Bootstrapped Mean Distributions and Sound Change

The bootstrap technique provides an estimate of how precisely located are the means of the distributions of F1-F2 measurements for each vowel. The bootstrap is discussed in detail in the Methods chapter. The clouds in Figures , ,  represent the intrinsic scatter in the estimate of the mean of each vowel's distribution. The true mean is some undetermined point within the cloud of points; if two clouds containing a couple hundred points each do not overlap each other, then it is quite unlikely that they could have the same mean.

Figure: Bootstrapped mean distributions.

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Figure: Bootstrapped mean distributions.

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Figure: Bootstrapped mean distributions.

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Figures such as these can most easily be interpreted by observing the relative positions of vowels in F1-F2 space, and comparing these relations to other known relations. Absolute frequencies are quite difficult to interpret (though not impossible, given information about the speaker's vocal tract dimensions, and given considerable experience in relating measurements to sound qualities). This discussion will focus on the clearly observable relative positions of vowel phonemes in this space.