Statistics Glossary

How to Use This Glossary

90 terms in plain language, each linked to the Stat Dojo page that explains it with a worked example. For formulas, see the formula sheet.

A

Alpha (α)

The significance level: the chance you accept of rejecting a true null hypothesis. Usually 0.05.See P-Values and Error Types

Alternative hypothesis (H₁)

The claim you are looking for evidence of, such as a difference between means.See P-Values and Error Types

Anderson-Darling test

A test of whether data follow a specified distribution, most often the normal. It is sensitive to differences in the tails.See Normality Tests

ANOVA

Analysis of variance. A test that compares the means of three or more groups by comparing the variation between groups with the variation within them.See One-Way ANOVA

Attribute data

Data that are categories or counts, such as pass/fail or defects per unit. Compare variable data.See Data Types and Scales

Average run length (ARL)

The average number of points plotted on a control chart before it signals. For a stable process with 3-sigma limits it is about 370.See Control Chart Theory

B

B10 life

The age by which 10% of units are expected to have failed.See Reliability and Weibull

Bartlett’s test

A test that variances are equal across groups. Powerful for normal data and unreliable otherwise.See Tests for Variances

Beta (β)

The probability of a Type II error: missing a real effect. Power is 1 − β.See Sample Size and Power

Bias

A systematic error that pushes results in one direction. A bigger sample does not remove it.See Sampling and the CLT

Binomial distribution

The distribution of the number of defective items in a sample of n, when each item is independently defective with the same probability.See Distributions

Box plot

A graph showing the median, the middle 50% of the data as a box, whiskers, and outliers.See Graphical Analysis

C

Censored data

Life data where some units had not failed when observation ended. Their times are known only to be at least as long as the time observed.See Reliability and Weibull

Central limit theorem

Averages of random samples tend toward a bell shape as the sample size grows, whatever the shape of the individual values.See Sampling and the CLT

Chi-square test

A test based on the chi-square distribution, used for association between categories, goodness of fit, and one variance.See Chi-Square Tests

Coefficient of determination (R²)

The share of the variation in the response explained by the model.See Simple Regression

Coefficient of variation

The standard deviation as a percentage of the mean. It compares spread between things with different averages.See Descriptive Statistics

Common-cause variation

The steady background variation built into a process. A stable process has only common causes.See Control Chart Theory

Confidence interval

A range of plausible values for a population quantity, built so that a stated share (such as 95%) of intervals from repeated samples would contain the true value.See Confidence Intervals

Confidence level

The long-run proportion of intervals that capture the true value, such as 95%.See Confidence Intervals

Continuous data

Measurements that can take any value in a range, such as weight or time.See Data Types and Scales

Control chart

A time-ordered plot of a statistic with a center line and limits that show what common-cause variation looks like.See Control Chart Theory

Control limits

Lines at three standard errors from the center line of a control chart. They describe the process, not the customer requirement.See Control Chart Theory

Correlation coefficient (r)

A number from −1 to +1 measuring the strength and direction of a linear relationship.See Correlation

Cp

Specification width divided by six within-sigma. Potential capability, ignoring centering.See Capability Statistics

Cpk

Capability that accounts for centering: the distance from the mean to the nearer limit, in units of three within-sigma.See Capability Statistics

D

Degrees of freedom (df)

The number of independent pieces of information available to estimate variation. For a sample standard deviation it is n − 1.See t-Tests

Descriptive statistics

Numbers that summarize data: center, spread, and shape.See Descriptive Statistics

Discrete data

Counts that take only certain values, such as 0, 1, 2 defects.See Data Types and Scales

Distribution

A description of how likely each possible value is.See Distributions

E

Effect (DOE)

The change in the response when a factor moves from its low to its high level.See Analyzing Designed Experiments

Expected value

The long-run average of a random quantity.See Distributions

F

F test

A test based on a ratio of variances, used in ANOVA, regression, and for comparing two variances.See One-Way ANOVA, Tests for Variances

Factor

An input deliberately varied in an experiment.See Analyzing Designed Experiments

Factorial design

An experiment that runs every combination of the factor levels.See Analyzing Designed Experiments

H

Histogram

A bar chart of how many values fall in each range.See Graphical Analysis

Hypothesis test

A procedure for deciding whether data provide enough evidence against a null hypothesis.See P-Values and Error Types

I

Independence

Observations are independent when knowing one tells you nothing about another.See Simple Regression

Interaction

The effect of one factor depends on the level of another. Lines on an interaction plot are not parallel.See Two-Way ANOVA, Analyzing Designed Experiments

Interquartile range (IQR)

The distance from the first to the third quartile; the spread of the middle half of the data.See Descriptive Statistics

K

Kruskal-Wallis test

A rank-based alternative to one-way ANOVA.See Nonparametric Tests

L

Levene’s test

A robust test that variances are equal across groups.See Tests for Variances

M

Main effect

The average effect of one factor on the response, across the levels of the other factors.See Analyzing Designed Experiments

Mann-Whitney test

A rank-based alternative to the two-sample t-test.See Nonparametric Tests

Mean

The sum of the values divided by their number.See Descriptive Statistics

Median

The middle value of the sorted data.See Descriptive Statistics

Mode

The most frequent value.See Descriptive Statistics

Moving range

The absolute difference between successive individual readings; used to estimate short-term variation.See Control Chart Theory

Multicollinearity

Predictors in a regression that are strongly related to each other, which makes coefficients unstable. Measured by VIF.See Multiple Regression

N

Nominal data

Categories with no order, such as supplier or defect type.See Data Types and Scales

Nonparametric test

A test that does not assume a specific distribution, often based on ranks.See Nonparametric Tests

Normal distribution

The symmetric bell-shaped distribution described by its mean and standard deviation.See Distributions

Null hypothesis (H₀)

The default claim of no effect or no difference that a test tries to find evidence against.See P-Values and Error Types

O

Ordinal data

Categories with a natural order but unequal gaps, such as a rating from 1 to 5.See Data Types and Scales

Outlier

A value far from the rest of the data. Investigate before removing.See Graphical Analysis

P

P-value

The probability of results at least as extreme as those observed, if the null hypothesis were true.See P-Values and Error Types

Paired data

Two measurements on the same item, such as before and after.See t-Tests

Pareto chart

A bar chart of categories sorted by size with a cumulative line, used to find the vital few.See Graphical Analysis

Poisson distribution

The distribution of the number of defects or events in a fixed area or time at a steady average rate.See Distributions

Population

The entire set of items or outcomes you want to learn about.See Sampling and the CLT

Power

The probability of detecting a real effect of a given size. Equals 1 − β.See Sample Size and Power

Ppk

Capability using the overall (long-term) standard deviation. Shows what the process actually delivered.See Capability Statistics

Prediction interval

A range likely to contain a single future observation. Wider than a confidence interval for the mean.See Simple Regression

Probability plot

A plot that straightens a distribution so you can see how well data fit it. Points near the line mean a good fit.See Normality Tests

Q

Quartile

One of the three values that divide sorted data into four equal parts.See Descriptive Statistics

R

Random sample

A sample in which every item has a known chance of selection.See Sampling and the CLT

Range

The maximum minus the minimum.See Descriptive Statistics

Rational subgroup

A small sample collected under conditions that make variation within it only common-cause.See Control Chart Theory

Regression

A method that fits an equation relating a response to one or more predictors.See Simple Regression, Multiple Regression

Reliability

The probability that a unit performs its function for a stated time under stated conditions.See Reliability and Weibull

Replication

Repeating the same experimental conditions to estimate pure error.See Analyzing Designed Experiments

Residual

The difference between an observed value and the value the model predicts.See Post-Hoc Comparisons

Run chart

A plot of values in time order with a median line, used to spot trends and shifts.See Graphical Analysis

S

Sample

The part of the population you actually measure.See Sampling and the CLT

Shape parameter (Weibull)

The Weibull parameter that sets how the failure rate changes with age.See Reliability and Weibull

Significance level

See alpha.See P-Values and Error Types

Skewness

A measure of lopsidedness. Positive skew means a long tail to the right.See Descriptive Statistics

Special-cause variation

Variation from a specific, identifiable source that is not part of the normal process.See Control Chart Theory

Standard deviation

The typical distance of values from the mean, in the units of the data.See Descriptive Statistics

Standard error

The standard deviation of a statistic such as the sample mean. For the mean it is s divided by the square root of n.See Sampling and the CLT

Stratified sampling

Taking random samples within groups, such as shifts or machines.See Sampling and the CLT

T

t test

A test on means that uses the t distribution because the standard deviation is estimated.See t-Tests

Tukey comparison

A multiple comparison method that controls the overall error rate when comparing all pairs of means.See Post-Hoc Comparisons

Type I error

Rejecting a true null hypothesis (a false alarm). Its probability is alpha.See P-Values and Error Types

Type II error

Failing to reject a false null hypothesis (a miss). Its probability is beta.See P-Values and Error Types

V

Variable data

Measurements, as opposed to categories or counts.See Data Types and Scales

Variance

The average squared deviation from the mean. The standard deviation squared.See Descriptive Statistics

Variance inflation factor (VIF)

A measure of how much a predictor’s variance is inflated by correlation with the other predictors.See Multiple Regression

W

Weibull distribution

A flexible life distribution described by a shape and a scale parameter.See Reliability and Weibull

Z

z score

The number of standard deviations a value lies from the mean.See Distributions

Related Pages and Tools

Statistics Glossary: Frequently Asked Questions

Sources and Further Reading