Statistics for College Students and Researchers

Statistics for College Students and Researchers, Second Edition - Revised 2026 is a practical and conceptually rigorous introduction to statistics built around a central principle: statistical calculation must follow the logic of research, not replace it.

Written for college students, graduate students, researchers, and independent learners, the book develops statistical reasoning from elementary foundations through increasingly complex experimental designs. The mathematics required is deliberately kept accessible. Formulas are introduced only after the ideas they summarize have been explained, allowing the reader to understand what a statistical procedure is doing before carrying out the calculation.

The book begins with the foundations of statistical thought: data, populations and samples, scales of measurement, measures of central tendency, variance, standard deviation, the normal distribution, z-scores, sampling distributions, and standard error. It then develops the logic of statistical inference, including null hypotheses, significance levels, p values, Type I and Type II errors, statistical power, and degrees of freedom.

Detailed chapters guide the reader through independent-samples and paired-samples t tests, confidence intervals, effect sizes, one-way analysis of variance, factorial ANOVA, main effects and interactions, repeated-measures ANOVA, and mixed or split-plot designs. Particular emphasis is placed on identifying the correct experimental structure and selecting the appropriate error term-issues that become especially important in complex research designs.

Worked examples are developed step by step from actual data. Calculations are accompanied by interpretation so that numerical results remain connected to the scientific question. The revised edition carefully distinguishes statistical significance from practical importance and emphasizes that a p value is not the probability that a hypothesis is true.

A substantial section on statistical design helps readers determine whether observations are independent, paired, repeated, or mixed; identify factors and levels; distinguish experimental from naturally occurring variables; and recognize the experimental unit. Practice cases require the reader to identify the appropriate analysis before choosing a formula.

The book also contains extensive calculation exercises, complete worked analyses, answer explanations, statistical tables, reporting templates, a concise formula reference, a glossary, and a quick answer key.

Features include:

The distinctive aim of the book is not to train readers merely to substitute numbers into equations. It is to teach them to recognize the structure of a scientific problem, understand the statistical model appropriate to that structure, perform the necessary calculations, and interpret the result responsibly.

Michael M. Nikoletseas, Ph.D. draws on decades of university teaching and scientific research in presenting statistics as part of the broader process of scientific reasoning. His approach reflects a lifelong concern with how evidence is obtained, measured, analyzed, and connected to defensible conclusions.

Revised 2026.