13 Essential Statistical Analysis Methods Every Researcher Should Know

Descriptive Statistics

Descriptive statistics organize and summarize data using charts or mathematical methods, describing distribution, numeric features, and relationships among variables. It includes three parts: measures of central tendency, measures of dispersion, and correlation analysis.

Central tendency analysis : uses mean, median, mode, etc., to indicate where data cluster (e.g., average test scores, skewness).

Dispersion analysis : uses range, interquartile range, variance, standard deviation, etc., to study data spread (e.g., comparing score dispersion between two classes).

Correlation analysis : examines statistical relationships between variables, including simple and multiple correlations, positive/negative associations, and correlation coefficients. Correlation does not address causality. With a correlation coefficient, one can estimate one variable from another via regression.

Inferential Statistics

Inferential statistics use sample data to test or reject hypotheses about populations. For example, comparing intelligence test scores of college versus high‑school graduates can reveal significant differences at a 0.01 level.

Normality tests (e.g., K‑test, P‑P plot, Q‑Q plot, W‑test, moment method) are performed first because many methods assume normal distribution.

Hypothesis Testing

Parametric Tests

Parametric tests assume known population distribution (usually normal) and test parameters such as mean, proportion, variance, or correlation coefficient.

U test: used when sample size is large and data are normally distributed.

T test: used when sample size is small and data follow a t‑distribution. One‑sample t test: compares sample mean to a known population mean. Paired‑sample t test: compares two related samples when the population mean is unknown. Independent‑samples t test: compares two unrelated groups.

Non‑Parametric Tests

Non‑parametric tests do not require knowledge of the population distribution and often test general assumptions (e.g., identical distributions, normality).

Applicable to ordinal data or continuous data with unknown or non‑normal distribution, or very small sample sizes.

Chi‑square test

Rank‑sum test

Binomial test

Runs test

K‑test

Reliability Analysis

Reliability (consistency of repeated measurements) is expressed by correlation coefficients and divided into stability, equivalence, and internal consistency coefficients. Main methods include test‑retest, parallel‑forms, split‑half, and Cronbach’s α.

Test‑retest reliability: administer the same questionnaire to the same respondents after a time interval and compute the correlation.

Parallel‑forms reliability: give two equivalent versions of a questionnaire simultaneously and compute the correlation.

Split‑half reliability: split the questionnaire into two halves and correlate the scores.

Cronbach’s α: calculates internal consistency; values above 0.8 are ideal, 0.7‑0.8 acceptable, below 0.6 require revision.

Contingency Table Analysis

Contingency tables display frequencies for two or more categorical variables, allowing assessment of association via chi‑square or likelihood‑ratio tests.

When sample size is small, Fisher’s exact test is used for 2×2 tables.

Correlation Analysis

Investigates whether variables are related and to what degree.

Simple correlation: one independent and one dependent variable.

Multiple correlation: two or more independent variables.

Partial correlation: correlation between two variables while controlling for others.

Analysis of Variance (ANOVA)

Used when samples are independent, drawn from normal populations with equal variances.

One‑factor ANOVA

Two‑factor ANOVA with interaction

Two‑factor ANOVA without interaction

ANCOVA (analysis of covariance)

Regression Analysis

Linear Regression

Simple linear regression: one predictor X and one response Y (both continuous, Y normal).

Multiple linear regression: several predictors.

Model diagnostics include residual tests, influence point detection (standardized residuals, Mahalanobis distance), and multicollinearity checks (tolerance, VIF, condition index).

Logistic Regression

Used when the response variable is categorical; no distributional assumption on Y.

Models can be conditional or unconditional depending on whether conditional probabilities are used.

Other regression types: nonlinear, ordinal, probit, weighted regression.

Cluster Analysis

Cluster analysis groups objects or variables based on similarity without pre‑defined categories.

Methods include hierarchical clustering, k‑means, k‑centroids, and various algorithmic approaches used in software such as SPSS and SAS.

Q‑type clustering: clusters samples.

R‑type clustering: clusters variables.

Methods: hierarchical, stepwise, k‑means, etc.

Discriminant Analysis

Discriminant analysis builds functions to classify new cases into known groups, minimizing misclassification.

Fisher discriminant: distance‑based (two‑class) or probability‑based (multi‑class).

Bayes discriminant: incorporates probability distributions.

Principal Component Analysis (PCA)

PCA transforms correlated variables into a set of uncorrelated principal components, preserving most of the variance.

It reduces dimensionality while retaining essential information.

Limitations: need sufficient cumulative contribution and interpretable components.

Factor Analysis

Factor analysis seeks latent factors that explain correlations among observed variables, differing from PCA by focusing on underlying structure.

Reduces variables and groups them based on shared variance.

Time‑Series Analysis

Time‑series analysis studies ordered observations to model trends, seasonality, cycles, and irregular fluctuations.

Methods include moving averages, exponential smoothing, ARIMA, ARIMAX, ARCH, etc., for description, analysis, forecasting, and control.

Survival Analysis

Survival analysis examines time‑to‑event data, describing distributions, comparing groups, assessing risk factors, and building models such as Cox proportional hazards.

Descriptive methods: Kaplan‑Meier, median survival.

Non‑parametric tests: log‑rank, Peto.

Semi‑parametric regression: Cox model.

Parametric models: exponential, Weibull, etc.

Canonical Correlation Analysis

Analyzes relationships between two sets of variables, extending correlation to multivariate contexts.

ROC Analysis

Receiver Operating Characteristic (ROC) curves plot true‑positive rate versus false‑positive rate for various thresholds, aiding in diagnostic test evaluation and optimal cut‑point selection.

Other Methods

Multiple response analysis, distance discrimination, projective methods, correspondence analysis, decision trees, neural networks, system equations, Monte Carlo simulation, and more.