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A Short Course: Using Modeling and Statistics

Creating Quantitative Models

Gathering Background Information

In order to create a quantitative model which will involve students in active learning about scientific phenomena, they will first need to have a conceptual understanding of the system they are investigating.  They can begin by exploring a variety of information sources relating to their interests.  Internet resources for a variety of topics are indexed in our course content.  There are also some example models which explain their theoretical basis and mathematical structure.  Background information can also be gathered from more traditional library and information sources.  For your own project, you should explore these examples for conceptualizations of the problem,  ideas about the nature of the relationships that have been tested before, and the availability of data.  As you do this, you should begin to formalize a conceptual model of the relationships.  You can use simple flow diagrams to note what you think is related: causes, effects, and conditions that might impact those relationships.  Where you find past work that has quantified those relationships, you can begin to annotate your diagram with the equations representing them.  Even if an exact equation is not available, you can define the relationships in descriptive terms -- for example, as the temperature goes up, the ability of air to hold moisture also goes up.

With the conceptual model in hand, you can then begin to look in more detail at other people's models and related data analysis.  Models produced with specialized software can be helpful even if you do not have the original modeling tools as long as they define the nature of the relationships that are modeled and the sources of their information.  Data for the areas or time periods you are interested in can also serve as a step toward model building -- either by providing a way to test your model or a way to derive it using statistical analysis.  Once you have an initial list of possible models and datasets, you are ready for the next step in modeling -- defining the quantitative relationships.

Creating a Quantitative Model

The models and datasets that you find may include a number of very complex relationships and calculations.  For the novice modeler, trying to understand and use such a model can be very discouraging.  Thus, you should simplify the first model you will try by focusing on one interesting aspect of the relationship.  You can then formulate some initial relationships to model and test.  For each relationship, you can create a hypothesis that will be the basis of your model and its test.  To quantify that relationship, you can then: 

• Find a mathematical formulation in the materials you gathered that can be tested for your area or time period.  You will need a dataset or theoretical formulation to test it against.
• Use visualization (graphing and related tools) to create graphs of the relationships from a real dataset to help define the nature of the relationships you might test.  Here, you can see if it is linear or non-linear and you can define which variables are related.
• Use statistical analysis on your dataset to create a quantitative equation of the expected relationship.  The statistical output can be used to define the level of error associated with your model.