Unit 1: Exploring One-Variable Data

• Categorical data (not numerical) is shown in two-way tables & bar graphs, analyzing proportions
• Quantitative data is displayed in histograms, dotplots, box plots, stem and leaf plots, and scatter plots
• Mean: non-resistant (affected by outliers)
• Median: resistant (affected by outliers)
• Shapes: Unimodal = one clear peak, Bimodal = two clear peaks, Uniform = no clear peaks, flat
• When analyzing distributions, always CUSS & BS in context - Center, Unusual features, Shape, Spread
• Normal distribution: mound-shaped and symmetric (μ = mean, σ = standard deviation)
• z-score = (value-mean)/SD, measuring how many SD a value is from the mean
• Empirical Rule: 68% (1 SD), 95% (2 SD), 99.7% (3 SD)

Unit 2: Exploring Two-Variable Data

• For quantitative data, describe associations with direction, strength, form
• Direction - positive / negative (slope)
• Form - linear / non-linear
• r (correlation coefficient) measures strength & direction, NOT FORM
• LSRL predicts values of response variable (y) given explanatory variable (x)
• LSRL written as ŷ = a + bx
• Residual = observed - predicted
• Look for random scatter on residual plot!
• s & R-sq influenced by outliers (s ↑, r-sq ↓)

Key Interpretations:

• Slope/b: As the [exp var] increases by 1 [unit], the [rsp var] is predicted to increase by b [units]
• Y-intercept: When there are zero [exp var], the predicted [rsp var] is a
• r²: About [r-sq]% of variation in [rsp var] is explained by the LSRL using [exp var]

Unit 3: Collecting Data

• Simple Random Sample (SRS) = every group of a certain size has an equal chance of being selected
• Cluster Sample = Divide pop. into heterogeneous groups [all from some]
• Stratified Random Sample = Divide pop. into strata of homogeneous groups [some from all]
• Bias types = undercoverage, nonresponse, response bias
• EXPERIMENTS ASSIGN TREATMENTS
• Confounding - When effects of variables can't be distinguished
• Experiments have comparison, random assignment, control, & replication
• Randomized block design: random assignment within each block
• Matched pairs = compare 2 treatments in block size 2

Unit 4: Probability, Random Variables, & Distributions

• Probability = the chance of an event occurring (0-1)
• P(event) = succ. outcomes / total outcomes
• Complement: P(not event) = 1 - P(event)
• P(A and B) = P(A∩B) = P(A) * P(B|A)
• P(A or B) = P(A U B) = P(A) + P(B) - P(A and B)
• Conditional Probability: P(A|B) = P(A and B) / P(B)
• Events are independent if P(A|B) = P(A) OR P(A and B) = P(A) * P(B)
• Expected Value: E(X) = Σ(x_i * p_i)
• Binomial: Binary, Independent, Number fixed, Same p
• Geometric: Number of trials until first success

Unit 5: Sampling Distributions

• X-bar estimates μ, p-hat estimates p
• Sampling distribution: distribution of statistic values across all possible samples
• Larger samples produce more precise estimates (↓ variability)
• p-hat is approximately normal if np ≥ 10 AND n(1-p) ≥ 10
• x-bar is approximately normal if population is normal OR n ≥ 30 (CLT)

3 Major Conditions:

• Normal/Large Counts: np>10, n(1-p)>10
• Independence: n < 10% of population
• Random: Should be stated in problem

Unit 6: Proportions

• Confidence Interval = Point Estimate ± Margin of Error
• One sample: C% Z-interval for p, Z-test for p
• Two sample: C% Z-interval for p₁-p₂, Z-test for p₁-p₂
• Note: There is NOT paired data for proportions

Key Interpretations:

• P-value: Assuming [Ho] is true, the probability of [statistic] as or more extreme is [p-value]
• Confidence interval: We are C% confident interval from [lower] to [upper] captures true [parameter]

Unit 7: Means

• One sample: C% t-interval for μ, t-test for μ
• Two sample: C% t-interval for μ₁-μ₂, t-test for μ₁-μ₂
• For paired data: Label parameter μ_diff, use one-sample t-interval/test for μ_diff
• Type I Error: Rejecting H₀ when it's true
• Type II Error: Failing to reject H₀ when it's false
• Power: 1 - P(Type II error)
• To increase power: increase sample size, significance level, or difference between H₀ and true H_a

Unit 8: Chi-Squares

• Formula: χ² = Σ((observed − expected)²/expected)
• 3 Tests: Goodness-of-Fit, Independence, Homogeneity
• Chi-Square is non-parametric (no distribution assumptions)
• Remember to calculate df (n-1)
• Conditions: random, independent, at least 5 expected counts

Unit 9: Slopes

• LSRL Equation: μ = α + βx
• 5 Conditions: Linear, Independent, Normal, Equal SD, Random
• Confidence interval: b ± t*(SE_b)
• Hypothesis test: (b - β₀)/SE_b
• For unit 9, df = n-2