clinical measurements are generally imprecise because they can not be measured directly 
 ( such as an organ size ) , or they are difficult to achieve ( such as knee joint 
 circumference ) .
hence , different methods of measuring the same phenomenon or different 
 ways of measuring the same variable on different types of physical records have been 
 proposed . however , even when a method is universal , double readings of the same quantity 
 by the same method and the same operator in order to confirm that readings agree well 
 enough are advised . by definition , repeatability is the closeness of agreement between successive readings 
 obtained by the same method on the same material and under the same condition ( same 
 operator , same apparatus , same setting and same time ) .
reproducibility is the closeness 
 of agreement between individual readings obtained by the same method on identical 
 testing material , but under different conditions ( different operator or different 
 apparatus or different setting or different time ) .
lack of precision means that repeated 
 measures of the same value under specified conditions are spread out or scattered . in orthodontics , locating the same point on the same image in repeated acts of landmark 
 location is always a daunting task .
( 1974 ) , in a classical paper , compared the positions of 15 
 landmarks calculated by the same observer from two lateral cephalometric radiographs 
 taken consecutively on each of 25 children and found statistically significant 
 differences for all of them .
according to 
 those authors , the greatest errors arise in point identification rather than in 
 measurement , but silveira and silveira ( 2006 ) performed various cephalometric measurements three times using 
 40 digital radiographs and concluded that differences among triple readings were 
 significant for most of the cephalometric measurements analyzed .
battagel ( 1993 ) reviewed the literature related to 
 the assessment of measuring cephalometric radiographs and provided some suggestions for 
 estimating all types of errors .
( 2005 ) studied statistical methods for evaluating 
 reproducibility of quantitative measurements in orthodontics and also offered many 
 suggestions .
the aim of this paper is to suggest that when repeatability needs to be assessed , a 
 control chart for means should be set up if a patient 's records are traced on the same 
 occasion , which is a common practice .
a control chart gives limits of agreement , 
 identifies possible outliers , makes the calculation of a coefficient of repeatability 
 straightforward and shows it when a serial correlation exists . if the order in which the 
 records were measured was randomized in a way that prevented the researcher from knowing 
 which patient he / she was measuring or re - measuring , the well - known plot proposed by 
 bland and altman ( 1986 ) should be set 
 up .
the data used in this study are from houston ( 1983 ) , a classical paper cited worldwide when repeatability , 
 reproducibility or precision in orthodontics are mentioned . for analyzing repeatability , 
 houston ( 1983 ) used pearson 's 
 correlation coefficients and paired t - tests , as shown in table 1 .
data analysis for upper - arch length projected onto the midsagittal plane in 
 millimeters measured from models and cephalometric radiographs , each on two 
 separate occasions ( in mm ) source : houston ( 1983 ) in this paper , scatter plots and regression lines both for radiographs and models were 
 also drawn .
control charts for differences between readings were constructed and 
 out - of - control points were counted .
upper and lower limits and coefficients of 
 repeatability were calculated . for discussion , standard deviations of the means assuming 
 that mean differences are zero , which have been popularized in orthodontics and facial 
 orthopedics as the dahlberg error , were also calculated .
a scatter plot of the two radiograph readings with the regression line is shown in figure 1 , and a scatter plot of the two model 
 readings with the regression line is shown in figure 
 2 .
intercept coefficients are not significantly different from zero ( p=0.0736 
 for radiographs and p=0.2854 for models ) , and slopes are significantly different from 1 
 for radiographs ( p=0.0401 ) and non significant for models ( p=0.3821 ) .
double readings of radiographs with the line of equality double readings of models with the line of equality control charts for the mean of the differences between radiograph readings are shown in 
 figure 3 and for models in figure 4 . an error analysis for houstons data of upper arch length 
 onto the midsagittal plane in millimeters measured from models and cephalometric 
 radiographs
coefficients 
 of repeatability were calculated by 
 the following equation : control chart for the mean of differences between radiographs readings control chart for the mean of differences between models readings error analysis for upper - arch length projected onto the midsagittal plane in 
 millimeters measured from models and cephalometric radiographs in health sciences , differences within meansd are generally considered 
 clinically unimportant .
differences between meansd and mean1.96 sd are 
 in a warning zone and differences out of these limits are out - of - control points .
their 
 percents are shown in table 2 for both methods 
 of measuring upper - arch length projected onto the midsagittal plane .
the correlation coefficients shown in table 1 
 look impressive , but they do not mean agreement . agreement is perfect only when the 
 points lie along the regression line , which means , a line with equation y = x , while 
 correlation is perfect when the points lie along any straight line . for radiographs , 
 although the correlation coefficient is 0.9951 , the slope is significantly different 
 from 1 .
houston ( 1983 ) has pointed 
 out there was a significant difference between measurements of radiographs and 
 considered standardization was a requirement for better results .
houston ( 1983 ) also calculated the correlation 
 coefficient between the averaged measurements ( time 1 and time 2 ) from models and 
 radiographs , which is 0.971 even the percent of radiograph enlargement is approximately 
 13% .
a control chart for analyzing errors in double readings is a better statistical tool , 
 since it is used to detect excessive process variability .
it serves to determine whether 
 the extent of variation of errors in double readings does not exceed that which is 
 expected , that means , an average not different from zero and , even considering the 
 natural statistical variability of the process , a coefficient of repeatability small in 
 relation to the measurement taken .
differences within meansd are clinically unimportant . differences between 
 meansd and mean1.96 sd are in a warning zone and differences out of 
 these limits are out - of - control points . out - of - control
therefore , the clinician should look for 
 them and decide whether they are in an acceptance zone , considering they should be zero . 

number of points in the warning zone and number of out - of - control points are shown in 
 table 2 for both methods of measuring upper 
 arch length projected onto the midsagittal plane .
it has to be noted that averages both 
 from radiographs and models are above zero and there are out - of - control points more than 
 2 sd far from means .
it has to be pointed out that many papers consider precision can be estimated by a 
 statistic known in orthodontics and facial orthopedics under the name of dahlberg 
 error .
it is well known that 
 when readings are independent , identically distributed random variables , sums or 
 differences between readings are independent , identically distributed random variables 
 with mean zero and variance : if a large number of readings are performed by the same operator and the same method on 
 the same material ( such as a blood sample or an oil sample ) , it can be assumed that 
 measurements are distributed closely to the true value . if readings are performed in 
 duplicates and the difference between a duplicate is calculated , it can be seen as a 
 difference between two values taken at random from the same probability curve .
when 
 another duplicate is read by the same method and the same operator on another sample of 
 the same material , these two readings can also be seen as two values chosen at random 
 from another probability curve of the same type as that of the previous one . by 
 continuing the process
, a series of differences is obtained that conforms to the series 
 of differences which would be obtained by choosing , at random and repeatedly , two values 
 from one and the same probability curve . under such circumstances , an estimate of the 
 standard deviation is calculated by adding the squares of the differences ( because the 
 mean is zero ) , dividing the sum by two times the number of differences ( because the 
 variance of the difference is 2s2 ) and extracting the root of the resulting figure , that 
 is , by calculating : this estimate of the standard deviation is a measure of dispersion ( and , inversely , 
 precision ) when double readings are performed on the same material ( a standard practice 
 in laboratories , which can be assumed as independent and identically distributed 
 variables ) .
this is not the case in cephalometric investigations , where double readings , 
 known as paired observations , are performed on the same radiograph .
therefore , 
 radiographs taken from different patients not only imply measurement errors , but also 
 take into account the variability of patients . anyway , the standard deviation using the dahlberg equation is 
 sx=0.437 mm for radiographs and 
 sx=0.345 mm for models , which does not have a 
 straightforward interpretation . in other areas , such as chemistry , where a gold standard 
 is always provided , the uncertainty of the measurement can be tested by an f - test .
on 
 the other hand , it is easy to interpret that the expected percent of differences between 
 double readings bigger than meansd is approximately 37% for radiographs and 
 approximately 27% for models .
in the study of repeatability , neither the correlation coefficient nor the regression 
 analysis is appropriate . the standard deviation dahlberg ( 1946 )
gives in his textbook can be used only when 
 readings are independent and identically distributed random variables and differences 
 between readings are on average zero , which is not the case in cephalometric 
 investigations . in clinical practice ,
when double readings are taken , a t - test should be carried out for 
 testing whether differences between double readings are on average zero or there is a 
 systematic error .
standard deviation is of course a measure of dispersion ( or , 
 inversely , precision ) and so is the coefficient of repeatability , but a control chart 
 should also be used for detecting outliers .
measurements made in out - of - control points 
 are uncertain and a risk of adverse results in treatment or diagnosis .
 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 . 
INTRODUCTION
MATERIAL AND METHODS
RESULTS
DISCUSSION
CONCLUSION