Statistical Analysis Essay ⋆ Political Science Essay Examples ⋆ EssayEmpire

Statistical analysis is concerned with ways of analyzing quantitative data using statistical methods. Data used in statistical analysis may come from a variety of sources, such as standardized surveys, content analysis of the media, standardized observation, experiments and quasi-experiments, censuses, official statistics, or election results. The two major elements of statistical analysis are description and inference. Statistical inference is either classical or Bayesian.

Descriptive Statistics

Descriptive statistics are used to summarize and explore data using measures that are more easily understood even by an inexperienced observer. For instance, a complete listing of all data points (e.g., a long list of political candidates favored by respondents in a poll) is substituted by a few numbers (e.g., a frequency distribution of the most popular candidates, or a modal candidate, or something similar). These summary descriptions, called descriptive statistics, are more meaningful for most purposes than a complete listing of the data, which may be enormous. (A survey may interview a few thousand respondents and record several dozen or even hundreds of responses.) The major challenge of descriptive statistics is to choose such data reduction techniques that will represent the data succinctly and adequately without distorting or losing too much of the existing information.

The most frequently used descriptive statistics are the mean, the median (and other percentiles), the mode, the range of values, the standard deviation, the variance, and the interquartile range. Graphical representation is a very useful and efficient way to describe data. Histograms, stem-and-leaf plots, pie charts, scatter plots, and box plots are perhaps the most commonly used graphs.

Statistical Inference

Statistical inference makes predictions and generalizations based on the data. Data may, for instance, represent a sample drawn from a larger population (e.g., a sample of voters chosen from all participants in a poll, or a sample of administrative units taken from a larger universe of such units). Samples are routinely taken to reduce cost and increase flexibility of data collection, yet the ultimate goal is always to learn about the population. Classical statistical inference consists of methods that use information based on a sample from a population (sample statistics) to make predictions about the parameters of that population. Bayesian inference differs from classical inference in that it blends sample characteristics and some prior knowledge to make predictions.

Inferential statistics are of two basic types: parametric and nonparametric. Parametric statistics is a branch of statistical inference that makes assumptions about the underlying mathematical distributional form of variables. Nonparametric statistics does not make such assumptions. Some statisticians claim that the use of parametric statistics is hardly ever defensible in the social sciences, yet they continue to be employed frequently. Nevertheless, nonparametric approaches represent a major growth area in political science, perhaps as a reaction to the nature of the data that political scientists may gather.

Statistical inference offers two types of predictions about population parameters. It produces point estimates and interval estimates. A point estimate is the single best guess of what the (unknown) population parameter might be. An interval estimate consists of a range of numbers around the point estimate in which the parameter is believed to be. An interval estimate helps express the accuracy of the point estimate.

Statistical inference is used also for the purpose of statistical hypotheses testing (i.e., to carry out significance tests). Significance tests tell us if (and with what level of certainty) something observed in the sample (such as an association between two variables) may be generalized to the population. There are a large number of concrete significance tests. The choice of the most appropriate test is guided by the nature of the data. There are tests for means, proportions, variances, correlations, and so on. There are tests for one, two-, and multiple-sample studies. There are also tests for nominal, ordinal, and interval variables. The chi-square test is a well-known example of a significance test.

Statistical inference requires a clear definition of the population to which the inference is applied. It also requires detailed knowledge of the sampling procedure. Statistical inference may be rather difficult (or even impossible) for some sampling techniques. While many sampling procedures are in use in the social sciences, statistical inference is possible only if data come from a probability sample (a simple random sample, a stratified random sample, a clustered random sample, or a systematic random sample). Nonprobability samples (such as volunteer samples, convenience samples, purposive samples, quota samples, or snowball samples) require adjustments.

Deviations from the probability sample requirement are quite common in political science. Researchers may, for instance, employ a coincidence sample consisting of all countries included in some publicly available database. Scholars also may have data on all relevant cases (e.g., on all states in the United States or on all EU countries).Then no sampling procedure has been involved in producing the data. Classical statistical inference is often criticized or abandoned in these situations. Bayesian inference is nevertheless possible and provides an alternative that is becoming increasingly popular. Yet another advantage of Bayesian inference involves the use of prior beliefs about parameters—for example, knowledge of historical election results may help us make predictions about future elections.

Statistical Analysis And The Social Sciences

All social science disciplines have been placing more and more emphasis on quantitative methods in recent decades. There are several reasons for this. First, research itself has taken on a more quantitative orientation. This is evident in published works as well as in the training of social scientists. Second, the computer revolution has made more quantitative data easily available. Survey data, for instance, are now routinely deposited in online data archives that often also offer rudimentary tools for online data analysis.

Finally, developments of computers and software applications make statistical methods faster, cheaper, more flexible, and more easily available than ever before. Whereas statistical analysis of quantitative data is the mainstream of empirical social science, it exists along with other respected methodological approaches such as interviews, participant observation, comparative historical methodology, the study of documents, ethnomethodology, and conversation analysis. There also exist established techniques to investigate qualitative information (text, picture, video) produced by these methodologies.

Bibliography:

Agresti, Alan, and Barbara Finlay. Statistical Methods for the Social Sciences, 4th ed. Upper Saddle River, N.J.: Prentice Hall, 2009.
Jackman, Simon. “Bayesian Analysis for Political Research.” Annual Review of Political Science 7 (2004): 483–505.
Treiman, Donald J. Quantitative Data Analysis: Doing Social Research to Test Ideas. San Francisco: Jossey-Bass, 2009.
Tufte, Edward R. The Visual Display of Quantitative Information. Cheshire, Conn.: Graphics Press, 1983.
Western, Bruce, and Simon Jackman. “Bayesian Inference for Comparative Research.” American Political Science Review 88, no. 2 (1994): 412–423.

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