Math & Statistics

63 Math & Statistics terms, defined in plain English — part of the 1345-term Finicade finance glossary. Each one has its own page, and links to the free game that teaches it.

Autocorrelation: Autocorrelation is a series being correlated with its own past values.
Bayes' Theorem: Bayes' theorem tells you how to update a probability when new evidence arrives, combining prior belief with the likelihood of what you observed.
Bayesian Inference: Bayesian inference treats unknown parameters as having probability distributions, starting from a prior and updating to a posterior as data arrives.
Binomial Distribution: The binomial distribution gives the probability of a number of successes in a fixed count of independent yes/no trials with constant probability.
Central Limit Theorem: The reason the bell curve is everywhere: add up enough independent random bits and their total tends to a normal distribution, whatever the pieces looked like.
Chain Rule: The rule for differentiating a function of a function — multiply the outer slope by the inner one.
Chi-Square Test: A chi-square test compares observed counts with expected counts — to test whether a distribution fits, or whether two categorical variables are independent.
Conditional Probability: Conditional probability is the chance of an event given that another has occurred, written P(A|B).
Confidence Interval: A range that likely contains the true value, with a stated level of confidence — say, '95% sure the mean is between 4 and 6'.
Confidence Level: How sure you want to be — 95%, 99% — when quoting a risk figure or a statistical estimate.
Continuous Compounding: Compounding not yearly or monthly but in infinitely small instants — the mathematical limit, powered by the number e.
Correlation vs Causation: Correlation measures whether two variables move together; causation claims one produces the other.
Degrees of Freedom: Degrees of freedom is the number of values in a calculation that are free to vary once constraints are imposed.
Derivative (Calculus): The rate at which something changes — the slope of a curve at a point.
Dot Product: Multiplying two lists of numbers pairwise and adding the results — the workhorse of portfolio maths.
e (Euler's Number): The constant ≈2.718 that shows up whenever growth compounds continuously.
Eigenvalue: An eigenvector is a direction a matrix stretches without rotating, and the eigenvalue is how much it stretches.
Endogeneity: Endogeneity means a predictor is correlated with the error term, which breaks the causal interpretation of a regression coefficient.
Expected Value: The long-run average of a random outcome — each result weighted by its probability.
Exponential Growth: Exponential growth feeds on itself, so the bigger it gets the faster it grows — the maths behind compound interest.
Geometric Series: A sum where each term is a fixed multiple of the last.
Heteroskedasticity: Heteroskedasticity means the variance of regression errors is not constant across observations — it wrecks standard errors, not the coefficients.
Hypothesis Test: A procedure for deciding whether data supports a claim — comparing what you observed against what pure chance would produce.
Instrumental Variable: An instrumental variable moves your predictor but affects the outcome only through it, letting you recover a causal effect despite endogeneity.
Integral: The area under a curve — adding up infinitely many tiny slices.
Interquartile Range: The interquartile range is the distance between the 25th and 75th percentiles — the width of the middle half of the data.
Law of Large Numbers: The law of large numbers says the sample average converges to the true mean as the sample grows.
Logarithm: The inverse of exponentiation — it answers 'what power turns this base into that number?'.
Lognormal Distribution: The distribution you get when the logarithm of a quantity is normal — skewed, never negative, with a long right tail.
Matrix: A matrix is a rectangular array of numbers that represents a linear transformation, and it's how portfolios are actually computed.
Maximum Likelihood Estimation: Maximum likelihood picks the parameter values that make the observed data most probable under the assumed model.
Mean Reversion: The tendency of a quantity to drift back toward its long-run average after straying.
Mean, Median and Mode: Three ways to name the 'typical' value: the mean (average), the median (middle) and the mode (most common).
Multicollinearity: Multicollinearity is when predictors in a regression are highly correlated with each other, so the model cannot tell their effects apart.
Normal Distribution: The bell curve — the symmetric spread where most outcomes cluster near the average and extremes are rare.
Null Hypothesis: The null hypothesis is the default claim a test tries to disprove — usually that there is no effect or no difference.
Omitted Variable Bias: Omitted variable bias occurs when a factor affecting the outcome and correlated with your predictor is left out, so its influence is misattributed.
Ordinary Least Squares: Ordinary least squares fits a line by minimising the sum of squared residuals — the workhorse estimator of applied economics and finance.
Outlier: An outlier is an observation far from the rest of the data.
Overfitting: Overfitting is building a model that captures the noise in your sample rather than the signal, so it performs beautifully in-sample and fails on new data.
P-Value: The probability of seeing data as extreme as yours if nothing real were going on.
Partial Derivative: The rate of change of a multi-input function as you nudge just one input, holding the rest fixed.
Percentile: A percentile is the value below which a given share of observations falls — the 90th percentile has 90% of the data beneath it.
Poisson Distribution: The Poisson distribution gives the probability of a number of events in a fixed interval when they occur independently at a constant average rate.
Principal Component Analysis: PCA rewrites correlated variables as a smaller set of uncorrelated components ordered by how much variance they explain.
Probability: How likely something is, on a scale from 0 (never) to 1 (certain).
Probability Distribution: A description of how likely each possible value of a random quantity is — the bell curve is the famous one.
R-Squared: R-squared is the share of the variation in the outcome that a regression explains, from 0 to 1.
Random Variable: A quantity whose value is set by chance — a coin flip, tomorrow's return.
Regression: Fitting a line (or curve) through data to describe how one thing moves with another — the workhorse behind estimating a stock's beta.
Residual: A residual is the gap between an observed value and what the model predicted.
Sampling: Studying a manageable subset to learn about a whole population you can't measure directly.
Selection Bias: Selection bias is when the sample you analyse isn't representative of the population you want to describe, so the answer is wrong before any statistics are run.
Simpson's Paradox: Simpson's paradox is when a trend that appears in every subgroup reverses when the groups are combined.
Standard Error: How much a sample estimate — like an average — would wobble if you redrew the sample.
Statistical Power: Statistical power is the probability of detecting an effect that genuinely exists — one minus the Type II error rate.
Statistical Significance: Statistical significance means a result is unlikely under the null hypothesis, conventionally at a p-value below 0.05.
Student's t-Distribution: The t-distribution is a bell curve with fatter tails than the normal, used when the variance is estimated from a small sample.
Survivorship Bias: Survivorship bias is measuring only the things that lasted long enough to be measured.
t-Test: A t-test asks whether a mean differs from a hypothesised value, or whether two group means differ, when the true variance is unknown and must be estimated.
Taylor Series: Approximating a curvy function by a polynomial built from its slopes at a point.
Type I and Type II Errors: A Type I error rejects a true null hypothesis — a false positive.
Vector and Matrix: A vector is an ordered list of numbers (portfolio weights, asset returns); a matrix is a grid of them (a covariance matrix).

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