BH Statistics

November 2, 1999

Developing a Measure of Association

We examined scatterplots of the rankings produced by your PlacesRating scoring scheme and the rankings produced by other students' scoring schemes. We noticed that the scatterplots made it very clear that some schemes produced rankings very similar to each other and other schemes produced rankings that were very different from each other.

We also noticed that, with many scatterplots, it was difficult to say which one showed greater similarity between ranks.

The aim of this assignment is for you to devise a formula that, when applied pairwise to rankings produced by any three scoring schemes, produces "measures of association" that are consistent with what your eyes tell you when looking at their respective scatter plots. Put another way, if it is evident to your eyes that the scatterplot of variables X and Y shows a stronger association than does the scatterplot of variables X and V, then the number you get by applying your formula to X and Y should represent a stronger relationship than the number you get by applying your formula to X and V.

Follow the verbal instructions given in class on how to use the modified Places Rating data file.

Use this table to keep track of what you find.

 Formula: Variable 1 Variable 2 Formula’s Value Variable 1 Variable 3 Formula’s Value Consistent w/Graphs? Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No