11.1 Paired t-test for a pairwise difference of means

Attendance has been sketchy. Facing a very small sample I opted to partially rig the paired marbles t-test exercise. In the past students have randomly selected marbles which had led to small differentials and ties where the two marbles are the same mass.

This term I rigged the game. Marbles less than or equal to 4.8 grams on one side, marbles greater than or equal to 5.2 grams on the other side. 

With seven students the p-value was not significant at an alpha of 0.05. Note that there was a near miss risk of 100% correct identifications. This suggests that exclusion of 4.9 and 5.1 gram marbles should not be done. A study of 45 differences of 0.1 grams either way produced a p-value of 0.00002. Using a chi-square test obtained a p-value of 0.0006. Students can detect differences as small as 0.1 grams. Of course, moving in a direction to make the call harder will result in a higher risk of failing to reject the null hypothesis, and in this demonstration the intent is to reject null without hitting that 100% success rate. Tough balancing act when students can theoretically determine a difference as small as 0.1 grams. 

Sonya arrived and tipped the result over to significance. That opened the door to an explanation of how sample size impacts study results.