Descriptive Statistics

Descriptive statistics are commonly encountered, relatively simple, and for the most part easily understood. Most of the statistics encountered in daily life, in newspapers and magazines, in television, radio, and Internet news reports, and so forth, are descriptive in nature rather than inferential. Compared with the logic of inferential statistics, most descriptive statistics are somewhat intuitive. Typically the first five or six chapters of an introductory statistics text consist of descriptive statistics (means, medians, variances, standard deviations, correlation coefficients, etc.), followed in the later chapters by the more complex rationale and methods for statistical inference (probability theory, sampling theory, t and z tests, analysis of variance, etc.)

Descriptive statistical methods are also foundational in the sense that inferential methods are conceptually dependent on them and use them as their building blocks. One must, for example, understand the concept of variance before learning how analysis of variance or t tests are used for statistical inference. One must understand the descriptive correlation coefficient before learning how to use regression or multiple regression inferentially. Descriptive statistics are also complementary to inferential ones in analytical practice. Even when the analysis draws its main conclusions from an inferential analysis, descriptive statistics are usually presented as supporting information to give the reader an overall sense of the direction and meaning of significant results.

Although most of the descriptive building blocks of statistics are relatively simple, some descriptive methods are high level and complex. Consider multivariate descriptive methods, that is, statistical methods involving multiple dependent variables, such as factor analysis, principal components analysis, cluster analysis, canonical correlation, or discriminant analysis. Although each represents a fairly high level of quantitative sophistication, each is primarily descriptive. In the hands of a skilled analyst, each can provide invaluable information about the holistic patterns in data. For the most part, each of these high-level multivariate descriptive statistical methods can be matched to a corresponding inferential multivariate statistical method to provide both a description of the data from a sample and inferences to the population; however, only the descriptive methods are discussed here.

The topic of descriptive statistics is therefore a very broad one, ranging from the simple first concepts in statistics to the higher reaches of data structure explored through complex multivariate methods. The topic also includes graphical data presentation, exploratory data analysis (EDA) methods, effect size computations and meta-analysis methods, esoteric models in mathematical psychology that are highly useful in basic science experimental psychology areas (such as psycho-physics), and high-level multivariate graphical data exploration methods.

Graphics and EDA

Graphics are among the most powerful types of descriptive statistical devices and often appear as complementary presentations even in primarily inferential data analyses. Graphics are also highly useful in the exploratory phase of research, forming an essential part of the approach known as EDA.

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Figure 1 Scatterplots of Six Different Bivariate Data Configurations That All Have the Same Pearson Product-Moment Correlation Coefficient

Graphics

Many of the statistics encountered in everyday life are visual in form—charts and graphs. Descriptive data come to life and become much clearer and substantially more informative through a well-chosen graphic. One only has to look through a column of values of the Dow Jones Industrial Average closing price for the past 30 days and then compare it with a simple line graph of the same data to be convinced of the clarifying power of graphics. Consider also how much more informative a scatterplot is than the correlation coefficient as a description of the bivariate relationship between two variables. Figure 1 uses bivariate scatterplots to display six different data sets that all have the same correlation coefficient. Obviously there is much more to be known about the structural properties of a bivariate relationship than merely its strength (correlation), and much of this is revealed in a scatterplot.

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