FERTILIZE THE FIELDS

To learn about the story behind this game, please use the menu to the left.

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 before and 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. We have maps of the 5 fields showing the shapes of the fertilizer areas in red. But 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 discover which map goes with this field.

Difference to Inference

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.