The QR overlay requirement is designed to teach students how numerical data are analyzed and interpreted in various academic disciplines.
QR overlay courses need to balance the following objectives:
Literacy. The number of topics and the depth of coverage should be sufficient to ensure that students have the basic knowledge they need in order to function in real life situations involving quantitative data.
Authenticity. Students should have experience in using authentic numerical data. The experience should arise naturally in the context of the course and actually advance the work of the course. Only with such experience is the literacy goal likely to be realized.
Applicability. The examples used in an overlay class should be adequate to convince the average student that the methods used in the analysis of data are of general applicability and usefulness.
Understanding. A student's experience with data analysis should not be limited to rote application of some involved statistical procedure. Rather, students should understand enough of what they are doing so that their experience of data analysis is likely to stay with them, at least as a residue of judgment and willingness to enter into similar data analyses in the future.
Practicality. The breadth of topics covered and the depth of coverage should be consistent with what an average Wellesley student can realistically absorb in a course that devotes only a part of its time to data analysis.
Necessary Minimum Exposure to the Analysis of Data
Any QR overlay course must address certain key topics in order to satisfy the goals of literacy and understanding. Additional applications are needed to meet the goals of authenticity and applicability. An overlay course must cover all of the required topics and at least one of the applications (or an application of similar merit). The relative emphasis of these topics and the manner in which they are treated will depend on the specific objectives of the course.
Framework for Data Analysis
A course satisfying the QR overlay requirement should provide a general overview for how empirical questions or hypotheses can be raised, how relevant data can be collected and analyzed to address these questions, and finally, what conclusions these data allow. Specifically, students should practice formulating questions that arise in the context of the course and that can be answered by analyzing data. They should then decide what type of data to collect, how to collect and analyze these data, and what conclusions their data support.
A QR overlay course should address issues of data quality. Are the data representative or biased? Are the data that are collected really relevant to the question being investigated? Certain courses might stress the importance of random samples, experiments versus observational studies, blind versus double blind experiments, and so forth.
A QR overlay course should stress different methods of representing data, including numerical representations (tables of data), visual representations (pie charts, scatter-plots, line graphs, and histograms), verbal representations (writing reasonable captions that describe a graph).
A course should stress different ways of summarizing data, including verbal summaries of data sets. A QR overlay course must include discussions of different measures of central tendency, including mean, median, or such other measures. An overlay course must also include address different measures of dispersion, including the range, standard deviation, and percentile ranks. Depending on the course, other measures might include index of diversity, index of qualitative variation, or absolute variation.
Because of the random component in sampling from a population, students should have some understanding of basic probability. This must include a working knowledge of how and when to use the addition and multiplication rules, and the vocabulary of statistical independence, mutual exclusivity, and the informal notions of the "Monte Carlo Fallacy" and the "Law of Averages."
Students in a QR overlay course should see different examples of distributions, including both normally distributed data sets as well as non-normally distributed data sets. They should know when to expect that a population will be normally distributed, and what it means for a distribution to be skewed. They should know what the mean, median, and standard deviation tell about a distribution. Finally, they should know that a normal distribution is fully specified by its mean and standard deviation and that the percentage of the population on a given interval can be determined from a table or a formula.
A QR overlay course should discuss sampling and stress the distinction between "sampling" and "collecting data." It should introduce the notion of sample mean, and discuss why the sample mean might well vary from the population mean. The distinction between sample statistics (e.g., the mean of a sample) and population parameters (e.g., the mean of the population) should be emphasized.
These applications have been selected with an eye toward the goals of authenticity and applicability. A QR overlay course should cover at least one of the applications (or an application of similar merit).
Issues Regarding Sampling
An overlay course could discuss the problems that can arise when one attempts to ascertain certain characteristics of a population by testing a sample of that population. Such problems include how one obtains a random sample and how one detects sample biases.
Making and Justifying Inferences from Data: Confidence Intervals and Hypothesis Testing
A QR overlay course could discuss confidence intervals and hypothesis tests. It could explore how one determines whether a measured variation cannot plausibly be attributed to chance alone.
A QR overlay course could study various methods for fitting curves to data and for analyzing the deviations of the data from these curves. The equation of the curve can be investigated as regards some explanation of the process that produced the data.
Different QR Overlay Course Models
There are at least two broad categories of courses satisfying the QR overlay requirement, lecture courses and laboratory courses.
In a lecture course, the required topics and course applications can be covered as a single block, or they can be distributed throughout the semester. Whether the topics are covered in one block or distributed more evenly, the total amount of time spent should be at least one third of the semester, or about 9 lectures.
Courses with Laboratories
The QR overlay requirement may fulfilled through the laboratory component of a science course. The laboratory provides a particularly rich and natural environment for the application of data analysis techniques. To be designated as a QR overlay class, a science laboratory must develop the core concepts of data analysis in ways that facilitate a flexible, useful, and general understanding of these techniques. The laboratory should introduction of the core concepts of data analysis followed by a series of applications in the context of laboratory measurements and analysis of the collected data.