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# Methods, Quantitative

BIBLIOGRAPHY

In the social sciences, quantitative research can be defined as any research that uses numbers as the basis for making inferences about the phenomenon under study. The hallmarks of quantitative research are control over extraneous influences (often involving experimental manipulation) and, more generally, statistical approaches to sampling, measurement, and data analysis. However, the simplicity of this general definition does not do justice to the full range of methodologies and data-analysis strategies that fall under the umbrella of quantitative research.

The goals of research represent a convenient way to discuss different types of quantitative research. Researchers employ a descriptive research strategy when they are interested in a numerical description of an object, event, or situation. For example, if a scholar were interested in the average class size of elementary schools in Spain, he or she might design a survey asking about the number of students and the number of classrooms (possibly among other variables) and send that survey to every elementary school in Spain. That researcher might also be interested in describing patterns of class sizes across different countries and parts of the world. Researchers employ a relational research strategy when they are interested in the extent to which two or more variables tend to co-occur. For instance, the scholar interested in class sizes may also be interested in the relationship between class size and the socioeconomic status of the neighborhood from which the students are drawn. One way to answer this question would be to survey schools and determine their average class size and the socioeconomic status of the surrounding neighborhood. The researcher could then compute a correlation coefficient that describes the magnitude of this relationship. Researchers employ an experimental research strategy when they are interested in causal relations. For example, a scholar might be interested in whether or not reducing class sizes will increase student achievement. One way to answer this question would be to randomly assign classrooms to be rather small or rather large, then measure student achievement after an appropriate interval of time. The performance of students in the smaller classes can then be compared to the performance of students in the larger classes.

A second useful distinction implied by the discussion above is between experimental and nonexperimental quantitative research. Experimental research is typified by the manipulation of a variable. For most questions that interest social scientists, the best way to explore the effects of manipulating a variable involves randomly assigning study participants to different levels of the variable, such as by randomly assigning a teacher to have a relatively large or a relatively small number of students. Nonexperimental research lacks this essential feature (and may not even involve a group comparison at all). In the social sciences, a common type of study known as a quasi-experiment bridges these two categories. The quasi-experiment shares many features with an experiment yet does not involve random assignment of study participants. In the class size example, teachers may choose to teach smaller or larger classes, school principals may choose which teachers teach which classes, and so on.

A final distinction evident in quantitative research is between cross-sectional and longitudinal research. Crosssectional research involves participants at one point in time (e.g., immediately before a political election). Longitudinal research involves participants at multiple points in time. An example of cross-sectional research is the political poll in which voters are surveyed for their preferences one time. In a longitudinal approach, researchers assess participants at multiple points in time. For example, researchers might identify likely voters one year before an election and track their expressed preferences one time a week until the election occurs. Cross-sectional research, therefore, provides a snapshot of participants at a single point in time, while longitudinal research allows for an analysis of change over time.

The branch of mathematics known as statistics is widely employed in quantitative research. Statistics is relevant to quantitative approaches to social science in three major ways. First, researchers rarely work with entire populations (e.g., all elementary students in a country), as these are generally too large to study. Instead, researchers work with samples, and statistics provides a way of quantifying the expected range of differences between a randomly drawn sample and the population. This is best illustrated in political polling, for example, when researchers telephone a random sample of households to assess voting intentions. Results are then reported in terms of the percentage of respondents who endorsed each candidate. They are accompanied by a margin of error that expresses the expected range of the differences between the actual sample of respondents and the population from which the sample was drawn.

A second major use of statistics in quantitative research is in group comparisons. In the effects of class size on academic achievement example above, the academic performance of students in small classrooms would be compared to the academic performance of students in larger classrooms. A statistical test (such as a t-test or an analysis of variance) could be conducted to assess whether the group averages differ more than would be expected if the groups differ only because of chance (that is, if class size does not affect student achievement).

A third major use of statistics in quantitative research involves statistical modeling of the interrelationships between variables. For instance, a clinical psychologist might be interested in how client personality, therapist personality and skill, and the quality of the relationship between the client and the therapist all work to affect the clients mental health. The psychologist might postulate a theoretical model involving these variables. Then, the psychologist would collect data on these variables and use techniques (such as structural equation modeling) to determine if the observed pattern of interrelations fits the theoretical model.

Quantitative research is often contrasted with qualitative research. The latter overlaps somewhat with descriptive approaches to quantitative research, but instead of resulting in numerical and statistical descriptions, qualitative research often is presented in narrative form. Historically, the distinction between qualitative and quantitative research created a rift among social scientists. At the extremes, quantitative social scientists have argued that a question is not truly scientific unless it can be formulated in mathematical or statistical terms, while qualitative social scientists have argued that quantitative approaches are too crude and can therefore never result in valid knowledge. Neither of these extreme views reflects the practice of scientists in other scientific disciplines (such as biology), and most modern social scientists believe that qualitative and quantitative methods can complement one another (Kuhn 1961). This recognition is reflected in the growing use of so-called mixed method research, in which both qualitative and quantitative methods are employed in the same research study (see Tashakkori and Teddlie 2003).

SEE ALSO Data; Data, Longitudinal; Experiments; Methodology; Methods, Qualitative; Methods, Research (in Sociology); Polling; Polls, Opinion; Regression; Regression Analysis; Social Science; Statistics; Structural Equation Models; Survey; Test Statistics

## BIBLIOGRAPHY

Kuhn, Thomas S. 1961. The Function of Measurement in Modern Physical Science. Isis 52 (2): 161193.

Shadish, William R., Thomas D. Cook, and Donald T. Campbell. 2002. Experimental and Quasi-experimental Designs for Generalized Causal Inference. Boston: Houghton Mifflin.

Tashakkori, Abbas, and Charles Teddlie, eds. 2003. Handbook of Mixed Methods in Social and Behavioral Research. Thousand Oaks, CA: Sage Publications.

Jeffrey C. Valentine