Population: The entire group being studied Sample: The part of the population actually measured Parameter: A number describing a population Statistic: A number describing a sample Categorical variable: Places individuals into groups Quantitative variable: Takes numerical values that can be measured or counted Discrete variable: Takes countable values Continuous variable: Takes any value in an interval Bar graph: Shows counts or percentages for categories Histogram: Bars showing how quantitative data are distributed Dotplot: Each value shown as a dot above a number line Boxplot: Display of the five-number summary Five-number summary: Minimum, Q1, median, Q3, maximum Interquartile range: Q3 minus Q1 Outlier rule: Values beyond 1.5 times IQR from the quartiles Mean: Sum of values divided by their number Median: Middle value when ordered Resistant measure: A statistic not strongly affected by outliers, like the median Standard deviation: Typical distance of values from the mean Variance: The square of the standard deviation Skewed right: Long tail toward larger values; mean greater than median Symmetric distribution: Both sides are mirror images Z-score: How many standard deviations a value is from the mean Normal distribution: Bell-shaped, symmetric distribution Empirical rule: About 68, 95 and 99.7 percent within 1, 2 and 3 standard deviations Percentile: Percent of values at or below a given value Scatterplot: Graph of two quantitative variables Correlation r: Measures strength and direction of a linear relationship, -1 to 1 Least-squares regression line: Line minimizing the sum of squared residuals Residual: Actual value minus predicted value Residual plot: Graph used to check if a linear model fits Coefficient of determination: r squared, share of variation explained by the model Slope: Predicted change in y for each one-unit increase in x Extrapolation: Predicting outside the range of the data, which is risky Influential point: A point that greatly changes the regression line Lurking variable: An unmeasured variable influencing the relationship Confounding: Effects of variables cannot be separated Simple random sample: Every group of the chosen size is equally likely Stratified random sample: Random samples from each subgroup Cluster sample: Randomly choose groups and survey everyone in them Systematic sample: Choose every kth individual Convenience sample: Easy-to-reach individuals; likely biased Voluntary response bias: Bias from people choosing to respond Undercoverage: Some groups are left out of the sampling frame Nonresponse bias: Selected individuals do not respond Response bias: Answers distorted by question wording or situation Observational study: Observes without assigning treatments Experiment: Researchers impose treatments on subjects Randomized block design: Group similar subjects into blocks, then randomize within blocks Matched pairs design: Subjects paired or each used twice to compare treatments Replication: Using enough subjects so results are reliable Blinding: Hiding treatment information to reduce bias Law of large numbers: Relative frequency approaches probability with more trials Sample space: All possible outcomes Complement rule: P(not A) = 1 - P(A) Addition rule: P(A or B) = P(A) + P(B) - P(A and B) Independent events: One does not change the probability of the other Conditional probability: P(A | B) = P(A and B) / P(B) Mutually exclusive: Events that cannot occur together Random variable: A numerical outcome of a random process Expected value: The long-run average of a random variable Binomial setting: Fixed trials, two outcomes, independent, constant probability Binomial mean: np Binomial standard deviation: sqrt(np(1 - p)) Geometric distribution: Counts trials until the first success Sampling distribution: Distribution of a statistic across all samples of a given size Unbiased estimator: A statistic whose mean equals the parameter Central limit theorem: Sample means become approximately normal as sample size grows Standard error: Estimated standard deviation of a statistic Margin of error: Critical value times the standard error Confidence interval: A range of plausible values for a parameter Confidence level: Long-run percent of intervals that capture the parameter Null hypothesis: The claim of no effect or no difference Alternative hypothesis: The claim tested for evidence P-value: Probability of results at least as extreme as observed if the null is true Significance level: Cutoff probability for rejecting the null, often 0.05 Type I error: Rejecting a true null hypothesis Type II error: Failing to reject a false null hypothesis Power: Probability of correctly rejecting a false null One-sample z-test for proportion: Tests a claim about a population proportion t-distribution: Used with sample standard deviation for means; heavier tails than normal Degrees of freedom: Number of independent pieces of information Two-sample t-test: Compares means of two independent groups Paired t-test: Compares means within matched pairs Chi-square goodness of fit: Tests whether counts match a claimed distribution Chi-square test of independence: Tests association between two categorical variables Expected count: Count predicted if the null is true Inference for slope: t-test of the slope of a regression line Conditions for inference: Random, independent (10 percent rule), and normal or large sample 10 percent condition: Sample should be under 10 percent of population for independence Large counts condition: np and n(1-p) each at least 10 Statistical significance: Results unlikely to be due to chance alone Causation conclusion: Only well-designed randomized experiments support causal claims Free flashcards from Peabody at peabody.kids/flashcards/tp-ap-statistics