## Stochastic Patchwork

Stochastic Patchwork is one of several interactive models for probability and statistics authored in the NetLogo modeling-and-simulation environment. The model is part of ProbLab, a curricular unit designed to enrich student understanding of the domain. The online unit package will include a suite of models, student worksheets, and a teacher guide. Below is an applet of Stochastic Patchwork. You can interact with this model by changing the slider values and then pressing Setup and Go to run this model under different settings. You may want to slow down the model in order to get to know it -- use the 'adjust speed' slider that is on the top-left corner of the graphics window. For more details, please see the model itself in the NetLogo library.

CM ProbLab: Stochastic Patchwork -- Connecting independent and dependent probabilities.
Don't see nothin'?

Gist

The %-TARGET-COLOR slider controls the probability of each square to be green, and the histogram shows the distribution of sample means. If a sample is completely green, the histogram will register a rise over the x-axis value '100%.' If 4 out of 9 squares are green, the histogram will register a rise over the x-axis value 100 * 4/9, that is at about 44.4%. What is the relation between the histogram and the %-TARGET-COLOR? This relation is deceivingly simple, due to the arrangement of the interface elements. Note how the probability slider neatly subtends the x-value of the plot. While the experiment is running, drag the probability slider and observe the shape of the distribution. One literally feels that one is dragging the histogram. However, this "mechanical" maneuver enfolds the deep relation between the 'micro' and the 'macro' in the domain of probability: The slider controls the probability of each square to be green, but the histogram shows the overall distribution of sample means taken from successive compound events.

Questions to Ponder

• Is the distribution range related to the probability? Should it be? Is there something wrong with the model? How long should we run it?

• Is the distribution 'normal' for all probability values?

• Why is the histogram denser for larger sample blocks?

• What, actually, are we measuring -- the greenness of the block, or the chance for an individual square to be green?

• Does it make sense to speak of a square as being .84 green? If not, how should we interpret a mean of .84 or 84% green?

• Is there a population that these samples are taken from? If so, where exactly is this population? How is this like or unlike statistics?

• How many different permutations are there for each block size, and how may this be related to the distribution range?

Stochastic Patchwork is a more general case of 9-Blocks, a ProbLab model in which the sample size is fixed at 3-by-3 and the probability is fixed at 50%. Stochastic Patchwork is also closely related to the ProbLab model 9-Block Stalagmite, in which samples move in the graphics window and sort themselves so as to reflect the sample-mean distribution.

[last updated July 8, 2005]