Statistics: Learning from Data 2nd Edition
Statistics is about learning from data and the role that variability plays in drawing conclusions from data. To be successful, it is not enough for students to master the computational aspects of descriptive and inferential statistics—they must also develop an understanding of the data analysis process at a conceptual level. The second edition of Statistics: Learning from Data is informed by careful and intentional thought about how the conceptual and the mechanical should be integrated in order to promote three key types of learning objectives for students:
● conceptual understanding
● mastery of the mechanics
● the ability to demonstrate conceptual understanding and mastery of the mechanics by “putting it into practice”
A Unique Approach
A number of innovative features distinguish this text from other introductory statistics books:
● A New Approach to Probability There is now quite a bit of research on how students develop an understanding of probability and chance. Using natural frequencies to reason about probability, especially conditional probability, is much easier for students to understand. The treatment of probability in this text is complete, including conditional probability and Bayes’ Rule type probability calculations, but is done in a way that eliminates the need for the symbolism and formulas that are a roadblock for so many students. For those who also want to provide students with a more traditional coverage, there is an optional new section that introduces probability rules.
● Chapter on Overview of Statistical Inference (Chapter 7) This short chapter focuses on the things students need to think about in order to select an appropriate method of analysis. In most texts, this is “hidden” in the discussion that occurs when a new method is introduced. Considering this up front in the form of four key questions that need to be answered before choosing an inference method allows students to develop a general framework for inference and makes it easier for students to make correct choices.
● An Organization That Reflects the Data Analysis Process Students are introduced early to the idea that data analysis is a process that begins with careful planning, followed by data collection, data description using graphical and numerical summaries, data analysis, and finally interpretation of results. The ordering of topics in the text book mirrors this process: data collection, then data description, then statistical inference.
● Inference for Proportions Before Inference for Means Inference for proportions is covered before inference for means for the following reasons:
● This makes it possible to develop the concept of a sampling distribution via simulation, an approach that is more accessible to students than a more formal, theoretical approach. Simulation is simpler in the context of proportions, where it is easy to construct a hypothetical population from which to sample (it is more complicated to create a hypothetical population in the context of means because this requires making assumptions about shape and spread).
● Large-sample inferential procedures for proportions are based on the normal distribution and don’t require the introduction of a new distribution (the t distribution). Students can focus on the new concepts of estimation and hypothesis testing without having to grapple at the same time with the introduction of a new probability distribution.
● Parallel Treatments of Inference Based on Sample Data and Inference Based on Experiment Data Many statistical studies involve collecting data from a statistical experiment. The same inference procedures used to estimate or test hypotheses about population parameters also are used to estimate or test hypotheses about treatment effects. However, the necessary assumptions are slightly different (for example, random assignment replaces the assumption of random selection), and the wording of hypotheses and conclusions is also different. Trying to treat both cases together tends to confuse students. This text makes the distinction clear.
New in This Edition
● New Sections on Randomization-Based Inference Methods Research indicates that randomization-based instruction in statistical inference may help learners to better understand the concepts of confidence and significance. The second edition includes new optional sections on randomization-based inference methods. These methods provide alternative analyses that can be used when the conditions required for normal distribution-based inference are not met. Each of the inference chapters (Chapters 9 through 13) now contains a new optional section on randomization-based inference that includes bootstrap methods for simulation-based confidence intervals and randomization tests of hypotheses. These new sections are accompanied by online Shiny apps, which can be used to construct bootstrap confidence intervals and to carry out randomization tests. The App collection that accompanies this text can be found at statistics.cengage.com/Peck2e/Apps.html.
● Restructured Chapters on Statistical Inference The chapters on statistical inference have been restructured to include methods for learning from experiments in the same chapter as methods for learning from samples. While the coverage of inference based on data from statistical experiments (Chapter 14 in the first edition) has been integrated into earlier chapters, the important distinction between inferences based on data from experiments and inferences based on data from sampling is maintained in order to highlight the differences in how hypotheses are worded, in conditions, and in the wording of conclusions in these two situations. The sections of the chapter on inference for two means have also been reordered to put inference for paired samples before inference for independent samples, in order to better connect the paired samples structure with one sample inference for a mean in Chapter 12.
● Expanded Treatment of Probability The second edition contains a new section titled “Calculating Probabilities—A More Formal Approach” for instructors who want to also provide a more traditional coverage of probability. For those who prefer the “hypothetical 1000” approach from the first edition, the newly added traditional section is optional and can be omitted without compromising any of the probability student learning objectives.
● Updated Examples and Exercises In our continuing effort to keep things interesting and relevant, the second edition contains many updated examples and exercises on topics of intere
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