5.5: Summary

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We have looked at three case studies, one involving nominal, one ordinal and one cardinal data. In each case, we were able to state a hypothesis and derive a quantitative prediction from it. Using appropriate descriptive statistics (percentages, observed and expected frequencies, modes, medians and means), we were able to determine that the data conform to these predictions – i.e., that the quantitative distribution of the values of the variables GIVENNESS (measured by PART OF SPEECH, ANIMACY and LENGTH across the conditions S -POSSESSIVE and OF -POSSESSIVE fits the predictions formulated.

However, these distributions by themselves do not prove (or, more precisely, fail to disprove) the hypotheses for two related reasons. First, the predictions are stated in relative terms, i.e. in terms of more-or-less, but they do not tell us how much more or less we should expect to observe. Second, we do not know, and currently have no way of determining, whether the more-or-less that we observe reflects real differences in distribution, or whether it falls within the range of random variation that we always expect when observing tendencies. More generally, we do not know how to apply the Popperian all-or-nothing research logic to quantitative predictions. All this will be the topic of the next chapter.