Abstract
Statistical analysis of data is crucial in cephalometric investigations. There are certainly excellent examples of good statistical practice in the field, but some articles published worldwide have carried out inappropriate analyses.ObjectiveThe purpose of this study was to show that when the double records of each patient are traced on the same occasion, a control chart for differences between readings needs to be drawn, and limits of agreement and coefficients of repeatability must be calculated. Material and methodsData from a well-known paper in Orthodontics were used for showing common statistical practices in cephalometric investigations and for proposing a new technique of analysis. ResultsA scatter plot of the two radiograph readings and the two model readings with the respective regression lines are shown. Also, a control chart for the mean of the differences between radiograph readings was obtained and a coefficient of repeatability was calculated. ConclusionsA standard error assuming that mean differences are zero, which is referred to in Orthodontics and Facial Orthopedics as the Dahlberg error, can be calculated only for estimating precision if accuracy is already proven. When double readings are collected, limits of agreement and coefficients of repeatability must be calculated. A graph with differences of readings should be presented and outliers discussed.
Highlights
Clinical measurements are generally imprecise because they cannot be measured directly
In Orthodontics, locating the same point on the same image in repeated acts of landmark location LV DOZD\V D GDXQWLQJ WDVN 0LGWJDUG HW DO7 (1974), in a classical paper, compared the positions of 15 landmarks calculated by the same observer IURP WZR ODWHUDO FHSKDORPHWULF UDGLRJUDSKV taken consecutively on each of 25 children and IRXQG VWDWLVWLFDOO\ VLJQL¿FDQW GLIIHUHQFHV IRU DOO RI WKHP 'LI¿FXOWLHV LQ ODQGPDUN LGHQWL¿FDWLRQ DUH emphasized by Houston, et al.4 (1986)
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Summary
Clinical measurements are generally imprecise because they cannot be measured directly (such DV DQ RUJDQ VL]H RU WKH\ DUH GLI¿FXOW WR DFKLHYH (such as knee joint circumference). In Orthodontics, locating the same point on the same image in repeated acts of landmark location LV DOZD\V D GDXQWLQJ WDVN 0LGWJDUG HW DO7 (1974), in a classical paper, compared the positions of 15 landmarks calculated by the same observer IURP WZR ODWHUDO FHSKDORPHWULF UDGLRJUDSKV taken consecutively on each of 25 children and IRXQG VWDWLVWLFDOO\ VLJQL¿FDQW GLIIHUHQFHV IRU DOO RI WKHP 'LI¿FXOWLHV LQ ODQGPDUN LGHQWL¿FDWLRQ DUH emphasized by Houston, et al. (1986). According to those authors, the greatest errors arise in point LGHQWL¿FDWLRQ UDWKHU WKDQ LQ PHDVXUHPHQW EXW Silveira and Silveira (2006) performed various. Martelli Filho, et al. (2005) studied statistical methods for evaluating reproducibility of quantitative measurements in Orthodontics and offered many suggestions
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