This first chapter begins by discussing what statistics are and why the study of statistics is important. Subsequent sections cover a variety of topics all basic to the study of statistics. One theme common to all of these sections is that they cover concepts and ideas important for other chapters in the book.
Graphing data is the first and often most important step in data analysis. In this day of computers, researchers all too often see only the results of complex computer analyses without ever taking a close look at the data themselves. This is all the more unfortunate because computers can create many types of graphs quickly and easily.
The of this chapter gives an example in which a well-construed graph makes it clear that there was a bias in the draft lottery of 1969. The two following sections discuss common graphs forand variables.
The introductory section gives more examples of bivariate relationships and presents the most common way of portraying these relationships graphically. The next five sections discuss Pearson’s correlation, the most common index of the relationship between two variables. The final section, “Variance Sum Law II” makes use of Pearson’s correlation to generalize this law to bivariate data.
The introductory section discusses the definitions of probability. This is not as simple as it may seem. The section on basic concepts covers how to compute probabilities in a variety of simple situations. The Gambler’s Fallacy Simulation provides an opportunity to explore this fallacy by simulation. The Birthday Demonstration illustrates the probability of finding two or more people with the same birthday. The Binomial Demonstration shows the binomial distribution for different parameters. The section on base rates discusses an important but often-ignored factor in determining probabilities. It also presents Bays’ Theorem. The Bays’ Theorem Demonstration shows how a tree diagram and Bays’ Theorem result in the same answer. Finally, the Monty Hall Demonstration lets you play a game with a very counterintuitive result.nbsp;
The introductory section defines the concept and gives an example for both a discrete and a continuous distribution. It also discusses how sampling distributions are used in inferential statistics.
The Basic Demo is an interactive demonstration of sampling distributions. It is designed to make the abstract concept of sampling distributions more concrete. The Sample Size Demo allows you to investigate the effect of sample size on the sampling distribution of the mean. The Central Limit Theorem (CLT) Demo is an interactive illustration of a very important and counter-intuitive characteristic of the sampling distribution of the mean.
The remaining sections of the chapter concern the sampling distributions of important statistics: the Sampling Distribution of the Mean, the Sampling Distribution of the Difference Between Means, the Sampling Distribution of r, and the Sampling Distribution of a Proportion.
The topics covered here in sections D, E, G, and H are typically covered in other texts in a chapter on Analysis of Variance. We prefer to cover them here since they bear no necessary relationship to analysis of variance. As has been pointed out elsewhere, it is not logical to consider the procedures in this chapter tests to be performed subsequent to an analysis of variance. Nor is it logical to call them post-hoc tests as some computer programs do.