# Advanced Quantitative Data Analysis

**Cramer, Duncan
Open University Press, Buckingham
2003
0335200591**

Texts that try to cover several advanced quantitative data analysis techniques are problematic. Quite a high level of theoretical knowledge is required to fully understand the principles behind the more advanced statistical techniques. At the same time, with the now near universal use of computer-based statistical packages for quantitative data analysis, no little skill is needed to interpret the often copious and complex printouts that these packages generate. Yet often the researcher or student has neither high levels of skill, nor an intrinsic interest in these areas. As a consequence the majority of the texts on advanced quantitative analysis are too complex and difficult for many of those attempting to learn about the subject. Cramer's text attempts to fill this gap.

There have been previous attempts to balance the need to explain theoretical principles and understand data printouts with the need for simplicity and economy. One of the better examples of this balancing act is Tabachnick and Fidell's Using Multivariate Statistics. However, while this is an admirable book it is still quite dense when discussing the principles of the techniques described, while comparatively short on detail when discussing the use and interpretation of statistical packages. As a consequence I have found that students and less experienced researchers have struggled to get to grips with this book. More recently we have seen the publication of Field's excellent text Discovering Statistics Using SPSS for Windows. As the title suggests however this book's focus is orientated towards what specifically SPSS has to offer the analyst. Now we come to Cramer's work, which tries to bring a more even balance between the need for theoretical knowledge with the need to be able to read and understand computer printouts.

The book is laid out into sections, each covering a different aspect of data analysis. Part 1 looks at ways of grouping variables, normally by reducing their number, using factor analysis, linear structural relations, and cluster analysis. In Part 2 multiple regression is used to show how to best explain variance within a quantitative dependent variable via a set of independent variables. Here Cramer concentrates on two popular multiple regression techniques, stepwise and hierarchical model building. Part 3 looks at ways of sequencing multivariate relationships using path analysis via regression and structural equation modelling, while in part 4 Cramer explains how binary logistic regression can be used to predict a dichotomous response variable from a set of influencing variables. In part 5 Cramer looks at analysing differences in group means through the use of ANOVA and ANCOVA, while in part 6 he shows how to use of discriminant analysis to investigate independent variable mean differences between groups within a dependent variable. In the final part Cramer explains how to conduct multivariate analysis of frequency tables using log-linear analysis.

Within the sections there are separate chapters where individual analytical techniques are described. Each section starts with a brief discussion on the technique to be used; what it does and how it does it. This is normally followed by a discussion on the data set to be used and how for example variables might affect each other. Next there are instructions for running the test on the statistical package, and finally a discussion on how to interpret relevant sections of the output file. For the most part the examples are worked through via SPSS, although the more specialist LISREL programme is occasionally used. At this point I think it is worth saying that the less user-friendly LISREL programme may prove quite difficult for inexperienced users to get to grips with. Throughout, the data used for analysis are fictitious. The data and variables are displayed in the text and the reader has to input it into the relevant statistical package. The data sets used are small, and for some tests the reader is directed to multiply the data in order to produce statistically significant results. The processes for doing the tests and analysing the results are clearly explained, with a good use of visual models where appropriate.

However, I would question the use of manufactured data sets which, for me, problematic. I would prefer to see a 'real life' data set included, as in my experience students prefer to use information that they believe comes from an real source. By inventing numbers there is a risk that the student will not engage with the analysis as they might regard the results as meaningless. Using real life data sets creates at least the illusion that one is studying the real world. I also feel that while using nice clean unproblematic data will make explaining statistical techniques and models easier, it does not help the reader understand and deal with the types of anomalies that occur with real data. Data screening is an important part of the analytic process, especially with parametric tests. I feel this aspect of data analysis is overlooked here. However, this is a minor complaint when compared to the positive aspects of this book.

Overall there is a good breakdown of methods and analysis. Before any analysis is done, the point of each test is carefully explained, and the data set is broken down in easily understandable components. The descriptions and analysis of the tests are sufficiently in-depth that the reader gets a genuine feel for how and why the methods work. However, the technical information is sufficiently simplified so as not to put non-statisticians off. Even with the more complex statistical techniques the weight of detail never becomes too daunting or overwhelming. Furthermore, the use of the same data set for several tests helps the reader get an understanding of how different statistical techniques can be used to bring out different aspects and meanings of the data.

Cramer's pedigree in writing texts on data analysis is impressive. His books on more basic quantitative analysis are very well written, easy to understand, and more than adequately cover the basics. They have aided many researchers into getting to grips with the subject, and have helped many reluctant social science students through their data analysis and quantitative methods courses. The question is whether this style and simplicity can be transported into explaining more advanced analytical techniques? My own view is that Cramer has succeeded in producing a very readable book on a traditionally difficult subject. There are faults with this book, but they are greatly outweighed by its strengths. Overall, I thought the book well up to Cramer's usual high standards, and I would have no problems recommending it to researchers, students of social statistics, and lecturers.

#### References

FIELD, A. 2000. Discovering Statistics Using SPSS for Windows. London: Sage.TABACHNICK, B.G. and Fidell, L.S. 2000. Using Multivariate Statistics. Fourth Edition. New York: Allyn & Bacon.

**Stephen Brindle**

University of Aberdeen