This text is a brief introduction to statistics. The main focus has been on the application, comprehension, interpretation, and a sense of appreciation for statistics. The hope is that the reader has become interested in statistics and will pursue the topic further. In fact, the main reason for including the regression chapter, Chapter 8, was to show additional possibilities that go beyond a single-variable analysis. It demonstrates that we can explore the influence of one or more variables on a variable of interest. Within the subject of regression, one can explore theoretical and empirical aspects of cross section and time series data. Regression analysis has been augmented to utilize data that are qualitative in nature. The qualitative data can be used as dependent variables or independent variables. Many economic decisions can be represented as qualitative dependent variables, for example, the decision to buy a good or not to buy it, obtain a college degree, take a vacation (i.e. consume leisure), or to save, to name a few. Qualitative variables can also be independent variables, such as race, gender, political persuasion, and nationality.
The domain of statistics is vast and covers numerous specialized fields such as econometrics, biostatistics, sampling, and actuary to name a few. However, there is not a field that does not utilize statistical analysis; from agriculture to zoology.
This text groups related topics and focuses on the interrelationship of different topics. The best way to see this is to refer to Table 1.1 in Chapter 1. The table divides descriptive statistics into two major categories of qualitative variables and quantitative variables. The scope of methods for quantitative variables is much broader than those for the qualitative variables because the methods used for qualitative variables are also applicable for the quantitative variable, but the reverse is not true necessarily. Within each category the analytical methods are broken down to tabular methods and graphical methods. Recall that these are all descriptive methods and their purpose is to provide insight to the nature of data and to condense the massive amount of information into as few parameters as possible. Although graphical and tabular methods are very helpful in providing a visual description of data, the analytical power of statistics is more evident in the numerical methods that apply to quantitative variables. Within the last category, it is customary to distinguish among three different classifications: measures of central tendency, measures of dispersion, and measures of association. Each of these measures provides different refinements to analytical power and allows researchers to differentiate among different types of data where certain aspects might be similar while the nature of data are very different, for example, as in the case of two populations with the same means but different variances. The knowledge about parameters provides an insight into the nature of data. Massive databases are like chaos of numbers. In spite of the fact that the human brain is extremely good at finding order in events when the order is not easy to detect, the data is too large, or the relationships are too complex, it needs statistics to comprehend what is going on. A good example to clarify the above point is the saying “to miss the forest for the trees.” Statistics provides a way of summarizing the evidence. The advantage of statistics is that it provides numerous descriptive and analytical tools that were not available prior to the discovery of statistics. Now it is possible to determine, with an appropriate level of probability, the outcome of a certain phenomenon or how to explain one or more variables using one or more other variables.
In Chapter 3, we put the few descriptive tools that were introduced in Chapter 2 into use by showing the applications of Z score and coefficient of determination. The chapter also provided additional tools to deepen the knowledge about life and to improve the analytical power of statistics. The concept of error is one of the major contributions of statistics to science. This notion allows us to divide variations in a phenomenon, which is ever-present in all real life situations, into two components: one that can be explained by statistical analysis and one that cannot be explained. One object of statistical analysis is to reduce the magnitude of the part that is unexplained. For example, the mean of a data explains part of the variation in it and leaves a part unexplained. In Chapter 8, we saw a glimpse of a regression analysis where part of the previously “unexplainable” error is explained by appropriate independent variables that are identified by economic theories or theories of other disciplines. This is just the beginning. There are numerous modifications to the simple regression analysis that allows us to reduce the unexplained portion by use of theory, assumptions, facts, prior information, and mathematical manipulations.
One mathematical manipulation is the discovery of different kinds of distribution functions. These mathematical relationships have certain known properties that are used to conduct statistical inference. They are also used to compare actual data to them and to apply the properties of these distribution functions to the actual data. The most important of such distribution functions is the normal distribution function. Although many natural events resemble the normal distribution function, many do not. Nevertheless, the use of theorems such as the Chebyshev’s theorem and the Central Limit Theorem allows us to use the properties of the normal distribution in dealing with some of the statistics obtained from real data that either have a complicated distribution function or do not even have a known distribution function. For example, the distribution function of the quantity demanded of a good is usually unknown. However, we can use the theories mentioned previosly to address the average quantity demanded. The link between the above theorems and statistics is the main subject of sampling distribution of sample statistics. We devoted Chapter 5 to this topic exclusively. The next step after identifying the distributional properties of the sample statistics is to use them to make inferences about population parameters. Population parameters determine the population and the underlying laws that govern them. The knowledge of parameters is similar to the knowledge about the phenomenon of interest, but in a manageable way.
The content of this text is a small portion of basic statistics. The next step for most economists is to learn regression analysis. The first step would be to learn simple and multiple regression for cross section data followed by the use of the same techniques modified to handle time series data. Almost all economic programs require at least one course in econometrics, which is the application of linear models such as regression analysis to economic issues. More serious students that pursue graduate work in economics are required to learn and sometimes prove the applicable theorems used in econometrics; however, a purely pragmatic approach of learning the methods is utilized by many programs. The next logical step is to combine the cross section and time series data, which since 1990 has become a distinct area commonly known as panel data analysis. In panel data analysis the problems that cause difficulty in the regressions using cross section or time series data are utilized to provide a better analysis. For example, the existence of correlation among units over time and the presence of correlations among independent variables are incorporated into the analysis rather than excluded or avoided. Probably the best example of this point is the analysis based on seemingly unrelated data. In this methodology, the fact that similar firms are subject to similar economic conditions and thus respond in similar manners in certain areas is the foundation of the methodology. Another recent development is spatial econometrics where the space related information is incorporated in the form of weight assigned to economic events. For example, it is reasonable to expect “neighboring” countries to act more similar than distant counties. There are numerous ways of defining neighbors, such as distance, existence of border, and so forth.
Finally, the hope is that the present text has been able to answer some of the questions readers had and also to spark an interest in this fascinating subject.