11.1 Paired marbles t-test

As a demonstration of the paired samples t-test the student are asked to choose one marble from the left side of a box, one marble from the right side of the a box. The marbles are presorted with less massive marbles on one side, more massive marbles on the other side. This avoids students having two marbles of the exact same mass. 

This term a split on 5.0 | 5.1 grams yielded excess massive marbles. 

The 5.1 marbles were then culled from both sides (three 5.1 gram marbles wound up in the less massive side, a scale measurement repeatability issue).  In prior terms culling a mass between the less and more massive marbles has led to extremely small p-values - there is a real risk of every student getting the mass difference correct. This example feels more realistic if some students do not correctly detect the difference in the masses. This allows one to say that the results could be random. If every student gets the mass difference correct, the argument that the results could be random is harder to make.

The new split was 5.0 | 5.2 with the 5.1 marbles now excluded. 

A marble is taken from each side.

This student guessed that the more massive marble was lighter. The difference was small at 0.2 grams. Data collection takes about 15 minutes. The spreadsheet was laid out ahead of time, except the student names, masses, and statistical functions up through the TTEST function.  

Although this example is used for a paired t-test, this example could also be done as a Chi-squared test. 

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