Massachusetts Institute of Technology
Department of Urban Studies and Planning

11.220 Quantitative Reasoning and Statistical Methods for Planning

Overview

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Quantitative Reasearch, Statistics, and Computing

At the end of this course, students will have earned the capacity to conduct their own quantitative research from the question to the conclusion using quantitative research methodology. The final paper requirement is an opportunity for students to exercise their own quantitative research as a whole.

1. Reasoning begins with questions/hypotheses and research design. The more specific your questions or hypotheses, the better for you. Research design involves so many considerations including (1) what is your population? (2) what is your sample? (3) what methodology would be appropriate to answer your question? and so forth.

Example research question:

Is there a wage or salary discrepancy between male and female workers in Lowell, MA?

Questions to be answered about the necessary data:

Who are workers? Part-time or full-time? Temporary or year-round? Private sector, public sector, or self-employed?

Full-time, year-round workers consists of people 16 years old and over who usually worked 35 hours or more per week for 50 to 52 weeks in 1999. (Census 2000)

2. Data collection is the next step. At this step, you are forced to be really specific about what you're trying to do. Otherwise, you cannot measure what you want to measure.

What is wage or salary?

Wage or salary income includes total money earnings received for work performed as an employee during the calendar year 1999. It includes wages, salary, armed forces pay, commissions, tips, piece-rate payments, and cash bonuses earned before deductions were made for taxes, bonds, pensions, union dues, etc. (Census 2000)

3. Data management. You will probably gather the data from different sources at different scales. The data requires management and manipulation to feed into your inquiry.

How to deal with big data sets and/or multiple data sets? How to boil them down to the data set that you need?

Database Management Systems (DBMS), such as MS-Access, comes into play. A spread sheet, such as MS-Excel, is not enough. For example, a survey about persons with housing unit info. The following are some issues: (1) One housing unit may have multiple persons. (one-to-many relationship) (2) As the research progresses, you might need to select a subset or re-organize the original dataset, so that you will have various tables. What happens if you update one cell of the original dataset? (query vs. static table) (3) When you want to modify or expand your research, spreadsheets are too static and inflexibile compared to a DBMS.

4. Descriptive Statistics. Summarizing the data into meaningful information is the next necessary step. Exploring the data gives researchers the necessary basic facts and "big picture," that later will guide the statistical analysis by suggesting possible hypotheses or the appropriate statistical method.

In the previous example, we might want to know the minimum/maxium wage/salary. A measure of central tendancy (a number, score or data value that represents the average in a group of data) and a measure of dispersion (the degree of clustering of the data about the mean) are typical questions. Often, we also need to see a graphical representation of the data, such as histogram.

5. Statistical Analysis (Inference). Statistical inference draws a conclusion about a population from evidence provided by a sample. Drawing conclusions in mathematics is a matter of starting from a self-evident truth and using a logical argument to prove without doubt that the conclusion follows. Statistics isn't like that. Statistical conclusions are uncertain, because the sample isn't the entire population. So statistical inference has to state conclusions and also say how certain they are.

Going back to our original question, we will most likely find different values for male and female wage/salary. These numbers come from the sample. Yet, if we draw another sample set, that is different from the previous one, it will yield another set of different values by chance. The population remains the same, but samples can produce different means, ranges, etc.. Are the wage/salary different by sex? How much certain are you? This inference is closely related to the notion of probability.

6. Conclusion. Finally, a claim is made based on the analysis. Often, the result needs to be translated into plain English for lay persons.

Overview Diagram

Course Organization -- Lecture, Recitation, and Computing Sessions

Lecture: What do we do in class? As you see above, research requires more than statistics. QR & Computing emphasizes the whole picture and the entire process of quantitative research. Particularly, instead of discussing the details of statistics, we will focus on the key concepts for quantitative research. For example, we will discuss things like, where should we start? How to deal with data? Is the data right for your research? What methodology would be the appropriate for our research? How to interpret the outcome? How to translate the result for a lay person? and so forth. Consequently, lectures can hardly cover as much detail of statistical methods as other traditional statistics courses might do. For the details of statistical methods, students need to utilize the recitations and readings.

Recitation: In recitations, along with the brief review of what's been discussed in lectures, students will have time to discuss statistical methods in detail including equations and calculations. Needless to say, it's hard to accomplish the goal above without a solid knowldege of statistics. Teaching and learning detailed statistics can be done better with a smaller group of people in a smaller room. Recitation is also flexible to meet each individual's questions and needs.

Computing Sessions: Computing is a powerful tool to enhance your quantitative research capicity. More often than not, quantitative research could not be done without computing. It includes data management (e.g. data gathering, data organization, data re-structuring, data preparation for analysis, etc.), statistical analysis (e.g. descriptive statistics, histogram, charts, chi-square test, regression, etc.) and spatial analysis (e.g. thematic mapping, buffering, etc.). Students will learn the underlying principles and theories about computing and have hands-on experience with Access (Microsoft), SPSS (SPSS Inc.), and ArcGIS (ESRI). In addition, students will have some exposure to Excel (Microsoft) which is a handy tool for quantitative analysis.

Created by Myounggu Kang on January 25, 2004. Edited by Rhonda Ryznar on January 22, 2005.