Defense Date


Document Type


Degree Name

Master of Science



First Advisor

Walter H. Carter Jr.


This thesis demonstrates that the assumption of normality used by Goodson results in the underestimation of the type I error rate of the tolerance method by a factor of 10. This underestimation is due to the positive kurtosis demonstrated in the distribution of replicate differences. Therefore, the assumption of normality does not seem warranted. It is shown here that a resampling technique more accurately estimates the type I error rate.

The estimates of false positive rates have important implications in the field of periodontics. When diagnostic decisions are based on single measurements, false positive rates are high. Even when thresholds as high as 3 mm. are used, over 3 out of 10 sites identified as "changed" have not changed. Unfortunately, in the clinical practice of periodontics, single measurements are commonly used. Therefore, clinicians who make treatment decisions based on attachment level measurements, may be treating a large percentage of sites that have not undergone destructive periodontal disease. Clinical periodontists generally regard a loss of attachment of 3 mm. or more as evidence of progressively worsening disease requiring additional therapy. The consequences of treating areas that are erroneously concluded as having progressed have to be compared to the consequences of not treating areas that are progressing. If a clinician treats sites when a change of 3 mm. in attachment level is detected, it is likely that as many as 32% of the sites may not have progressed. However, if the change in attachment level is real and the site is not treated, a significant proportion of the attachment may be lost. Changes of 3 mm. are large compared to the length of the root of the tooth. Weine (1982, p. 208-209), using Black's (1902) description of tooth anatomy, presents average root length of 13 categories of teeth. Average root lengths range from 12 to 16.5 mm. for the 13 categories. If a tooth with a root of 14 mm. (near the middle of the range of average tooth length) has a change in attachment level measurements of 3 mm., the clinician is faced with a dilemma as to whether the site should be treated. The dilemma is increased if prior to the change of 3 mm., the site had already lost 50% of its attachment. In this situation the 3 mm. change represents nearly half of the remaining attachment. For these reasons, better measurement techniques would be beneficial in the clinical practice of periodontics.

A controversy exists in the periodontal literature on the ability of single attachment level measurements to find actual change in attachment level. Two recent reports are in general agreement with this study. Imrey (1986) evaluates the ability of single measurements of attachment level to find change in attachment level. He concludes: "If true disease is uncommon and sensitivity to it is not high, these false positives may exceed in number the true positives detected" (p. 521). Ralls and Cohen (1986) reach similar conclusions: "the major issue is that 'bursts' of change can be explained by chance events which arise from measurement error and which occur at low but theoretically expected levels" (p. 751). The results of the present research demonstrate that a large percentage of the perceived change in attachment level is due to measurement error, but not to the degree that Imrey (1986) and Ralls and Cohen (1986) suggest. These researchers attribute almost all the attachment level changes to measurement error. In contrast, Aeppli, D. M., Boen, J. R., and Bandt, C. L. (1984) reach a different conclusion: "using an observed increase of greater than 1 mm. as a diagnostic rule leads to high sensitivity and yet satisfactorily high specificity" (p. 264).

All three of the above referenced studies base their conclusions on estimates of sensitivity and specificity. The methods of obtaining estimates of sensitivity and specificity vary between the studies. Aeppli, D. M., Boen, J. R., and Bandt, C. L. base their estimates of specificity and sensitivity on a calibration study involving 34 patients and 3 examiners. Their distribution of differences in replicated measurements is similar to the distribution that Goodson (1986) reports. Irnrey (1986) and Ralls and Cohen ( 1986), instead of using actual data, simulate the distribution of differences by using a normal approximation with standard deviations of 1.125 mm. and 1 mm. respectively. Even though the methods of obtaining data vary, all the reports obtain high values of specificity (Table 6). However, estimates of sensitivity vary both within and among the three studies. Table 6 demonstrates that for similar thresholds the studies obtain a wide range of estimates of sensitivity. Within each study estimates of sensitivity are shown to be highly dependent on the assumed magnitude of actual change and the threshold used to detect the change. As the threshold decreases or the assumed attachment level change increases, sensitivity increases. The possible wide range of estimates that can be obtained within a study is demonstrated by Ralls and Cohen (1986). Their estimates of sensitivity range from .0668 to .9772. As discussed in chapter 1, the broad range of estimates of sensitivity and those estimates' basis on arbitrary assumptions brings to question their value.


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