In Chapter 17, we introduce the design and analysis of experiments using one, two, or more factors. Designs for eliminating the effects of one or two nuisance variables along with a method of estimating one or more missing observations are given. We include two nonparametric tests, the Kruskal–Wallis and the Friedman test, for analyzing one‐way and randomized complete block designs. Finally, models with fixed effects, mixed effects, and random effects are also discussed.
Chapter 18 introduces a special class of designs, the so‐called
In Chapter 19, we introduce the topic of response surface methodology (RSM). First‐order and second‐order designs used in RSM are discussed. Methods of determining optimum or near optimum points using the “method of steepest ascent” and the analysis of a fitted second‐order response surface are also presented.
Chapters 20 and 21 are devoted to control charts for variables and attributes used in phase I and phase II of a process. “Phase I” refers to the initial stage of a new process, and “phase II” refers to a matured process. Control charts are used to determine whether a process involving manufacturing or service is “under statistical control” on the basis of information contained in a sequence of small samples of items of interest. Due to lack of space, these two chapters are not included in the text but is available for download from the book website: www.wiley.com/college/gupta/statistics2e.
All the chapters are supported by three popular statistical software packages, MINITAB, R, and JMP. The MINITAB and R are fully integrated into the text of each chapter, whereas JMP is given in an independent section, which is not included in the text but is available for download from the book website: www.wiley.com/college/gupta/statistics2e. Frequently, we use the same examples for the discussion of JMP as are used in the discussion of MINITAB and R. For the use of each of these software packages, no prior knowledge is assumed, since we give each step, from entering the data to the final analysis of such data under investigation. Finally, a section of case studies is included in almost all the chapters.
Chapter 2 Describing Data Graphically and Numerically
The focus of this chapter is a discussion of methods for describing sets of data.
Topics Covered
Basic concepts of a population and various types of sampling designs
Classification of the types of data
Organizing and summarizing qualitative and quantitative data
Describing qualitative and quantitative data graphically
Determining measures of centrality and measures of dispersion for a set of raw data
Determining measures of centrality and measures of dispersion for grouped data
Determining measures of relative position
Constructing a box whisker plot and its use in data analysis
Determining measures of association
Using statistical packages MINITAB, R, and JMP
Learning Outcomes
After studying this chapter, the reader will be able to do the following:
Select an appropriate sampling design for data collection.
Identify suitable variables in a problem and determine the level of measurement.
Organize, summarize, present, and interpret the data.
Identify the difference between a parameter and a statistic.
Calculate measures of the data such as mean, mode, median, variance, standard deviation, coefficient of variation, and measure of association and interpret them.
Identify outliers if they are present in the data.
Apply the statistical packages MINITAB, R, and JMP to analyze various sets of data.
2.1 Getting Started with Statistics
2.1.1 What Is Statistics?
The term statistics is commonly used in two ways. On the one hand, we use the term statistics in day‐to‐day communication when we refer to the collection of numbers or facts. What follows are some examples of statistics:
1 In 2000, the salaries of CEOs from 10 selected companies ranged from $2 million to $5 million.
2 On average, the starting salary of engineers is 40% higher than that of technicians.
3 In 2007, over 45 million people in the United States did not have health insurance.
4 In 2008, the average tuition of private colleges soared to over $40,000.
5 In the United States, seniors spend a significant portion of their income on health care.
6 The R&D budget of the pharmaceutical division of a company is higher than the R&D budget of its biomedical division.
7 In December 2009, a total of 43 states reported rising jobless rates.
On the other hand, statistics is a scientific subject that provides the techniques of collecting, organizing, summarizing, analyzing, and interpreting the results as input to make appropriate decisions. In a broad sense, the subject of statistics can be divided into two parts: descriptive statistics and inferential statistics.
Descriptive statistics uses techniques to organize, summarize, analyze, and interpret the
