We understand Dr Ghazal’s concern about the combined sample used in this 2-center study. However, the Michigan Growth Study (Ann Arbor) and the Bauru Dental School Growth Study (Bauru, São Paulo, Brazil) have published 2 atlases representing the cephalometric standards of their respective underlying populations. Considering that the combined sample of this study was selected from this set of subjects and that their evaluated characteristics had similarities with other population studies, we have no reason to believe that the Michigan and Bauru subjects enrolled in this study were not representative of the population characteristics. Furthermore, the sample size was calculated to achieve a representative number of subjects in each group, and this procedure was based on statistical parameters of other population studies, which have also used combined samples, including subjects from the University of Michigan Elementary and Secondary Growth Study (Ann Arbor), the Broadbent-Bolton Collection at the Bolton-Brush Growth Study Center (Cleveland, Ohio), and the Denver Growth Study (Colo). Thus, our sample was as representative as those of other studies regarding population parameters.
Furthermore, even if a sample is selected from a single population and subsequently divided into groups, there is an actual likelihood that these groups will have statistical differences and heterogeneous variances, especially if the sample division into groups was not proportional. Because of the smaller number of available orthodontic records, the Bauru subjects represented about a third of the total study sample. In spite of this, the comparison of the cephalometric standards between the Michigan and Bauru subjects showed a high statistical similarity regarding the means and variances ( Table I ). Only 4 of the 21 evaluated variables had significant differences between the Michigan and Bauru subjects, and only 2 of the 21 variables showed heterogeneous variances ( Table I ). Thus, these populations do not seem to be as different as suspected, and this should not be highlighted as a significant limitation of this study. In fact, it can be speculated that a similar participation of each growth study center in the sample composition would produce an even greater variance homogeneity. Probably, the similar age, sex distribution, and ethnicity (most subjects had white ancestry) may have significantly contributed to this homogeneity ( Table II ). Perhaps this should have been mentioned in the article.
|Variable||Michigan subjects, age 8.68 ± 0.75 y||Bauru subjects, age 8.71 ± 0.97 y||t test (P)||Brown-Forsythe test (P)|
|Maxillary skeletal components|
|Mandibular skeletal components|
|P-Nperp (mm)||−6.14||4.54||−5.02||3.51||0.116||0.013 ∗|
|Co-Go (mm)||45.75||3.26||47.84||2.95||0.001 ∗||0.338|
|SN.PP (°)||6.93||2.78||8.31||2.42||0.002 ∗||0.634|
|LAFH/PFH (%)||93.67||6.94||91.03||6.47||0.021 ∗||0.989|
|Maxillary dentoalveolar components|
|Mx1-NA (mm)||3.89||1.92||2.91||1.65||0.001 ∗||0.175|
|Mandibular dentoalveolar components|
|Md1.NB (°)||26.19||6.64||26.19||4.97||0.995||0.041 ∗|