Foundations & hypothesis testing
Population and sample
statistical population · sample
A population is the entire group of units you want to make a claim about — all patients, every product from a line.
Mean, median and mode
measures of central tendency · average
The mean, median and mode are measures of central tendency — a single number summarizing where the data lie.
Standard deviation and variance
SD · spread
Variance is the average squared deviation of values from the mean; the standard deviation (SD) is its square root and has the same units as the data.
Normal distribution
Gaussian distribution · bell curve
The normal (Gaussian) distribution is a symmetric bell-shaped distribution described by its mean and standard deviation.
p-value
probability value · significance probability
The p-value is the probability of obtaining a result at least as extreme as the one observed if the null hypothesis (e.g. "the groups do not differ") were true.
Confidence interval
CI · confidence limits
A confidence interval is a range of values that, with a stated confidence (most often 95 %), covers the true value of a population parameter — a…
Significance level and Type I / Type II errors
alpha · beta · false positive
The significance level α is the maximum risk of a Type I error — rejecting a null hypothesis that is actually true (a false alarm).
Effect size
Cohen's d · eta squared · R squared
Effect size expresses how large a difference is or how strong an association is — independently of sample size.
Statistical power and sample size
power analysis · sample size calculation
Statistical power is the probability that a test detects an effect that really exists (1 − β).
Statistical tests
t-test
Student's t-test · paired t-test · two-sample t-test
The t-test compares means: the one-sample version compares a mean with a fixed value, the two-sample version the means of two independent groups…
ANOVA (analysis of variance)
one-way ANOVA · factorial ANOVA · repeated-measures ANOVA
ANOVA (analysis of variance) tests whether the means of three or more groups differ.
Post-hoc tests
multiple comparisons · Tukey's test · Scheffé's test · Bonferroni correction
Post-hoc tests follow a significant ANOVA and compare groups pairwise to show which ones really differ.
Chi-square test
χ² test · test of independence · contingency table
The chi-square test works with category counts.
Nonparametric tests
Mann–Whitney U test · Wilcoxon signed-rank test · Kruskal–Wallis ANOVA · Friedman test
Nonparametric tests do not assume a normal distribution — they work with the ranks of values rather than the values themselves.
Normality test
Shapiro–Wilk test · Kolmogorov–Smirnov test · Lilliefors test
A normality test checks whether data come from a normal distribution — an assumption of the t-test, ANOVA, regression and capability indices.
Correlation
Pearson correlation coefficient · Spearman correlation · correlation matrix
Correlation measures the strength and direction of a linear relationship between two quantities with a number from −1 to 1.
Regression & models
Linear regression
multiple regression · least squares · regression model
Linear regression describes how a dependent variable (yield, price, consumption) depends on one or more explanatory variables using a line or plane estimated by least squares.
Logistic regression
logit model · odds ratio · binary classification
Logistic regression models the probability of a binary outcome — a patient responds to treatment or not, a customer churns or stays — as a function of explanatory variables.
Nonlinear regression
nonlinear estimation · curve fitting · Levenberg–Marquardt algorithm
Nonlinear regression fits data with a model that is nonlinear in its parameters — exponential growth, a logistic curve, Michaelis–Menten kinetics, dose–response.
Generalized linear models (GLM)
GLZ · general linear models · Poisson regression
Generalized linear models extend linear regression to outcomes that are not normally distributed: binary (logistic regression), counts (Poisson…
Time series and forecasting
ARIMA · exponential smoothing · seasonal decomposition
A time series is a sequence of values measured over time — monthly sales, daily temperature, energy consumption.
Survival analysis
Kaplan–Meier estimate · Cox regression · censored data
Survival analysis models time to an event — death, relapse, machine failure, customer churn — and can handle censored observations where the event did not occur during follow-up.
Multivariate methods
Principal component analysis (PCA)
PCA · dimensionality reduction · principal components
Principal component analysis (PCA) condenses many correlated variables into a few new uncorrelated components that capture as much of the original variability as possible.
Factor analysis
latent factors · Varimax rotation · exploratory factor analysis
Factor analysis looks for a small number of hidden (latent) factors that explain the correlations among many measured variables — e.g. items of a…
Cluster analysis
clustering · k-means · hierarchical clustering · segmentation
Cluster analysis divides observations into groups (clusters) so that units within a cluster are as similar as possible and clusters differ from each…
Discriminant analysis
LDA · classification functions · Fisher's discriminant
Discriminant analysis finds combinations of variables that best separate groups known in advance — healthy from ill, good parts from rejects, three…
Quality control & SPC
Control charts (SPC)
statistical process control · Shewhart charts · X-bar and R chart
A control chart is the basic tool of statistical process control (SPC): it plots measurements over time with a centre line and ±3σ control limits…
Process capability (Cp, Cpk)
capability indices · Pp and Ppk · capability analysis
Capability indices compare process variability with the customer's tolerance limits.
Design of experiments (DOE)
DOE · factorial experiment · Taguchi designs · response surface methodology
Design of experiments (DOE) is a systematic way to find out, with a minimum of runs, which factors (temperature, pressure, material) affect a result and how to set them.
Six Sigma
DMAIC · sigma level · DPMO
Six Sigma is a data- and statistics-driven methodology for process improvement.
Measurement system analysis (Gauge R&R)
MSA · repeatability and reproducibility · Gage R&R
Measurement system analysis (MSA) determines how much of the observed variability is caused by the measurement itself.
Pareto chart
Pareto analysis · 80/20 rule · ABC analysis
A Pareto chart is a bar chart of causes or defect categories sorted from most to least frequent, with a cumulative-share curve.
Data mining & machine learning
Decision trees
classification and regression trees · C&RT · CHAID · CART
A decision tree splits data by a sequence of simple rules ("age > 45 and income < 30 thousand") into ever more homogeneous groups until the leaves…
Random forests and boosting
random forest · boosted trees · gradient boosting · ensemble methods
Random forests and boosting are ensemble methods that combine hundreds of decision trees into one more accurate model.
Neural networks
artificial neural networks · MLP · multilayer perceptron · SANN
An artificial neural network is a model built from layers of connected "neurons" that learns from data to approximate even very complex nonlinear…
Cross-validation
k-fold cross-validation · training and test data · holdout
Cross-validation estimates how well a model will perform on new data.
ROC curve and AUC
sensitivity and specificity · area under the curve · classification threshold
The ROC curve shows how a classifier's sensitivity (share of correctly caught positives) and false-positive rate change as the decision threshold moves.
Overfitting
overfitted model · generalization · regularization
Overfitting happens when a model learns not only the real relationships but also the random noise of the training data — it looks great on them and fails on new data.
Model scoring and deployment
scoring · deployment · PMML · predictive model in production
Scoring is applying a trained model to new data — assigning a prediction or probability to every customer, sample or product.
Text mining
text analytics · natural language processing · document mining
Text mining converts unstructured text — complaints, service notes, open survey answers, reports — into structured data that statistics can work with.
Data & visualisation
Box plot
boxplot · box-and-whisker plot · quartile plot
A box plot shows a distribution with five numbers: the box spans from the lower to the upper quartile (the middle 50 % of values), the line inside is…
Histogram
frequency distribution · frequency bar chart
A histogram shows the distribution of a continuous variable: values are divided into intervals (bins) and the height of each bar shows how many observations fall into it.
Outliers
extreme values · influential points · anomalies
An outlier is an observation that differs conspicuously from the rest — a measurement or entry error, a different population, or a genuine rare event.
Missing data
missing values · imputation · non-response
Missing data are gaps in the dataset — an unmeasured sample, an unanswered question, a sensor outage.
Updated: September 2026.