Paired data presentations in statistics

The basic statistics of paired data was introduced in a week of lecture and gathered data examples. Monday I did time versus distance for a RipStik ridden at a constant velocity over a distance of 30 meters to produce an obviously linear relationship.

Wednesday was slated to be swizzle rate versus velocity. A decision to try  to find another system to use explored resting heart rate versus sit-rise-test scores. This exercise went variably well as an exercise, better in the second section than in the first, but generated ultimately unsatisfying data. Too, the SRT data is arguably interval level data at best, perhaps almost ordinal level for the students given the small number of unique values and narrow range of SRT scores they produce. 

Complicating interpretation of the results was the finding of a positive relationship where higher heart rates suggested the possible correlation to higher SRT scores. Upon further analysis, this would prove to be spurious and no relationship was found.  While students should meet variables that are not related, day two of paired variables with a population that only believes the word linear relationship applies to data which all fall exactly on the regression line is suboptimal. At this point the students need to break free from the idea that relationships hold only when all of the points are on the regression line. 

Friday wrapped up with a review of homework and a video on errors in the interpretation of correlation and the direction of the cause. Monday data was gathered for the third presentation of the term, bouncing balls.

Gina and Avonelle drop from 40 centimeters in the first exploration

The bouncing balls open data exploration asks the student to explore the relationships between drop heights and bounce heights for bouncing balls. There are two explorations to be completed. The first explores the relationship between drop heights and the height of the first bounce for different drop heights. The second explores the relationship the bounce number and the bounce height for each successive bounce when a bouncy ball is always dropped from a height of 100 centimeters. For each exploration the student is to generate a table, an xy scattergraph, add a trendline, and report appropriate statistics. This exercise is not a fully open data exploration but rather a guided data exploration in that a table, scattergraph, and trendline are requested of the students. 

Wednesday was a working day, presentations were on Friday morning.


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