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The apparent lack of agreement between the two measuring techniques is thus largely correctable. This procedure closely resembles the calibration of a measuring instrument. The determination of the functional relation itself, i. The Pearson correlation coefficient 2 between the two measuring techniques is often considered to demonstrate a linear relationship thus, a specific kind of functional relationship between them.
Indeed, a coefficient with a high absolute value near 1 or —1 does indicate such a relationship. A common error, however, is to misinterpret the implications of significance tests that are applied to correlation coefficients.
A finding that the correlation between two measuring techniques differs significantly from zero does not necessarily indicate that the two techniques are in good agreement. Even the slightest, practically irrelevant relationship between two techniques could, in principle, yield a statistically significant finding of this type.
We now turn to the topic of ratings on a nominal scale. Song et al. What does this mean in concrete terms? The diagnoses of the two doctors are shown in the Table in Box 1. Let us suppose that two doctors Raters 1 and 2 examine patients for the presence of a particular disease and then state whether each patient is healthy or ill. Suppose further that Raters 1 and 2 arrive at the same diagnosis in 70 of patients. The above contingency table contains all of the relevant data on the absolute and relative frequencies of agreement and disagreement in our fictitious example.
Yet, even if one rater or both were assigning diagnoses at random, the two of them would sometimes agree. For clarity in the following discussion, we will not always represent fractions and probabilities as percentages, but will sometimes write them as numbers between 0 and 1 instead: for example, 0.
We do so by dividing the value p 0 — p e , whatever it may be, by the highest value it can theoretically have, which is 1 — p e. The two doctors arrived at the same diagnosis in 70 of cases.
This figure alone, however, is not very useful in assessing concordance, because a certain number of like judgments would be expected even if one of the doctors or both! On average, in this particular example, approximately 57 agreements would be expected by chance alone, as explained in Box 1. This would be a very discouraging finding indeed. A value of —1 would mean that the two raters arrived at opposite judgments in absolutely every case; this situation clearly arises very rarely, if ever.
Box 2 generalizes the foregoing discussion to nominal rating scales with any number of categories, i. The contingency table below applies to the more general problem of comparing two raters who use a rating scale with an arbitrary number of categories—not necessarily two, as in our discussion up to this point. The row and column totals are a i.
In general, the value of any descriptive statistic e. For this reason, descriptive statistics are usually reported with a confidence interval. In the present case, we are making use of an approximation to the normal distribution. We can now calculate a confidence interval for the numerical example presented above in Box 1 and discussed in the corresponding section of the text. Using the formula above, we find:. A statistically significant test result is often wrongly interpreted as an objective indication of agreement.
Thus, the use of significance tests to judge concordance is a mistake. When comparing ordinal ratings, one may wish to give different weights to the differences between two consecutive ratings e. A weighted kappa is used for this purpose. Interrater agreement can be assessed in other situations, too, e.
Sensitivity and specificity are often used to compare a dichotomous rating technique with a gold standard 8. These two statistics describe the degree of agreement between the technique in question and the gold standard, in each of the two subpopulations that the gold standard defines. Statistical methods of assessing the degree of agreement between two raters or two measuring techniques are used in two different situations:.
In the first situation, it is advisable to use descriptive and graphical methods, such as point-cloud plots around the line of agreement and Bland-Altman diagrams. Although point clouds are more intuitive and perspicuous, Bland-Altman diagrams enable a more detailed analysis in which the differences between the two raters are assessed not just qualitatively, but also quantitatively. The limits of agreement in a Bland-Altman diagram may be unsuitable for assessing the agreement between two measuring techniques if the differences between measured values are not normally distributed.
In such cases, empirical quantiles can be used instead. The distribution of the differences between two measured values can be studied in greater detail if, as first step, these differences are plotted on a histogram 3. In many cases, when the two measuring techniques are linked by a good linear or other functional relationship, it will be possible to predict one of the measurements from the other one, even if the two techniques yield very different results at first glance.
The Pearson correlation coefficient is a further type of descriptive statistic; it indicates the presence of a linear relationship. A significantly nonzero correlation coefficient, however, cannot be interpreted as implying that two raters are concordant, as their ratings may still deviate from each other very strongly even when a significant correlation is present. The mere demonstration that a correlation coefficient differs significantly from 0 is totally unsuitable for concordance analysis.
Such tests are often wrongly used. As alluded to above, correlation is not synonymous with agreement. Correlation refers to the presence of a relationship between two different variables, whereas agreement looks at the concordance between two measurements of one variable. Two sets of observations, which are highly correlated, may have poor agreement; however, if the two sets of values agree, they will surely be highly correlated.
The other way to look at it is that, though the individual dots are not fairly close to the dotted line least square line;[ 2 ] indicating good correlation , these are quite far from the solid black line, which represents the line of perfect agreement Figure 2 : the solid black line. In case of good agreement, the dots would be expected to fall on or near this the solid black line.
Scatter plot showing correlation between hemoglobin measurements from two methods for data shown in Table 3 and Figure 1. The dotted line is a trend line least squares line through the observed values, and the correlation coefficient is 0.
However, the individual dots are far away from the line of perfect agreement solid black line. For all the three situations shown in Table 1 , the use of McNemar's test meant for comparing paired categorical data would show no difference.
However, this cannot be interpreted as an evidence of agreement. Similarly, the paired t -test compares mean difference between two observations in a group. It can therefore be nonsignificant if the average difference between the paired values is small, even though the differences between two observers for individuals are large.
The readers are referred to the following papers that feature measures of agreement:. Qureshi et al. It is a useful example. However, we feel that, Gleason's score being an ordinal variable, weighted kappa might have been a more appropriate choice. Carlsson et al. Kalantri et al. National Center for Biotechnology Information , U.
Journal List Perspect Clin Res v. Perspect Clin Res. Priya Ranganathan , C. Pramesh , 1 and Rakesh Aggarwal 2. Author information Copyright and License information Disclaimer. Address for correspondence: Dr.
E-mail: moc. This article has been cited by other articles in PMC. Abstract Agreement between measurements refers to the degree of concordance between two or more sets of measurements. Keywords: Agreement, biostatistics, concordance. Table 1 Results of 20 students, each evaluated independently by two examiners. Over time, however, the books of Apocrypha were eliminated from the King James Bible. The most modern King James Version does not have the Apocrypha in it.
Title page and dedication from a King James Bible. In this Bible, there is also the obvious distinction between the second person singular and the second person plural.
Knowing the difference between thou and you as well as thou and thee is important when using this version of the Holy Scripture. This makes it hard for someone who has been brought up without knowledge of Old English to understand the King James Bible.
King James Bible is the Protestant bible. However, later versions of the King James Bible do not have these books as the bible publishers considered them less important. The King James Version has been known for centuries all throughout the world as the one that makes use of what is considered as the Old English language.
On the contrary, the Catholic Bible is written in the modern day English. Knowing about what the two versions of the Holy Scripture have to offer is a great help in determining which one to get a hold of. As any examination of history will show very clearly, the deuterocanonical books were part of the Greek Septuagint version of the Hebrew Scriptures at the time of Jesus, which was considered by the ancient world a superb translation from the original Hebrew.
From the beginning, the Septuagint was the version of the Hebrew Scriptures used by the Church in the Greek-speaking world, because it was the version used by Jews in the Greek speaking world. In AD a Jewish council which rejected the Christian New Testament Scriptures declared that the Deuteroanonical books were not part of their canonical Scriptures. Others in the Reformation movement put it back where it belonged!
To sum up, the Deuterocanonicals are actually an integral part of the Christian Bible. Jesus and the disciples quoted from the Septuagint and for years it had been used and accepted by the jews.
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