Statistical Inference and Probability

Understanding Inference and Probability

Statistical inference can feel like a dense technical subject, but John MacInnes turns it into a grounded conversation about how we draw conclusions from data. As the third volume in The SAGE Quantitative Research Kit, this ebook works both alongside the wider series and as a self-contained introduction to the logic behind probability, estimation, and hypothesis testing.

MacInnes avoids treating statistics as a collection of formulas to memorize. Instead, he helps readers see why inferential methods exist, what questions they answer, and how to interpret results in real research contexts. The focus is on reasoning clearly about uncertainty, sample variation, and the strength of evidence.

Core Statistical Ideas, Step by Step

The book moves carefully through the ideas that make quantitative research possible:

• Probability, randomness, and sampling distributions
• Null hypothesis significance testing, p-values, and confidence intervals
• Chi-square tests, t-tests, and Fisher’s exact test
• Regression, ANOVA, and multiple regression
• Power, effect size, and inverse probability
• The ASA principles for sound inference

Each chapter builds on earlier material, with appendices and worked examples that reinforce conceptual understanding. The author repeatedly connects statistical decisions to the logic of scientific argument, showing how inference can support or undermine causal claims.

From Samples to Regression and Beyond

Later chapters examine more advanced topics without losing the reader. Multiple regression, analysis of variance, and transformations are treated as extensions of the same inferential framework, while the discussion of Bayesian-style inverse probability offers a valuable alternative to conventional null hypothesis testing.

The final chapter brings the threads together with a practical checklist for sound inference, based on the American Statistical Association’s guidance. Researchers who work with surveys, experiments, observational data, or policy evaluations will find the material directly relevant to the challenges of drawing credible conclusions.

Why This Book Stands Out

Rather than presenting inference as a set of mechanical steps, MacInnes emphasizes judgment, interpretation, and the importance of research design. That makes the book especially useful for graduate students, early-career researchers, and anyone who needs to read or produce quantitative evidence with confidence.