Further Observations

The /r/-gliding diphthongs^7.21 fall into two groups according to how they pattern in Rita's speech, shown in Figure . For /iy, ey, /, the corresponding Vr vowels /ir, er, / are located about 300Hz to the back (lower F2 frequency), and 50 to 100Hz lower (higher F1 frequency). For /, ow/, on the other hand, the corresponding Vr vowels /r, or/ are located higher and to the back. /r/ is significantly raised and backed relative to //, while the mean measured nuclei for /or/ are barely different from those for /ow/ (the distributions of re-estimated means overlap, but just slightly, so the difference is probably genuine).

Jim's /, r/ form a single cloud, and thus share an identical nucleus; /y/ is raised, while /w/ is backed from //. (His /ir/ was not shown in Figure  in order to keep the chart readable; it lies between and overlapping with /ey, , er/.)

In all three charts, /r, or/ are back-raised from /, ow/ (/r/ insignificantly so for Judy and Jim). /ir, er/ are insignificantly different for Judy but well separated for Rita; this may reflect insufficient data to show Judy's distinction clearly.

/oy/ is not shown in Rita's chart because it occurs only 5 times, not enough to give a precisely located distribution of bootstrapped means. If plotted, this distribution extends from // to the high-back corner, overlapping the realizations of /ow, or, l/. For Judy, the estimated mean for /oy/ may be anywhere from the low-back corner to mid-back. Insufficient numbers of tokens make estimating a mean for this vowel difficult.

An illustration of a limitation of the bootstrap technique (and other statistical methods) was made by applying it, facetiously, to Jim's single token of /oy/. No matter how many times a sample of one is resampled, estimates of the mean taken from the resampled data are invariant. What appears to be a single ``+'' is actually two hundred re-estimated means laid on top of one another, taken from this sample of one data point, an obvious misuse of the bootstrap technique. (Similarly, the standard deviation of a sample of one is always zero.) Statistics require reasonable amounts of data.

The distribution of reestimated means for syllabic /l/ is also not shown. For Rita, it overlaps /ow, or/ and ranges up toward the high-back corner. It does not overlap /, , uw/ and other vowels located to its front.