Title: Statistical Control Applet

Project director: Carl W. Roberts

Abstract:

Understanding correlations and partial correlations requires that students see these numbers as "transparent" (i.e., as windows into specific patterns among their data). What better way to develop this understanding than by having students create data that correspond to specific sets of correlations? Trial and error is important here. Students may think they know how men's and women's educations and incomes may differ such that an overall positive association would "disappear" when controlling for
gender. Weakening faulty presuppositions thus becomes just as important as confirming correct ones. Yet creating and analyzing data sets is so time-consuming that in their frustrating pursuit of "the right answer," students commonly lose sight of the ultimate objective (namely, seeing statistics as windows into their data). The applet developed in this project dramatically reduces the "busy work" in this exercise, by automatically generating and analyzing data while students are freed to concentrate on real-time creation of those data patterns they imagine to correspond to specific correlations among a set of variables.

Project description:

The applet's user interface has four parts: two over which the user has control, and two in which information is displayed. User control is over the placement of data points between two axes, and over the selection of an inkwell (representing one of a control variable's two levels). The information displayed consist of the data matrix that correspond to the user-specified data points and four correlations calculated from these data. The largest area is bounded at left and bottom respectively with Y and X axes. Below and to the left of this area are two "inkwells" of different colors. The user is then able to place single data points on the area between the axes by "dipping" the computer's pointer into an inkwell and placing a dot-of-that-color onto the area. The vertical axis (Y) should represent to the student the range of values taken by the dependent variable (e.g., income); the horizontal axis (X) should represent the range of values taken by the independent variable (namely, a measure, like
education, thought of as having some causal influence on the dependent variable). A third variable (a.k.a. a control variable) is introduced via the inkwells. This inkwell-variable can represent gender (male vs. female), race (African-American vs. white), or another 2-level variable. To the right of the space between the axes, the user can see the data matrix that is being built as data points are added between the axes. Zeros in the 3rd column of the data matrix correspond to data points associated with the upper inkwell; ones correspond to those associated with the lower one. Finally, only once two dots of each color are placed between the axes do four correlations appear below the X axisthree
zero-order correlations (i.e., between each pair of variables) plus the partial correlation between X and Y while controlling for the inkwell-variable.

Applet URL:

http://statwebserver.stat.iastate.edu/croberts/applets/partialnp.html