Quantitative methods are the tools that social scientists use to find measurable results of various phenomena, following the general sequence of the scientific method, from hypothesis to evaluation. Finding the right quantitative tool to measure something like the effect that the color of paint in a child's bedroom will have on her psyche can lead to considerable debate, but quantitative methods have come into common use in such social fields as political science, sociology, psychology and anthropology, and are accepted as the best way to test the truth of hypotheses in those fields.
Most quantitative research projects have a statistical component to them, particularly in the social sciences and economics. Researchers collect large samples of data and manipulate various factors based on the hypothesis at hand. For example, if you want to measure the effect that nutrition has on a student's ability to retain material, you would manipulate the amount and nutritional quality of breakfasts consumed across your research sample. Opinion surveys with five- or seven-point attitudinal scales are also common tools. Depending on the statistical method, various regression methods (linear or non-linear, for example) are applied to the data to see if there are significant links between factors and outcomes.
How well do these surveys actually work as far as giving a meaningful result to the questions that researchers want to answer? This is where item-response theory (IRT) comes in. According to the assumptions of IRT, if you are looking at one particular trait, such as reading level or strength of feeling about the designated-hitter rule, and you keep your questions independent and you can render your respondents' answers in a mathematical way, then your assessment should render valid, meaningful results.
The Rasch Model
This model primarily works with measurement of personality characteristics, aptitudes and attitudes. You could use the Rasch model to figure out, for example, how a person feels about the right to bear arms using a questionnaire. While it is useful to find out one particular trait or attitude, it is not the ideal tool to use if you are trying to measure several factors at once.
Effective or Not?
Researchers who are skeptical about quantitative methods tend to point to the complexity of factors in any situation involving research in the social sciences. For example, if you're going to measure the importance of a healthy breakfast for student learning, how can you isolate the choice between Frosted Flakes and All-Bran from other factors that affect that learning, such as sleep patterns, emotional turbulence in the home, disciplinary differences and other elements? Those who argue for quantitative methods insist that the results can be valuable if the researcher ensures a minimal disturbance from outside factors.