Paired t-test fail

The small size of the class allowed for a paired t-test paper aircraft flight experiment. I asked the students to build any kind of paper airplane they knew to make. Then (curricular intervention) I taught them a new design with the hope that the new design would outperform their planes. The result was useful from the perspective of demonstrating a non-significant t-test for paired dependent variables.

spreadsheet

This would be hard to do in a larger class - the process takes times. The idea is that this mimics the sort of study in education or health where a pre-test or pre-survey is done, an intervention is taken (a new reading program, a new approach to treating symptoms for chronic pain that does not respond well to pain killers, etc.) and then a post-test or post-survey is administered. 

The failure of the above was actually quite useful as it allowed for coverage of the issue of publication pressures, p-hacking, and the replication crisis seen in many fields. This null result would not be deemed worthy of publication. And the loss of null result articles means a terrible bias in so many fields of science.

The function driving this is a two-tailed TTEST for a difference of sample means for paired data. Yes, there were only four students in attendance. An earlier article covered why the class is so small. And, yes, I should probably be doing a Bayesian analysis given that priors are known - there is an average of 562 cm 799 prior plane flights. There is prior knowledge of how this system behaves. That said, I do not know how to do such an analysis given the above data, nor how the prior information would necessarily impact this paired comparison. I have no prior knowledge of the paper aircraft building skill of these particular students. Ultimately I cannot see how use of a frequentist approach would be unwarranted in this situation.