In less than 100 pages, author Maroof provides a brief and highly selective overview of topics in statistics, psychometrics and research design. His style is informal and conversational. There are no statistical formulae and no mathematical proofs.
In Chapter 1, the author describes his approach to statistical analysis. He indicates that it is not his intention to provide the reader with a comprehensive coverage of statistics. Chapter 2 is a basic discussion of validity as applied to neuropsychological tests. Readers might find the first chapter in A Compendium of Neuropsychological Tests (Strauss, Sherman, & Spreen, 2006) to provide superior coverage of this topic.
I found Chapter 3 (Assumptions of Statistical Analyses) confusing. It appears that the author is discussing the statistical assumptions underlying the general linear model, which includes analysis of variance and ordinary least-squares regression. The author makes references to data and variables being “normally distributed.” However, these statistical assumptions apply to the residuals or errors, not to individual variables. Specifically, the assumptions are that the errors or residuals are independent, normally distributed, have a constant variance (homoscedasticity), and have a mean of zero at all values of x (linearity of the model; Berry, 1993).
Chapter 4 explores exploratory factor analysis (EFA). It would have been helpful had the author differentiated EFA from principal component analysis (PCA). He describes EFA as a “data reduction procedure.” Actually, it is probably more accurate to characterize PCA as the data reduction method. In contrast, the primary goal of EFA is to identify latent constructs, that is, understanding the structure of the correlations among the variables. EFA is based on the common factor model, that is, each test score in a battery of tests is a linear function of one or more common factors and one unique factor. Common factors are latent or unobserved factors. Conversely, PCA does not differentiate between common and unique variance. All of the observed variance is analyzed in PCA. Only the shared variances are analyzed in EFA. Although PCA and EFA can produce similar results, this is not always the case. Differences emerge when communalities are low (e.g., 0.40).
Chapter 5 briefly discusses selected issues in normative data in the neuropsychological examination. Readers wanting a more thorough treatment of this topic are referred to Smith, Ivnik, and Lucas (2008).
Chapters 6–8 provide brief overviews of analysis of covariance, regression, and binary logistic regression, respectively. These are important and useful statistical techniques in neuropsychological research. The author wisely urges caution in the use of stepwise variable selection techniques. Readers should be aware of newly developed statistical techniques that can assist the investigator in variable selection and model validation, for example, Bayesian model averaging, bootstrapping, and bagging and boosting (Harrell, 2001; Steyerberg, 2009).
Chapter 10 covers multivariate analysis of variance (MANOVA). The author notes the restrictive statistical assumptions of MANOVA (multivariate normality and homogeneity of covariance matrices) as well as the challenges in identifying which variables are important in differentiating the groups. He correctly points out that follow-up univariate analyses fail to account for the relationships among the set of variables. In addition, a statistically significant MANOVA does not protect against Type I errors if the investigator chooses to conduct follow-up univariate tests. Actually, the α level for each subsequent univariate test is less than the that for the MANOVA only when the MANOVA null hypothesis is “true” (Huberty & Morris, 1989). Given these constraints, binary logistic regression and its generalizations to multiple groups (i.e., ordinal logistic regression and multinomial logistic regression; Hardin & Hilbe, 2012) would seem to offer significant advantages over MANOVA/discriminant function analysis in exploring and explaining group differences (Harrell, 2001). For example, logistic regression does not require multivariate normality or homogeneity of covariance matrices and can handle a mixture of continuous, binary, and nominal variables. It is a straightforward process of simultaneously determining which variables are most important in differentiating the groups in logistic regression. Exponentiating the logistic regression coefficients produces easily interpretable odds ratios.
Chapter 10 concludes this book with a discussion of critically reading the scientific literature. Again, this is an important topic; however, I found this chapter too general to be helpful. I would recommend How to Read a Paper (Greenhalgh, 2010).
Maroof is to be applauded for taking on this ambitious project. However, in the end, I cannot recommend this book. In his conciseness, I found insufficient detail. In his informality and practicality, I was frequently confused. Readers wanting a brief, focused, and non-technical treatment of statistical topics may be better served by books by Good and Hardin (2012) and van Belle (2008) along with the Statistics Notes in the British Medical Journal: http://www-users.york.ac.uk/~mb55/pubs/pbstnote.htm.