Although most researchers tend to compute a few summary statistics and then carry out
statistical tests, data analyses should begin by exploring the data more thoroughly than is
usually done. This means not only calculating alternative statistics that tell us something
about the location, variability, and shape of the distribution of data, but also graphing the data
in various ways. Chapter 2 presents useful statistics and methods of graphing for univariate
data, that is, for cases involving a single variable. Chapter 3 does the same for bivariate
data, cases in which the relation between two variables is of interest.
Theoretical distributions play a central role in procedures for drawing inferences about
population parameters. These can be divided into two types: discrete and continuous. A
variable is discrete if it assumes a finite, countable, number of values; the number of individuals
who solve a problem is an example. In contrast, a continuous variable can take on
any value in an interval. Chapter 4 presents an important discrete distribution, the binomial
distribution, and uses it to review some basic concepts involved in testing hypotheses about
population parameters. Chapter 5 provides a similar treatment of an important continuous
distribution, the normal distribution, extending the treatment of inference to concepts involved
in estimating population parameters, and intervals in which they may lie. Chapter 6
continues the treatment of continuous distributions and their applications to inferences about
population parameters in the context of the t distribution, and it also introduces the concept
of standardized effect size, a measure that permits comparisons of treatment effects obtained
in different experiments or with different measures. Chapter 7 concludes our review
of continuous distributions with a discussion of the chi-square (x2) and F distributions.
As we noted in the preceding section, there are many different experimental designs.
We may assign subjects to blocks on the basis of a pretest score, or age, or gender, or some
other variable. We may test the same subject under several levels of an independent variable.
We may sequence the presentation of such levels randomly or in an arbitrary order designed
to balance practice or fatigue effects across treatments. These various experimental designs,
and the analyses appropriate for each, are discussed in Chapters 8-17.
Most of the analyses presented in the experimental design chapters are usually referred
to as analyses of variance. An analysis of variance, or ANOVA, is a special case of multiple
regression analysis, or MRA, a general method of analyzing changes in the dependent
variable that are associated with changes in the independent variable. Chapters 18-21
develop this regression framework, including estimation and statistical tests, and its relation
to ANOVA.