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Background: This project relates prevalence-time data, incidence rate data, age of onset, system plateau level and system time constant, using exponential equations, as they apply to progressive myopia, useful over several decades. Methods: Cross-sectional refractive data is analysed for nine studies with a total number of subjects at 444.6 K (345, 981, 7.6 K, 39, 421 K, 383, 2 K, 12 K, 255), with ages ranging from five to 39 years. Basic exponential equations allow calculation of the prevalence versus time function Pr(t) as a percentage and the incidence rate function In(t) (percentage per year), system time constant t0 (years), onset age t1 (years) and saturation plateau level (percentage). Results: The prevalence of myopia as a function of time Pr(t) (years) and incidence of myopia as a function of time In(t) (percentage per year) are continuously generated and compared with prevalence/incidence data from various reports investigating student populations. For a general medical condition, typical values for time constant t0 may range from one week to five years, depending on the health condition. Typical plateau levels for myopia may range from 35 to 95 per cent. Herein, data from nine demographic studies of myopia are analysed for prevalence Pr(t) with an accuracy within 14 per cent and incidence In(t) within 2.6 per cent per year, onset t1 = 1.5 years, time constant t0 = 4.5 year. By comparison, linear regression can predict the prevalence of myopia Pr(t) within 11 per cent and estimates a constant incidence rate for myopia In(t) of 4.7 per cent per year (95 per cent CI: 2.1 to 7.3 per cent per year]. Conclusions: The initial incidence rate at onset age In(t1) and system time constant t0 are inversely related. For myopia, onset age, time constant and saturation plateau level are fundamental system parameters derived from age-specific prevalence and incidence data.

The hypothesis was tested that syntactic constructions would be easier to deal with when they were being used for their natural semantic function rather than for an unnatural function. The experimental task required subjects to decide whether pairs of sentences had the same or a different meaning. The results confirmed the prediction that deciding about pairs of affirmative and negative sentences would be relatively facilitated when the negative was performing its natural function of signalling a change of meaning. In contrast, performance was facilitated when pairs of active and passive sentences had the same meaning. These results are discussed in connexion with the relation between syntactic competence and semantic context.

The primary finding of this research is that the prevalence ratio of high myopes (R < -6.0 D) to common myopes is expected to increase from 15% entering college to 45% or more after college and graduate school. These statistics are particularly relevant to the many years of study required by M.D., Ph.D., and M.D./Ph.D. programs.

The experiments reported here were designed to investigate the effects on linguistic performance of varying the interaction between the syntactic form of sentences and their semantic function. The experimental task required subjects to decide whether pairs of sentences had the same or a different meaning. The results of Experiment I confirmed the prediction that the times taken to decide about pairs of affirmative and negative sentences would be shorter when the negative was performing its natural function of signalling a change of meaning. To a lesser extent, performance on pairs of active and passive sentences was facilitated when the two sentences meant the same thing. These results were found both with “meaningful” sentence material and with abstract x–y sentences. A second experiment provided a control for the possibility that the results were due to syntactic derivational factors rather than to the semantic function interaction.

Wales and Grieve (1969) report an experiment in which they show that a factor of "confusability" affects the comprehension of affirmative and negative sentences, and then claim that this is a relevant factor in explaining the difficulty of negatives. The present paper submits arguments and experimental evidence to dispute this claim.