Glossary

Plain-English definitions of the 57 ideas this course leans on most. Type to filter.

Population: The entire collection of individuals, objects, or measurements you want to draw conclusions about. Its characteristics are fixed but usually unknown. → Descriptive statistics & data basics
Sample: A subset of the population that you actually observe and measure, used to make inferences about the larger population. → Descriptive statistics & data basics
Parameter vs. statistic: A parameter is a fixed numerical summary of a population (e.g. the true mean μ); a statistic is a computed summary of a sample (e.g. the sample mean x̄) used to estimate it. → Descriptive statistics & data basics
Variable types: Categorical variables record group membership (nominal or ordinal), while quantitative variables record numeric amounts (discrete counts or continuous measurements). → Descriptive statistics & data basics
Mean: The arithmetic average of a set of values, found by summing them and dividing by the count. It is sensitive to extreme values. → Measures of center
Median: The middle value when data are sorted (or the average of the two middle values). It is robust to outliers and skew. → Measures of center
Standard deviation & variance: Variance is the average squared deviation of values from their mean; standard deviation is its square root, expressing spread in the original units. → Measures of spread
Quartiles & IQR: Quartiles split sorted data into four equal parts; the interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50% and is robust to outliers. → Measures of spread
Skewness: A measure of asymmetry in a distribution; a right- (positive) skew has a long upper tail, a left- (negative) skew a long lower tail. → Shape of distributions
Outlier: An observation that lies unusually far from the rest of the data, often flagged when it falls beyond 1.5 × IQR from the nearest quartile. → Exploring data & boxplots
Z-score: The number of standard deviations a value lies above or below its mean, computed as (x − mean) / standard deviation. It standardizes values onto a common scale. → Standardization
Probability: A number between 0 and 1 quantifying how likely an event is, interpreted as its long-run relative frequency over many repetitions. → Introduction to probability
Sample space & event: The sample space is the set of all possible outcomes of a random process; an event is any subset of those outcomes whose probability we assess. → Introduction to probability
Conditional probability: The probability of event A given that event B has occurred, written P(A | B) = P(A and B) / P(B). It updates likelihood in light of new information. → Conditional probability & independence
Independence: Two events are independent if knowing one occurred does not change the probability of the other, i.e. P(A | B) = P(A). → Conditional probability & independence
Bayes' theorem: A rule for reversing conditional probabilities: P(A | B) = P(B | A) P(A) / P(B). It updates a prior belief into a posterior using observed evidence. → Bayes' theorem
Random variable: A variable whose value is a numerical outcome of a random process; it can be discrete (countable values) or continuous (values over an interval). → Random variables
Expected value: The long-run average value of a random variable, computed as the probability-weighted sum (or integral) of its possible values. → Random variables
Probability distribution: A description of how probability is allocated across the possible values of a random variable, via a mass function (discrete) or density function (continuous). → Random variables
Binomial distribution: The distribution of the number of successes in a fixed number of independent trials, each with the same success probability p. → Discrete distributions
Poisson distribution: The distribution of the count of events occurring in a fixed interval of time or space when events happen independently at a constant average rate. → Discrete distributions
Normal distribution: A symmetric, bell-shaped continuous distribution fully described by its mean and standard deviation; many statistics are approximately normal. → The normal distribution
Empirical (68-95-99.7) rule: For a normal distribution, about 68%, 95%, and 99.7% of values fall within one, two, and three standard deviations of the mean, respectively. → The normal distribution
Sampling distribution: The distribution of a statistic (such as x̄) across all possible samples of a given size; it describes how the estimate varies from sample to sample. → Sampling distributions
Standard error: The standard deviation of a statistic's sampling distribution, measuring the typical sampling variability of the estimate (e.g. SE of the mean = σ/√n). → Sampling distributions
Central Limit Theorem: For a large enough sample size, the sampling distribution of the sample mean is approximately normal regardless of the population's shape, centered at the population mean. → The Central Limit Theorem
Point estimate: A single best-guess value for an unknown parameter computed from sample data, such as using x̄ to estimate the population mean. → Estimation
Bias of an estimator: The difference between an estimator's expected value and the true parameter; an unbiased estimator is correct on average over repeated sampling. → Estimation
Confidence interval: A range computed from data by a procedure that, in repeated sampling, captures the true parameter in a stated percentage (e.g. 95%) of intervals; that percentage describes the method's long-run capture rate, not the probability for any one interval. → Confidence intervals
Confidence level: The long-run proportion of intervals produced by the procedure that contain the true parameter; a 95% level means 95% of such intervals would capture it over many repetitions. → Confidence intervals
Margin of error: The half-width of a confidence interval, equal to a critical value times the standard error; it sets how far the estimate may plausibly lie from the parameter. → Confidence intervals
Null & alternative hypotheses: The null hypothesis (H₀) is a default claim of no effect or no difference; the alternative (Hₐ) is the competing claim the test seeks evidence for. → Hypothesis testing
Test statistic: A standardized number computed from the data (e.g. a t or z value) that measures how far the sample result is from what the null hypothesis predicts. → Hypothesis testing
P-value: The probability, assuming the null hypothesis is true, of observing a test statistic at least as extreme as the one obtained. It is not the probability that the null hypothesis is true. → P-values
Significance level (alpha): A pre-chosen threshold (commonly 0.05) for the p-value; if the p-value is below it, the result is declared statistically significant and H₀ is rejected. → Hypothesis testing
Statistical significance: A result is statistically significant when the data are unlikely under the null hypothesis (p < alpha); it indicates an effect is detectable, not that it is large or important. → Hypothesis testing
Type I & Type II errors: A Type I error is rejecting a true null hypothesis (false positive, rate alpha); a Type II error is failing to reject a false null hypothesis (false negative, rate beta). → Errors & power
Statistical power: The probability that a test correctly rejects a false null hypothesis (1 − beta); it rises with larger effect size, larger sample size, and higher alpha. → Errors & power
Effect size: A measure of the magnitude of a difference or relationship (e.g. Cohen's d) that is independent of sample size, complementing significance testing. → Errors & power
One- vs. two-tailed test: A two-tailed test looks for a difference in either direction; a one-tailed test looks only in a single pre-specified direction, concentrating alpha in one tail. → Hypothesis testing
Inference for a proportion: Procedures (z-based intervals and tests) for estimating or testing a population proportion p using the sample proportion p̂ and its standard error. → Inference for proportions
Student's t-distribution: A bell-shaped distribution with heavier tails than the normal, used for inference about a mean when the population standard deviation is unknown and estimated from the sample. → t-tests
Degrees of freedom: The number of values free to vary when computing a statistic; it indexes the t and chi-square distributions and typically equals sample size minus the number of estimated parameters. → t-tests
One-sample t-test: A test comparing a single sample mean to a hypothesized value when the population standard deviation is unknown, using a t test statistic. → t-tests
Two-sample & paired t-tests: A two-sample t-test compares means of two independent groups; a paired t-test compares two related measurements per subject by analyzing their differences. → t-tests
ANOVA: Analysis of variance tests whether three or more group means differ by comparing variation between groups to variation within groups via an F-statistic. → ANOVA
F-statistic: A ratio of two variances (e.g. between-group to within-group variability); large values give evidence against equal group means in ANOVA. → ANOVA
Chi-square test: A test comparing observed counts to expected counts under a null hypothesis, used for goodness-of-fit and for independence between two categorical variables. → Chi-square tests
Correlation coefficient: A number between −1 and 1 (Pearson's r) measuring the strength and direction of the linear association between two quantitative variables. → Correlation
Simple linear regression: A model fitting a straight line ŷ = b₀ + b₁x to predict a response from one predictor, with the slope giving the predicted change in y per unit change in x. → Linear regression
Least squares: The fitting method that chooses regression coefficients to minimize the sum of squared residuals (vertical distances between observed and predicted values). → Linear regression
Residual: The difference between an observed value and its value predicted by the model; residual patterns are used to check model assumptions. → Linear regression
R-squared: The proportion of variance in the response explained by the regression model, ranging from 0 to 1, with higher values indicating better fit. → Linear regression
Multiple regression: A regression model with two or more predictors, where each coefficient estimates the effect of its predictor while holding the others constant. → Multiple regression
Confounding variable: An outside variable associated with both the predictor and the response that can distort or fake an apparent relationship between them. → Multiple regression & causation
Bootstrap: A resampling method that draws many samples with replacement from the observed data to approximate a statistic's sampling distribution and build confidence intervals. → Bootstrap & resampling
Permutation test: A test that builds a null distribution by repeatedly shuffling group labels, then compares the observed statistic to that distribution to obtain a p-value without distributional assumptions. → Permutation tests