You are here

Elementary Statistics: A Step by Step Approach

Allan G. Bluman
Publication Date: 
Number of Pages: 
[Reviewed by
Martin Feuerman
, on

In the preface, the author of this popular text (now in its 6th edition) states that this book is meant to be a non-theoretical introduction to the elements of statistics, utilizing just basic algebra. The goal is to explain basic concepts intuitively with abundant examples and applications in diverse fields which utilize statistics. In this regard, the author has done an admirable job.

As with the previous editions, the author covers the basic topics that one would expect in an elementary text. There is undoubtedly more than enough material for a three credit semester course. A quick internet search uncovered several instructors who utilized the 5th edition, and their course outlines appear to cover the first 10 of the 14 chapters. Topics covered in these ten chapters are as follows: frequency distributions and graphs, measures of central tendency and variation, introductory probability, discrete probability distributions (mainly binomial), the normal distribution, confidence intervals and sample size, hypothesis testing, testing the difference between two means and two proportions, and correlation and regression. There are an enormous number of exercises, and instructors who have used the 5th edition may be interested to know the number of exercises have been increased from about 1800 to 2100.

There are numerous positive features of this book. There is a constant attempt on the part of the author to show how the material is relevant to real world applications, e.g., research studies, media articles, business, medical, social science, etc. Real data is constantly used in the examples and exercises. We all know that students often find statistics a difficult subject, and the literal “step-by-step” approach obviously is very appealing to the beginning student of statistics. Instructors are aware that students may have forgotten some of their basic algebra; fortunately, there is an algebra review section in the appendix.

This reviewer feels that the author was generally correct in marking certain items as “optional”. For example, for the discrete probability distributions, the limited material on multinomial, poisson and hypergeometric distributions were designated as optional; full material of course was provided for the binomial distribution, which is more widely used in statistical practice. Multiple regression was discussed in Chapter 10 as an optional topic and Analysis of Variance (ANOVA) was placed near the end of the text (Chapter 12). This also seems reasonable, since multiple regression and ANOVA often serve as the basis of a second course in statistics.

Another positive feature of the book is the decision by the author to let the instructor determine how much technology he or she wishes to utilize for the course. The author provides detailed write-ups on performing the statistical tests, whether one uses a graphics calculator, EXCEL, or MINITAB. The latter is a package specifically designed for statistical analysis, and would give the student a feel as to how the professional statistician does his or her “number crunching”.

This reviewer was pleasantly surprised to see some very nice useful practical topics and applications in the book, often not seen in other books. For example, when discussing percentiles, the author provided a percentile chart of weights of girls by age (the kind of tool a pediatrician would use). Also, a “rule of thumb” was discussed, i.e., a standard deviation can sometimes be estimated by calculating 25% of the range. Very gratifying was the wealth of material on sample size determinations for confidence intervals of the mean and proportions. After all, a basic question that a client (who was once probably an elementary statistics s tudent) asks of the statistician is “How large a sample do I need”?

This reviewer feels there are, nevertheless, a few relatively minor shortcomings to this book. For one thing, the book will probably retail for well over $100 (the 5th edition was about $115 at Barnes and Noble). In addition, the student might be interested in purchasing the study guide, the student solution manual, and/or one of three specially written manuals which describes the software used for the course (i.e., graphics calculator manual, the Minitab 14 Student Version manual, or EXCEL manual). These “add-ons” could probably make the total cost of books for the course in excess of $200, which seems like an expensive outlay for just an introductory course.

Another potential problem with the text is that material on nonparametric statistics (techniques which do not assume normally distributed data) appears near the end of the text (Chapter 13). It is not unusual to see this topic relegated to the end (and consequently often not covered due to lack of time). The fact is that much of real data is not normally distributed; consequently, students s hould at least be exposed to this important area in a first course. Possibly, a minor rearrangement of the ordering of the chapters would be appropriate.

A final point of criticism is that some algebra-based statistical texts will in fact provide a few elementary mathematical proofs which utilize just basic algebra. In particular, the basic properties of summation (sigma) notation could be developed, and a few simple proofs may be presented. For example, the simple proof which derives the computational formula for the sample variance from the definitional formula is often provided in such texts. Although the author did state in the preface that no proofs are provided, what harm would be done in providing (possibly as an optional topic) a few such algebraic-based proofs?

Despite these minor shortcomings, this book clearly dispels the popular contention that statistics is a dry and dull topic; the colorful nature of the material (literally and figuratively) of the varied applications discussed in the text should be very appealing and friendly to both instructor and student.

Martin Feuerman is a biostatistician in the Department of Academic Affairs at Winthrop-University Hospital in Mineola, Long Island,New York. He previously served in a similar capacity at the University of Medicine and Dentistry of New Jersey. He has also taught elementary statistics at the Bronx campus of Mercy College.


1 The Nature of Probability and Statistics

1-1 Introduction

1-2 Descriptive and Inferential Statistics

1-3 Variables and Types of Data

1-4 Data Collection and Sampling Techniques

1-5 Observational and Experimental Studies

1-6 Uses and Misuses of Statistics

1-7 Computers and Calculators

1-8 Summary

2 Frequency Distributions and Graphs

2-1 Introduction

2-2 Organizing Data

2-3 Histograms, Frequency Polygons, and Ogives

2-4 Other Types of Graphs

2-5 Summary

3 Data Description

3-1 Introduction

3-2 Measures of Central Tendency

3-3 Measures of Variation

3-4 Measures of Position

3-5 Exploratory Data Analysis

3-6 Summary

4 Probability and Counting Rules

4-1 Introduction

4-2 Sample Spaces and Probability

4-3 The Addition Rules for Probability

4-4 The Multiplication Rules and Conditional Probability

4-5 Counting Rules

4-6 Probability and Counting Rules

4-7 Summary

5 Discrete Probability Distributions

5-1 Introduction

5-2 Probability Distributions

5-3 Mean, Variance, Standard Deviation, and Expectation

5-4 The Binomial Distribution

5-5 Other Types of Distributions (Optional)

5-6 Summary

6 The Normal Distribution

6-1 Introduction

6-2 Properties of the Normal Distribution

6-3 The Standard Normal Distribution

6-4 Applications of the Normal Distribution

6-5 The Central Limit Theorem

6-6 The Normal Approximation to the Binomial Distribution

6-7 Summary

7 Confidence Intervals and Sample Size

7-1 Introduction

7-2 Confidence Intervals for the Mean (s Known or n³30) and Sample Size

7-3 Confidence Intervals for the Mean (s Unknown or n<30)

7-4 Confidence Intervals and Sample Size for Proportions

7-5 Confidence Intervals for Variances and Standard Deviations

7-6 Summary

8 Hypothesis Testing

8-1 Introduction

8-2 Steps in Hypothesis Testing - Traditional Method

8-3 z Test for a Mean

8-4 t Test for a Mean

8-5 z Test for a Proportion

8-6 Chi Square test for a Variance or Standard Deviation

8-7 Additional Topics Regarding Hypothesis Testing

8-8 Summary

9 Testing the Difference Between Two Means, Two Variances, and Two Proportions

9-1 Introduction

9-2 Testing the Difference Between Two Means: Large Samples

9-3 Testing the Difference Between Two Variances

9-4 Testing the Difference Between Two Means: Small Independent Samples

9-5 Testing the Difference Between Two Means: Small Dependent Samples

9-6 Testing the Difference Between Proportions

9-7 Summary

10 Correlation and Regression

10-1 Introduction

10-2 Scatter Plots

10-3 Correlation

10-4 Regression

10-5 Coefficient of Determination and Standard Error of the Estimate

10-6 Multiple Regression (Optional)

10-7 Summary

11 Other Chi-Square Tests

11-1 Introduction

11-2 Test for Goodness of Fit

11-3 Tests Using Contingency Tables

11-4 Summary

12 Analysis of Variance

12-1 Introduction

12-2 One-Way Analysis of Variance

12-3 The Scheffé Test and the Tukey Test

12-4 Two-Way Analysis of Variance

12-5 Summary

13 Nonparametric Statistics

13-1 Introduction

13-2 Advantages and Disadvantages of Nonparametric Methods

13-3 The Sign Test

13-4 The Wilcoxon Rank Sum Test

13-5 The Wilcoxon Signed-Rank Test

13-6 The Kruskal-Wallis Test

13-7 The Spearman Rank Correlation Coefficient and the Runs Test

13-8 Summary

14 Sampling and Simulation

14-1 Introduction

14-2 Common Sampling Techniques

14-3 Surveys and Questionnaire Design

14-4 Simulation Techniques

14-5 The Monte Carlo Method

14-6 Summary

Appendix A: Algebra Review

Appendix B-1: Writing the Research Report

Appendix B-2: Bayes's Theorem

Appendix B-3: Alternate Method for the Standard Normal Distribution

Appendix C: Tables

Appendix D: Data Bank

Appendix E: Glossary

Appendix F: Bibliography

Appendix G: Photo Credits

Appendix H: Selected Answers