Meta-structure. In the Difference to Inference Game students plan a strategic series of two-group experiments whose data will discriminate among five theories. Students must choose which of five theories (visual patterns) best describes an unseen visual pattern hidden behind a screen.

Deduction. First they must make deductions from the level of theory to the level of research design. They must deduce how to construct crucial experiments which will eliminate some theories but not others. This is done by critically examining the five theories and determining where the theories make different predictions.

Induction. Second, after collecting research data, students must use inductive logic to go from the data back to theory. Theories make predictions about data; the data obtained from research studies may or may not be inconsistent with each theory's predictions. Students run empirical studies and then must decide if they can eliminate one or more theories on the basis of the research data.

Inference. Finally students must make theoretical inferences based on all this deductive and inductive logic. They must conduct a series of research projects until they discover one and only one theory which remains consistent with all the known data.

The game structure of Difference to Inference requires students to integrate deductive, inductive and inferential logic to choose the best of five theories.

Game format. To begin, students receive a research grant amounting to 500 grant bucks. The game is an important assignment in a university class; to get full course credit they must earn more grants until they have a minimum of 2000 grant bucks. Various research activities such as collecting data, analyzing data, and submitting incorrect theoretical conclusions cost grant bucks. In the long run these costs can be reduced by carefully deducing an efficient series of studies to isolate the "correct" theory (i.e., that one theory among the five which, in the game's simulated reality, will be consistent with the results of all possible studies). When students think they have figured out which theory remains consistent with data across many studies, they submit their conclusion. If they are wrong it costs them grant bucks. If they are right they receive another grant. The game can then be played again with five new theories. By repeatedly playing the game with new theories, students can build up their grant bucks toward the 2000 grant bucks required as a minimum for their course grade. Moreover, the login names of the students with the top 10 grant buck earnings are posted automatically by a JAVA applet interacting with an Oracle database. Publicly posting the top 10 earnings allows those who wish to do so to compete with other students. Inevitably there is a large group of students who earn well above the minimum course requirements as they attempt to get the top grant buck score. (Any resemblance to the scientific community is purely coincidental.)

Game Story. Computer games typically provide a game story or other framework to give the game activities meaning. The Difference to Inference gives a player a choice of two stories, one based on the work of the seminal statistician, R. A. Fisher, and the other based on hurricane damage and deforestation. The game plays exactly the same whichever framework the player chooses. I will describe only the first framework here.

Historical Note. In the 1920's mathematician R. A. Fisher developed the statistical procedures known as the Analysis of Variance. The F test is named for him. Fisher worked in Britain and developed many of his procedures while working with farmers on agricultural yield. He developed inferential statistics which allowed him to determine if different plots of ground yielded different amounts of food. I probably shouldn't mention this because I probably won't hear the end of it, but Fisher worked a lot with the effects of fertilizers on yield. For that reason the statistics he developed, for example ANOVA, have sometimes been called, especially by critics, "manure pile statistics."

A Historically Based Puzzle. The current Difference to Inference puzzle will be based (with substantial changes in methodology) on this part of the history of inferential statistics. Let's say the dependent variable (DV) is the amount of corn in bushels per acre. The independent variable (IV) is placing or not placing a certain fertilizer on a plot of ground. There are 5 fields, each one divided up into a 7 by 7 grid of 49 plots. In each field the fertilizer was placed on a subset of these 49 plots during the growing season. Now it is harvest time. The shape of the area with fertilizer is a little different from field to field and is shown in red. The area in each field that has no fertilizer is shown in green. Here's the puzzle. There are 5 different fields. You have maps of the 5 fields showing the shapes of the fertilized areas in red. The yields should be higher in the red areas (fertilized) and lower in the the green areas (unfertilized). The problem is that the records indicating which map goes with which field have been lost. You are standing in one field. You know that one of the 5 maps applies to this field. Your job is to measure crop yields in this field to discover which map applies to it.

Game Strategy. Like most games, Difference to Inference offers strategic advice to players about game play.

Inference from difference. You are standing in a field looking for the edge of the pattern which divides fertilized (red) from non-fertilized (green) plots. To do this, you will be able to use a Horizontal or Vertical Tool to collect samples of data on crucial adjacent plots. Use the data from the samples to decide if there is a difference in yield in the two adjacent plots. After you collect data a few times you should be able to infer, from the differences you find (or don't find), which of the 5 maps applies to the field in which you are standing.

Seek the edge. Remember one of the fundamentals of human pattern perception: The important information is at the edge of the pattern.

Seek difference. Use the Horizontal Tool or Vertical Tool to determine if the yields (expressed as samples of numbers indicating bushels of corn per acre) of any two adjacent plots are the same or different. If they are different, then you've found an edge of the pattern. But difference alone is not enough. There are other challenges.

Differences that make a difference. One challenge is that various fertilizer patterns share the same shape on parts of their edges. Study the 5 maps noticing those crucial places where the shapes of the patterns are different. These places--where the 5 theories differ in their predictions--are where you should put your attention and do your research. These are the differences that make a difference. These are the crucial differences at the edge.