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