Statistics (university) glossary
67 key terms from Statistics (university), A to Z. Each is explained in one plain sentence and links to its free lesson.
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A
- Addition ruleProbability
- For two events, P(A or B) = P(A) + P(B) - P(A and B).
B
- Bayes' theoremProbability
- Bayes' theorem turns P(B given A) into P(A given B): P(A given B) = P(B given A) x P(A) / P(B).
- Binomial distributionRandom variables and discrete distributions
- The binomial distribution counts successes in n independent trials, each with the same success chance p.
C
- Central limit theoremSampling and estimation
- The central limit theorem says that sample means from almost any population are close to normal when n is large enough (often 30 or more).
- Chi-square goodness of fitComparing categories and many groups
- This test asks whether observed counts match the counts a model predicts.
- Chi-square test of independenceComparing categories and many groups
- This test checks whether two categorical variables are related.
- Conditional probabilityProbability
- Conditional probability is the chance of A once you know B happened: P(A given B) = P(A and B) / P(B).
- Confidence interval for a meanSampling and estimation
- A confidence interval is a range likely to contain the true parameter.
- Confidence interval for a proportionSampling and estimation
- For a sample proportion p-hat from n trials, the standard error is the square root of p-hat(1 - p-hat) / n.
- Correlation and causationCorrelation and regression
- Correlation means two variables move together.
- Correlation coefficientCorrelation and regression
- The correlation r measures the strength and direction of a straight-line link between two numerical variables.
- Cumulative distribution functionRandom variables and discrete distributions
- The cumulative distribution function (CDF) gives P(X <= x), the chance the variable is at most x.
E
- Effect sizeComparing categories and many groups
- Effect size measures how big a difference is, not just whether it is detectable.
- Expected countsComparing categories and many groups
- In a two-way table, the expected count for a cell is (row total x column total) / grand total.
- Expected valueRandom variables and discrete distributions
- The expected value E(X) is the long-run average of a random variable.
- Exponential distributionContinuous distributions and the normal curve
- The exponential distribution models the waiting time until the next event when events occur at rate lambda.
F
- F statisticComparing categories and many groups
- The F statistic is the mean square between groups divided by the mean square within groups.
G
- Geometric distributionRandom variables and discrete distributions
- The geometric distribution models the number of trials until the first success, when each trial has success chance p.
I
- Independent eventsProbability
- Events are independent if one happening does not change the chance of the other.
- Inference for the slopeCorrelation and regression
- To test whether x really predicts y, test H0: true slope = 0.
L
- Law of large numbersSampling and estimation
- As a sample gets bigger, the sample mean gets closer to the true mean.
- Law of total probabilityProbability
- If events B1, B2, ... split all outcomes into separate cases, then P(A) is the sum of P(A given Bi) x P(Bi).
- Least squares regression lineCorrelation and regression
- The least squares line y-hat = b0 + b1 x is the straight line that makes the sum of squared vertical gaps to the points as small as possible.
- Linear rules for mean and varianceRandom variables and discrete distributions
- For constants a and b: E(aX + b) = a E(X) + b, and Var(aX + b) = a squared x Var(X).
M
- MeanDescribing data
- The mean is the sum of all values divided by how many there are.
- Median and modeDescribing data
- The median is the middle value when data is sorted.
- Multiple regressionCorrelation and regression
- Multiple regression uses several predictors: y-hat = b0 + b1 x1 + b2 x2 + ...
- Mutually exclusive eventsProbability
- Two events are mutually exclusive if they cannot both happen at once.
N
- Normal approximation to the binomialContinuous distributions and the normal curve
- A binomial with large n can be approximated by a normal with mean np and SD square root of np(1-p).
- Normal distributionContinuous distributions and the normal curve
- The normal distribution is the symmetric bell curve, set by its mean mu and standard deviation sigma.
- Normal probabilities and percentilesContinuous distributions and the normal curve
- To find a probability, convert to z and read the area.
- Null and alternative hypothesesHypothesis testing
- The null hypothesis H0 is the default claim of no effect or no difference.
O
- One-sample t testHypothesis testing
- A one-sample t test compares a sample mean with a claimed value when sigma is unknown.
- One-way ANOVAComparing categories and many groups
- Analysis of variance (ANOVA) compares the means of three or more groups at once.
- OutliersDescribing data
- An outlier is a value far from the rest.
P
- p-valueHypothesis testing
- The p-value is the probability of getting data at least as extreme as yours if the null hypothesis were true.
- Paired t testHypothesis testing
- A paired t test compares two measurements on the same subjects, such as before and after.
- Permutations and combinationsProbability
- A permutation counts arrangements where order matters: nPr = n! / (n - r)!.
- Point estimate and biasSampling and estimation
- A point estimate is a single number guessing a parameter, such as the sample mean for the population mean.
- Poisson distributionRandom variables and discrete distributions
- The Poisson distribution counts events in a fixed time or space when they happen at a steady average rate lambda and independently.
- Population and sampleSampling and estimation
- A population is the whole group you want to know about.
- Post-hoc comparisonsComparing categories and many groups
- After a significant ANOVA, a post-hoc test such as Tukey's finds which pairs of groups differ.
- Power of a testHypothesis testing
- Power is the probability of rejecting the null when a real effect exists: power = 1 - beta.
- Probability density functionContinuous distributions and the normal curve
- A probability density function (PDF) is a curve for a continuous variable.
Q
- Quartiles and IQRDescribing data
- Quartiles cut sorted data into four equal groups.
R
- R-squaredCorrelation and regression
- R-squared is the share of the variation in y explained by the model: 1 - (residual sum of squares / total sum of squares).
- Random variableRandom variables and discrete distributions
- A random variable is a number that depends on chance.
- Rank-based testsComparing categories and many groups
- Rank-based (nonparametric) tests replace the data with ranks, so they do not need a normal shape.
- Regression assumptionsCorrelation and regression
- Linear regression assumes a straight-line relationship, independent errors, errors with constant spread, and roughly normal errors.
- ResidualsCorrelation and regression
- A residual is observed y minus predicted y.
S
- Sample space and eventsProbability
- The sample space is the list of every possible outcome.
- Sample varianceDescribing data
- Sample variance divides the sum of squared gaps by n minus 1, not n.
- Sampling distribution and standard errorSampling and estimation
- A sampling distribution shows how a statistic, such as the sample mean, varies from sample to sample.
- Significance level and decisionHypothesis testing
- The significance level alpha is the cut-off you set before the test, often 0.05.
- SkewnessDescribing data
- Skewness describes lopsided data.
- Slope and interceptCorrelation and regression
- The slope is the predicted change in y for each one-unit increase in x.
- Standard deviationDescribing data
- The standard deviation measures how far values typically sit from the mean.
- Standard normal and z-scoresContinuous distributions and the normal curve
- The standard normal has mean 0 and SD 1.
- Sums of normal variablesContinuous distributions and the normal curve
- If X and Y are independent normals, X + Y is also normal.
T
- t distributionSampling and estimation
- When sigma is unknown, replace it by the sample SD s and use the t distribution instead of the normal.
- Test for a proportionHypothesis testing
- A one-proportion z test checks a claimed share p0.
- Two-sample t testHypothesis testing
- A two-sample t test compares the means of two independent groups.
- Type I and Type II errorsHypothesis testing
- A Type I error is rejecting a true null (a false alarm).
- Types of dataDescribing data
- Data is either categorical (labels, like eye colour) or numerical (amounts, like height).
U
- Uniform distributionContinuous distributions and the normal curve
- A uniform distribution on the range a to b makes every stretch of equal width equally likely.
V
- Variance of a random variableRandom variables and discrete distributions
- The variance Var(X) measures spread around the expected value: Var(X) = E(X squared) - (E(X))^2.
Z
- z-scoreDescribing data
- A z-score says how many standard deviations a value is from the mean: (value minus mean) divided by standard deviation.