Paper aircraft flight distances run as a two independent samples t-test for a difference of means
Usually the "paper aircraft exercise" is done as an example designed to capture a known, pre-existing population mean. This term a string of rainy mornings prevented this exercise from occurring in chapter ten. Good weather landed on the morning of 11.2, so I opted to divide the class into a group one and a group two and then testing to see which group, if either, could achieve a greater average flight distance. Given that there were no criterion for being in one or the other group (the students were split by the side of the room in which they choose to sit), the expectation would be no difference in the means.
Distances were measured perpendicular to the building. Aircraft that landed on the first floor porch were negative distances.
Once the data was entered and the means were calculated I asked the class, "If we threw the planes again, would we get the same average distance? Could the averages reverse the result of which group had the higher average distance?" Then I noted that we did not need to throw the planes again, the standard deviation in the data, the variation between the planes, provided an estimate of the variation in subsequent flights. And the sample means from those hypothetical future flights would distribute normally around the population mean for those samples. This allows us to use statistics to determine whether the mean might be different in a hypothetical future run. There are two sections of the course, 8:00 and 9:00, each section was split in two.
The results were as anticipated, no statistically significant separation in the means.
The 95% confidence intervals for the samples all overlap each others sample means, there is no statistically significant separation. And for each class, the p-values (unlabelled 0.76 and 0.42 above) are not surprising. We fail to reject a null hypothesis of no difference. Of course if the test were of all four samples, then a Bonferroni correction would be necessary, but the result would not change because there is no significant difference.
This exercise went well structurally. Whether the students learned from this remains to be assessed.
Folding
Flying
Distribution on the ground
Distances were measured perpendicular to the building. Aircraft that landed on the first floor porch were negative distances.
Once the data was entered and the means were calculated I asked the class, "If we threw the planes again, would we get the same average distance? Could the averages reverse the result of which group had the higher average distance?" Then I noted that we did not need to throw the planes again, the standard deviation in the data, the variation between the planes, provided an estimate of the variation in subsequent flights. And the sample means from those hypothetical future flights would distribute normally around the population mean for those samples. This allows us to use statistics to determine whether the mean might be different in a hypothetical future run. There are two sections of the course, 8:00 and 9:00, each section was split in two.
The results were as anticipated, no statistically significant separation in the means.
The 95% confidence intervals for the samples all overlap each others sample means, there is no statistically significant separation. And for each class, the p-values (unlabelled 0.76 and 0.42 above) are not surprising. We fail to reject a null hypothesis of no difference. Of course if the test were of all four samples, then a Bonferroni correction would be necessary, but the result would not change because there is no significant difference.
This exercise went well structurally. Whether the students learned from this remains to be assessed.
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