Example 6.1 Figure 6.1 shows 19 measurements of wind direction and ozone concentration taken at 6.00am at four-day intervals between April 18th and June 29th, 1975, at a weather station in Milwaukee. (The data are listed in Appendix B18.) It is of interest to ascertain whether there is any association between ozone concentration and wind direction.

Example 6.2 Figure 6.2 shows the orientations (θi) of the nests of 50 noisy scrub birds along the bank of a creek bed, together with the corresponding directions (ϕi) of creek flow at the nearest point to the nest. (The data are listed in Appendix B19.) The separate data sets for the nest orientations and the creek flows are shown, together with a joint data plot. The directions of creek flow suggest that the creek has a small bend in the vicinity of data collection. The joint data plot consists of a scatterplot of the values (θi, ϕi), i = 1,…, n, together with a duplicate set (θi + 360°, ϕi + 360°), i = 1,…,n (shown here in radians) to avoid difficulties due to transferring the data to the x-y plane. […]