to find left-tail, right-tail, and between-interval probabilities — everything you need to navigate standardized normal distributions with confidence.
Statistics, Data, and Variables
Break down the foundational building blocks of statistics, from the distinction between descriptive and inferential statistics to populations, samples, parameters, and statistics. Explore how variables are classified as quantitative or qualitative, discrete or continuous, and how nominal, ordinal, interval, and ratio levels of measurement determine which methods apply. Sampling techniques like stratified and cluster sampling are also covered.
T Distribution
Understand how the t distribution differs from the standard normal curve, and why its heavier tails and degrees of freedom matter when working with small samples or an unknown population standard deviation. This pack covers key concepts including the t test statistic, critical values, and constructing confidence intervals using x̄ ± t* · (s / √n) — everything you need to apply the t distribution with confidence.
The Exponential Distribution
Master the exponential distribution by working through its core mechanics, from the probability density and cumulative distribution functions to the mean and standard deviation of 1/λ. This pack covers the memoryless property, its connection to the Poisson process, and probability calculations using P(X > x) = e^(−λx) — everything you need to confidently apply this single-parameter distribution.