Appendix D: Glossary

Statistics has its own language. This glossary translates it into plain English, with biological context.

Terms are listed alphabetically. Cross-references appear in italics.

Adjusted R-squared. A modified version of R-squared that penalizes the addition of unnecessary predictors. Unlike R-squared, adjusted R-squared can decrease when a non-informative variable is added to a model. Preferred over R-squared for comparing models with different numbers of predictors.

Alpha (significance level). The threshold you set before testing for declaring a result statistically significant. Conventionally 0.05 (5%), meaning you accept a 5% chance of a Type I error. In genome-wide studies, often set much lower (5 x 10^-8 for GWAS).

Alternative hypothesis (H1). The hypothesis that there is an effect or a difference. The complement of the null hypothesis. Example: “Drug-treated tumors are smaller than untreated tumors.”

ANOVA (Analysis of Variance). A test for differences in means across three or more groups. Extends the t-test to multiple groups by comparing between-group variance to within-group variance. Produces an F-statistic.

AUC (Area Under the Curve). In the context of ROC analysis, the probability that a randomly chosen positive case ranks higher than a randomly chosen negative case. An AUC of 0.5 is random guessing; 1.0 is perfect classification.

Batch effect. Systematic technical variation introduced by processing samples in different batches, on different days, or with different reagents. A major confounder in genomics. Must be addressed through experimental design (randomization) or statistical correction (ComBat, limma).

Bayesian statistics. An approach to inference that combines prior knowledge with observed data to produce posterior probability distributions. Contrasts with frequentist statistics, which relies on long-run frequencies. Allows statements like “there is a 95% probability the true effect lies in this interval.”

Benjamini-Hochberg (BH). A multiple testing correction method that controls the false discovery rate (FDR) rather than the family-wise error rate. Less conservative than Bonferroni. The standard correction in genomics.

Beta (Type II error rate). The probability of failing to reject the null hypothesis when it is actually false. Power equals 1 - beta. A beta of 0.2 means a 20% chance of missing a real effect.

Bias. Systematic deviation of an estimate from the true value. Distinct from random error (variance). An estimator can be precise (low variance) but biased (consistently wrong in one direction).

Bimodal distribution. A distribution with two peaks. In gene expression, bimodality often indicates two distinct cell populations or states (e.g., expressed vs. silenced genes).

Blinding. Concealing group assignments from participants, clinicians, or analysts to prevent bias. Single-blind: participants do not know their group. Double-blind: neither participants nor clinicians know.

Bonferroni correction. The simplest multiple testing correction: multiply each p-value by the number of tests (or equivalently, divide alpha by the number of tests). Controls the family-wise error rate but is very conservative for large numbers of tests.

Bootstrap. A resampling method that estimates the sampling distribution of a statistic by repeatedly drawing samples with replacement from the observed data. Does not assume any particular parametric distribution.

Box plot. A visualization showing the median, quartiles, and outliers of a distribution. The box spans the interquartile range (IQR); whiskers extend to 1.5 * IQR; points beyond are outliers.

Categorical variable. A variable that takes a limited set of discrete values (e.g., genotype: AA, AB, BB; tissue type: liver, brain, kidney). Contrasts with continuous variable.

CDF (Cumulative Distribution Function). The probability that a random variable takes a value less than or equal to x. F(x) = P(X <= x). Ranges from 0 to 1.

Central limit theorem. The theorem stating that the sampling distribution of the mean approaches a normal distribution as sample size increases, regardless of the shape of the original population distribution. The foundation of most parametric tests.

Chi-square test. A test for association between two categorical variables. Compares observed frequencies in a contingency table to expected frequencies under independence. Requires expected cell counts >= 5; otherwise use Fisher’s exact test.

Clinical significance. A difference large enough to matter in practice, regardless of statistical significance. A drug that lowers blood pressure by 0.5 mmHg might be statistically significant with a large enough sample but clinically irrelevant.

Clustering. Grouping observations (samples, genes, cells) by similarity. Common methods: k-means (requires specifying k), hierarchical (produces a dendrogram), DBSCAN (finds clusters of arbitrary shape).

Coefficient of variation (CV). The ratio of the standard deviation to the mean, expressed as a percentage. Useful for comparing variability across measurements with different scales. CV = (SD / mean) * 100%.

Confidence interval (CI). A range of values that, if the experiment were repeated many times, would contain the true parameter value in the stated percentage of cases. A 95% CI does not mean “95% probability the true value is in this range” (that is the Bayesian credible interval).

Confounding variable. A variable that influences both the independent and dependent variables, creating a spurious association. Age confounds many gene expression studies because both expression and disease risk change with age.

Continuous variable. A variable that can take any value within a range (e.g., expression level, concentration, temperature). Contrasts with categorical variable.

Correlation. A measure of linear association between two variables. Pearson correlation (r) measures linear relationships; Spearman correlation (rho) measures monotonic relationships. Ranges from -1 to +1.

Cox proportional hazards. A regression model for survival analysis that estimates the effect of covariates on the hazard (instantaneous risk) of an event. Does not assume a particular survival distribution. Reports hazard ratios.

Credible interval. The Bayesian analog of a confidence interval. A 95% credible interval means there is a 95% probability the true parameter lies within the interval, given the data and prior. Requires specifying a prior distribution.

Degrees of freedom (df). The number of independent values that can vary in a statistical calculation. For a t-test with n1 and n2 observations, df is approximately n1 + n2 - 2 (for Student’s) or a more complex formula (for Welch’s).

Differential expression. A gene is differentially expressed if its expression level differs significantly between conditions (e.g., treated vs. control). Typically assessed with a negative binomial model (DESeq2, edgeR) and BH correction.

Effect size. A measure of the magnitude of a difference or association, independent of sample size. Common measures: Cohen’s d (standardized mean difference), odds ratio, hazard ratio, R-squared.

Cohen’s d. A standardized effect size for the difference between two means: d = (mean1 - mean2) / pooled_SD. Conventions: 0.2 = small, 0.5 = medium, 0.8 = large.

Eta-squared. An effect size for ANOVA representing the proportion of total variance explained by the group factor. Analogous to R-squared in regression.

Empirical distribution. The distribution derived directly from observed data, without assuming a parametric form. Used in permutation tests and bootstrap methods.

Enrichment analysis. Testing whether a set of genes (e.g., differentially expressed genes) contains more members of a particular pathway or GO category than expected by chance. Uses the hypergeometric distribution or GSEA.

False discovery rate (FDR). The expected proportion of rejected null hypotheses that are false positives. Controlled by Benjamini-Hochberg correction. At FDR = 0.05, you expect 5% of your “significant” findings to be false.

Family-wise error rate (FWER). The probability of making at least one Type I error across all tests. Controlled by Bonferroni and Holm corrections. More conservative than FDR control.

Fisher’s exact test. A test for association in 2x2 contingency tables that computes the exact probability under the hypergeometric distribution. Preferred over chi-square when sample sizes are small or expected cell counts are below 5.

Fold change. The ratio of a value in one condition to the value in another. A fold change of 2 means doubled; 0.5 means halved. Often reported on the log2 scale: log2(FC) = 1 means doubled.

Forest plot. A visualization for meta-analysis showing effect sizes and confidence intervals from multiple studies, plus a combined estimate. Each study is a horizontal line; the diamond shows the pooled effect.

Frequentist statistics. The dominant framework in biostatistics, based on long-run frequencies. P-values, confidence intervals, and hypothesis tests are frequentist concepts. Contrasts with Bayesian statistics.

GSEA (Gene Set Enrichment Analysis). A method that tests whether a predefined set of genes shows concordant differences between conditions. Unlike overrepresentation analysis, GSEA uses the full ranked gene list rather than an arbitrary significance cutoff.

GWAS (Genome-Wide Association Study). A study design that tests hundreds of thousands to millions of genetic variants for association with a phenotype. Requires stringent multiple testing correction (typically p < 5 x 10^-8).

Hazard ratio (HR). The ratio of hazard rates between two groups in survival analysis. HR = 0.7 means the treatment group has 30% lower instantaneous risk. HR = 1 means no difference. Estimated by Cox proportional hazards regression.

Heteroscedasticity. Unequal variance across groups or across the range of a predictor. Violates assumptions of standard t-tests and linear regression. Detected by residual plots. Addressed by Welch’s tests or robust standard errors.

Hierarchical clustering. A clustering method that builds a tree (dendrogram) by iteratively merging (agglomerative) or splitting (divisive) clusters. Common linkage methods: ward, complete, average, single.

Holm correction. A step-down multiple testing correction that is uniformly more powerful than Bonferroni while still controlling the FWER. Rejects the smallest p-value at alpha/m, the next at alpha/(m-1), and so on.

Homoscedasticity. Equal variance across groups or across the range of a predictor. An assumption of Student’s t-test and standard linear regression.

Hypothesis testing. A formal procedure for deciding between two competing hypotheses (null and alternative) based on observed data. Produces a test statistic and p-value.

Interquartile range (IQR). The range between the 25th and 75th percentiles. Contains the middle 50% of the data. A robust measure of spread, less sensitive to outliers than standard deviation.

Kaplan-Meier estimator. A non-parametric method for estimating survival probabilities over time, accounting for censored observations. Produces the familiar step-function survival curve.

k-means clustering. A clustering algorithm that partitions n observations into k clusters by minimizing within-cluster variance. Requires specifying k in advance. Sensitive to initialization; run multiple times.

Kruskal-Wallis test. The non-parametric alternative to one-way ANOVA. Tests whether multiple groups have the same distribution. Based on ranks rather than raw values.

Linear regression. A model that predicts a continuous outcome as a linear function of one or more predictors: y = beta_0 + beta_1 * x_1 + … + epsilon. Assumes normally distributed residuals and constant variance.

Log-rank test. A test for comparing survival curves between two or more groups. Tests the null hypothesis that the groups have equal hazard functions. The standard test for comparing Kaplan-Meier curves.

Logistic regression. A regression model for binary outcomes (0/1, yes/no, case/control). Models the log-odds of the outcome as a linear function of predictors. Reports odds ratios.

Manhattan plot. A visualization for GWAS results showing -log10(p-value) vs. genomic position. Significant associations appear as tall peaks above the genome-wide significance line. Named for its skyline-like appearance.

Mann-Whitney U test. A non-parametric alternative to the two-sample t-test. Tests whether one group tends to have larger values than the other. Based on ranks. Also called the Wilcoxon rank-sum test.

Mean. The arithmetic average. Sum of all values divided by the number of values. Sensitive to outliers. For skewed data, the median is often more representative.

Median. The middle value when data is sorted. Robust to outliers. Preferred over mean for skewed distributions. The 50th percentile.

Meta-analysis. A statistical method for combining results from multiple independent studies to produce a single pooled estimate. Uses weighted averages based on study precision. Visualized with forest plots.

Mixed-effects model. A regression model that includes both fixed effects (variables of interest) and random effects (grouping variables like patient, batch, or site). Accounts for non-independence in hierarchical or repeated-measures data.

Mode. The most frequently occurring value (discrete data) or the peak of the density curve (continuous data). A distribution can be bimodal or multimodal.

Multiple testing correction. Adjusting p-values or significance thresholds when performing many simultaneous tests to control the overall error rate. Methods include Bonferroni, Holm, Benjamini-Hochberg, and permutation testing.

Negative binomial distribution. A discrete distribution for count data that allows the variance to exceed the mean (overdispersion). The standard model for RNA-seq differential expression (DESeq2, edgeR).

Non-parametric test. A statistical test that does not assume a specific parametric distribution (e.g., normality). Examples: Mann-Whitney U, Kruskal-Wallis, Wilcoxon signed-rank. Generally less powerful than parametric tests when assumptions hold.

Normal distribution. The symmetric, bell-shaped distribution described by a mean and standard deviation. Many biological measurements are approximately normal, especially after log transformation. The basis for most parametric tests via the central limit theorem.

Null hypothesis (H0). The hypothesis that there is no effect, no difference, or no association. Statistical tests assess evidence against the null. Example: “There is no difference in gene expression between treated and control groups.”

Odds ratio (OR). The ratio of odds of an event in one group to odds in another. OR = 1 means no association. OR > 1 means increased odds. Commonly reported in logistic regression and case-control studies.

Outlier. An observation that is unusually far from the rest of the data. In a box plot, observations beyond 1.5 * IQR from the quartiles. Can indicate errors, biological extremes, or violations of assumptions.

Overdispersion. Variance exceeding the mean in count data. Poisson models assume variance = mean; when this is violated, negative binomial models are more appropriate. Nearly universal in RNA-seq data.

Paired test. A test that accounts for the natural pairing of observations (e.g., before/after measurements on the same subject). More powerful than unpaired tests because pairing removes between-subject variability.

Parametric test. A statistical test that assumes the data follows a specific probability distribution (usually normal). Examples: t-test, ANOVA, Pearson correlation. More powerful than non-parametric tests when assumptions hold.

PCA (Principal Component Analysis). A dimensionality reduction method that finds orthogonal linear combinations of variables (principal components) that capture maximum variance. PC1 captures the most variance, PC2 the next most, and so on.

PDF (Probability Density Function). For continuous distributions, the function whose integral over an interval gives the probability of falling in that interval. The height of the curve at a point is not a probability.

Pearson correlation. A measure of linear association between two continuous variables. Ranges from -1 (perfect negative) to +1 (perfect positive). Assumes both variables are approximately normally distributed.

Permutation test. A non-parametric test that estimates the null distribution by repeatedly shuffling group labels and recomputing the test statistic. The p-value is the proportion of permuted statistics as extreme as the observed. Makes minimal assumptions.

PMF (Probability Mass Function). For discrete distributions, the function that gives the probability of each possible value. P(X = k) = pmf(k).

Posterior distribution. In Bayesian statistics, the updated distribution of a parameter after observing data. Combines the prior distribution with the likelihood. Posterior is proportional to prior times likelihood.

Power. The probability of correctly rejecting the null hypothesis when it is false. Power = 1 - beta. Conventionally set at 0.8 (80%). Depends on sample size, effect size, alpha, and variability.

Prior distribution. In Bayesian statistics, the distribution representing beliefs about a parameter before observing data. Can be informative (based on previous studies) or non-informative (vague).

p-value. The probability of observing data as extreme as (or more extreme than) what was observed, assuming the null hypothesis is true. It is not the probability that the null hypothesis is true.

Q-Q plot (Quantile-Quantile plot). A diagnostic plot that compares the quantiles of observed data to the quantiles of a theoretical distribution (usually normal). Points on the diagonal indicate good fit. Used to check normality and to assess genomic inflation in GWAS.

Quartile. Values that divide the data into four equal parts. Q1 (25th percentile), Q2 (50th percentile = median), Q3 (75th percentile). The IQR is Q3 - Q1.

Randomization. Random assignment of subjects to treatment groups to ensure that confounding variables are equally distributed across groups. The gold standard for causal inference in clinical trials.

Relative risk (RR). The ratio of risk (probability) of an event in the exposed group to risk in the unexposed group. RR = 1 means no association. Reported in cohort studies and clinical trials. Distinct from odds ratio.

Resampling. Methods that generate new datasets from the observed data by sampling with or without replacement. Includes bootstrap and permutation methods. Useful when parametric assumptions are questionable.

Residual. The difference between an observed value and the value predicted by a model. Patterns in residuals indicate model misspecification. Residual plots are essential diagnostics for regression.

ROC curve (Receiver Operating Characteristic). A plot of sensitivity (true positive rate) vs. 1-specificity (false positive rate) at various classification thresholds. The AUC summarizes overall discrimination.

R-squared (coefficient of determination). The proportion of variance in the outcome explained by the model. Ranges from 0 to 1. R-squared = 0.7 means the model explains 70% of the variability. Always increases with more predictors; use adjusted R-squared for model comparison.

Sample size. The number of observations in a study. Larger samples give more precise estimates and greater power. Sample size calculations use power analysis to determine the minimum n needed for a given effect size and alpha.

Sensitivity. The proportion of true positives correctly identified. Sensitivity = TP / (TP + FN). Also called the true positive rate or recall. A test with high sensitivity rarely misses real positives.

Spearman correlation. A non-parametric measure of monotonic association. Computed by applying Pearson correlation to the ranks of the data. Does not assume linearity or normality.

Specificity. The proportion of true negatives correctly identified. Specificity = TN / (TN + FP). A test with high specificity rarely produces false positives.

Standard deviation (SD). The square root of variance. Measures the typical deviation of observations from the mean. Reported in the same units as the data. About 68% of normal data falls within one SD of the mean.

Standard error (SE). The standard deviation of a sampling distribution. SE of the mean = SD / sqrt(n). Decreases with larger sample sizes. Used to construct confidence intervals.

Survival analysis. Statistical methods for analyzing time-to-event data with censoring. Key tools: Kaplan-Meier estimator, log-rank test, Cox proportional hazards model.

t-test. A test for comparing means of two groups. Student’s t-test assumes equal variances; Welch’s t-test does not. For paired observations, use the paired t-test. Assumes approximately normal data or large samples.

Tukey HSD. A post-hoc test for all pairwise comparisons after a significant ANOVA. Controls the family-wise error rate across all comparisons. Preferred when comparing all group pairs.

Type I error. Rejecting the null hypothesis when it is actually true (false positive). The probability of a Type I error is alpha. In genomics, controlled by multiple testing correction.

Type II error. Failing to reject the null hypothesis when it is actually false (false negative). The probability of a Type II error is beta. Reduced by increasing sample size or effect size.

Variance. The average squared deviation from the mean. Var = sum((x_i - mean)^2) / (n - 1) for a sample. Measures the spread of a distribution. The square of the standard deviation.

VIF (Variance Inflation Factor). A measure of multicollinearity in regression. VIF = 1 means no correlation between predictors; VIF > 5-10 suggests problematic multicollinearity. Computed for each predictor.

Volcano plot. A visualization for differential expression showing -log10(p-value) vs. log2(fold change). Significant and biologically meaningful genes appear in the upper left (downregulated) and upper right (upregulated) corners.

Wilcoxon signed-rank test. A non-parametric alternative to the paired t-test. Tests whether the median of paired differences is zero. Based on the ranks of the absolute differences.