Syllables per second versus seconds per syllable when measuring reading speed

SYLL/SEC AND SEC/SYLL SCORES ARE NOT EQUIVALENT, EVEN IF THEY COME FROM THE SAME TEST The diagnosis of developmental dyslexia requires measures of reading ability to be at least two standard deviations (SD) below age mean, encompassing accuracy, speed, and comprehension (ICD10, WHO, 1992). Reading speed is typically measured in either seconds per syllable (sec/syll) or syllables per second (syll/sec). Although syll/sec seems to be more common in text or sentence reading tests while sec/syll seems to be preferred for word and non-word reading tests, the two scores are often provided interchangeably for the same test. Italian standardized tests offer a clear example: the “official” text-reading test (Cornoldi et al., 1986, 2011) and the widely used Battery for the Diagnosis of Reading and Spelling Disabilities (Sartori et al., 1995, 2007) provide norms measured as either syll/sec or total reading time (i.e., sec/syll multiplied by a constant—the overall number of syllables), depending on the edition or the specific version of the text. The purpose of our work is to discuss the use of syll/sec and sec/syll when these are derived from a same, single test. Intuitively, in this situation syll/sec and sec/syll scores have exactly the same meaning—the underlying numbers, of syllables and of seconds, are the same, with the former being the numerator and the latter the denominator of the fraction or vice-versa. Indeed they are treated as generally equivalent. When reading speed is taken as an inclusion criterion for research studies, most papers do not even specify whether a sec/syll or syll/sec score was used. However, sec/syll and syll/sec scores from a same test, as any pair of mutual reciprocals, are non-linearly related to each other, with the curve being a hyperbolic function (Figure 1). This has a number of unsuspected consequences. First, diagnostic decisions can be completely different if one relies on one or the other score. For instance, a child whose sec/syll score is in the pathological range (z = +2.00) would be placed in the borderline range, close to normal, by using syll/sec (z = −1.36). Similarly, a syll/sec z-score of−1.73 which is borderline, couples with a sec/syll zscore of +3.00 indicating severe deficit (Figure 1, top-right table, Mean/SD ratio = 5; these data are from a Monte Carlo study reported in the next paragraph). In the range of gross impairment, discrepancies widen more and more, and can become huge. Indeed, syll/sec is bounded in the deficit direction, with the scale being extremely “compressed” in that region. By contrast, sec/syll has no limit in the pathology direction. Thus, a child who improves from 10 to 5 sec/syll (with normal children having Mean = 0.5 and SD = 0.1), will have a “huge” change of 50 z-units on the sec/syll scale, and a “minuscule” improvement of only 0.2 z-units in the compressed syll/sec scale. One might wonder exactly how large the expected sec/syll-syll/sec discrepancies are in a given real dataset. To answer this question we performed an extensive Monte Carlo simulation study (Figure 1, top-right table). The expected discrepancy is a function of the ratio between mean and SD of the standardization sample on one of the two scores. If the sample has a mean that is many times bigger than its internal variability, the discrepancy between the two diagnostic outcomes will in general be relatively small. Unfortunately, this is not the case in real standardization samples: mean values tend to be only 5– 10 times as large as the SD (Cornoldi et al., 1986, 2011; Sartori et al., 1995, 2007; Lewandowski et al., 2003). So discrepancies in real data are likely to be sizeable. The reader can use our table in Figure 1 to have an approximate idea of the discrepancy range of any given data set. Another kind of serious discrepancies can emerge when differences of differences (interaction terms in factorial designs) are considered. Two differences might well be equal on the syll/sec scale: a child might improve from z = −4 to z = −3 and another child from −2 to −1, but, because of the non-linear function relating the two scores, those improvements will in general be different on the sec/syll scale. Interaction terms are critical in intervention studies, which compare the effects of two or more types of treatment in different groups of children who are tested before and after treatment. It is well possible that an interaction is highly significant with one score, and nonsignificant with the other score, with obvious consequences on the conclusions of those studies. In summary, when one derives sec/syll and syll/sec scores from a same test performance, the pronounced non-linearity of the function relating them can produce important discrepancies between results obtained with each score, both in clinical practice and in experimental research.