Keeping the overlap of the distributions in mind, let's consider how much confidence we may have in the claim that the means are different for these pairs. As discussed in the Methods chapter, I use a rather new statistical technique, called the bootstrap resampling method, to evaluate this kind of claim. This technique is useful in determining the degree of precision to be attributed to any estimated statistic. Here the relevant statistic is the mean of a given vowel's distribution in F1-F2 space. Again, the bootstrap resampling method works as follows. A large number of resampled data sets are constructed by randomly choosing from the original data set (of size N) an equal number (N) of observations, with replacement. The mean of each of the new resampled data sets is calculated and plotted, so that the distribution of resampled means may be seen directly. If less than 5% of the re-estimates for one distribution overlap with those of another one, then they are significantly different with estimated probability 33#3395%. The distribution of resampled means shows directly the amount of scatter intrinsic to the estimate of the mean taken from the original sample.
Making use of this method, Figures and show the distributions of 200 resampled means for each of the non-rhotic Jamaican Creole vowels, for both Juba and Roasta.
Juba's chart shows quite clearly that the long vowels occupy the corners of the vowel space, while the short vowels are less peripheral and lower. Each vowel is very clearly different from every other vowel, on average. None of the distributions of re-estimated means overlap with any other. In fact, no pair of vowels have any overlap; even /ii, ie/ do not overlap, though they are very close to each other, even more for Roasta than for Juba. The clear differences here are even clearer when the differences between long and short vowels is considered. The long and short pairs of vowels have quite clearly different means. In fact, no long vowel has a nearest neighbor which is its corresponding short vowel, for either speaker. The converse is true for the short vowels, too. Every vowel's nearest neighbor is a vowel that is not its short or long counterpart. We can conclude with complete confidence that long and short vowels have very different average nuclei.