Agreement Vs Correlation


For ordinal data where there are more than two categories, it is useful to know whether the ratings of the different evaluators varied by a small measure or a large quantity. For example, microbiologists can assess bacterial growth on culture plates as: none, occasional, moderate or confluent. Here, evaluations of a particular plate by two assessors as “occasional” or “moderate” would imply a lower degree of discord than if these scores were “growth-free” or “confluent”. Kappa`s weighted statistics take this difference into account. This therefore gives a higher value if the respondents` responses match more closely, with the maximum values for a perfect match; Conversely, a larger difference between two ratings provides a lower weighted kappa value. The techniques for assigning the weighting of the difference between categories (linear, square) may vary. ( Two radiologists evaluated 85 patients in terms of liver damage. The ratings were labeled on an ordinal scale as follows: The wrong association between ui and vi, as indicated by the product-moment correlation, contradicts the perfect conceptual correlation between the two variables. Therefore, the time of the product and its sample counterpart, the Pearson correlation, generally do not apply to nonlinear relationships. This report has two main objectives.

First, we combine well-known analytical approaches to conduct a comprehensive assessment of the correspondence and correlation of scoring pairs and unravel these often confusing concepts by providing an example of concrete data best practices and a tutorial for future reference. Second, we are investigating whether a screening questionnaire designed for use with parents can be reliably used with daycare teachers to assess early expressive vocabulary. A total of 53 vocabulary assessment pairs (34 parent-teacher pairs and 19 mother-father pairs) are assessed for two-year-olds (12 bilingual). First, reliability between evaluators is assessed using the intraclass correlation coefficient (ICC) both within and between subgroups. Then, based on this analysis of the reliability and test-retest reliability of the tool used, the inter-evaluator agreement is analyzed, the size and direction of the scoring differences are taken into account. Finally, the Pearson correlation coefficients of the standardized vocabulary values are calculated and compared between subgroups. The results highlight the need to distinguish between reliability measures, consistency and correlation. They also show the impact of applied reliability on the evaluation of agreements. This study provides evidence that parent-teacher assessments of children`s early vocabulary can achieve a match and correlation comparable to those of mother-father assessments on the graded vocabulary scale. The child`s bilingualism reduced the likelihood of approval by the evaluators.

We conclude that future reports on the consistency, correlation and reliability of ratings will benefit from better definition of terms and stricter methodological approaches. The methodological tutorial provided here has the potential to increase the comparability of empirical reports and can help improve research practices and knowledge transfer in educational and therapeutic contexts. Note that p⌢ICC is not a valid measure of the correspondence between yi1 and yi2 for the data in Example 5 because the data do not meet the assumption of a common mean between yi1 and yi2. However, it is precisely this hypothesis that completely distinguishes p⌢ICC from the Pearson correlation p⌢ =(1). We can revise the model in (9) to account for the bias of the judges` assessments: consider a situation in which we want to assess the correspondence between hemoglobin measurements (in g/dl) using a bedside hemoglobinometer and the formal photometric laboratory technique in ten people [Table 3]. The Bland-Altman graph for these data shows the difference between the two methods for each person [Figure 1]. The mean difference between the values is 1.07 g/dL (with a standard deviation of 0.36 g/dL) and the compliance limits of 95% are 0.35 to 1.79. This implies that a particular person`s hemoglobin level, measured by photometry, can vary from the bedside hemoglobin level measured by the method from as low as 0.35 g/dl higher to 1.79 g/dl higher (this is the case in 95% of individuals; in 5% of individuals, variations could be outside these limits). This, of course, means that the two techniques cannot be used as a substitute for each other.

It is important to note that there is no single criterion for what constitutes acceptable limits of agreement; This is a clinical decision that depends on the variable to be measured. The ACRN DICE study has already been discussed in this course. In this study, participants underwent blood samples every hour once a week between 8:00 p.m. and 8:00 a.m. to determine the area of cortisol under the curve (AUC). The participants hated it! They complained about the sleep disorder every hour when the nurses came to draw blood, so the ACRN wanted to determine for future studies whether the cortisol AUC, calculated every two hours on the measurements, was in good agreement with the cortisol AUC calculated on the hourly measurements. Baseline data were used to determine the extent to which these two measures matched. If there is a good agreement, the protocol could be changed to draw blood every two hours. Correlation focuses on the association of changes in two outcomes, outcomes that often measure very different constructs such as cancer and depression. Pearson correlation is the most popular measure of the association between two continuous outcomes, but it is only useful for measuring linear relationships between variables. In general, if the relationship is nonlinear, Pearson correlation does not provide a good indication of the association between variables. Another problem is that using the standard interpretation of Pearson correlation coefficients can lead to incorrect conclusions in certain circumstances.

Example 1. Suppose that ui and vi are perfectly correlated and follow the nonlinear relationship ui=vi9. Moreover, suppose that vi follows a standard normal distribution N(0, 1) with an mean 0 and a variance 1. Next, the product-moment correlation is as follows: An advantage of the Spearman rank correlation coefficient is that the X and Y values can be continuous or ordinal and no approximate normal distribution for X and Y is required. Similar to Pearson`s (r_p), fisher`s Z transformation can be applied to the Spearman (r_s) to obtain a statistic, (z_s), which has an asymptotic normal distribution to compute an asymptotic confidence interval. ProC CORR will do the same. Two methods are available to evaluate the correspondence between measurements of a continuous variable through observers, instruments, points in time, etc. One of them, the intraclass correlation coefficient (ICC), provides a single measure of the degree of agreement, and the other, the Bland-Altman diagram, further provides a quantitative estimate of the proximity of the values of two measures. As stated above, correlation is not synonymous with agreement. Correlation refers to the presence of a relationship between two different variables, while agreement examines the concordance between two measures of a variable. Two groups of highly correlated observations may have a bad agreement; However, if the two sets of values match, they will certainly be highly correlated. For example, in the example of hemoglobin, although the match is poor, the correlation coefficient between the values of the two methods is high [Figure 2]; (r = 0.98).

The other way to look at it is that, although the individual points are not close enough to the dotted line (smaller square line;[ 2] which indicates a good correlation), they are quite far from the solid black line which represents the perfect match line (Figure 2: the continuous black line). In case of a good match, the points should fall on or near this line (the solid black line). Brown, J. D., Wissow, L. S., Gadomski, A., Zachary, C., Bartlett, E., and Horn, I. (2006). Mental Health Assessments of Parents and Teachers of Children Using Primary Care Services: Interract Agreement and Impact on Mental Health Screening. Ambulat. Pediatrics 6, 347–351. doi: 10.1016/j.ambp.2006.09.004 Note that the Pearson correlation p⌢=0.531 has a higher upward trend than the product-moment correlation p=0.161; This is due to the small sample size n = 12.

As the sample size increases, p⌢ p, a property called “consistency” in statistics, approaches. For example, we also simulated (ui, vi) with n = 1000 and got p ⌢ = 0.173, much closer to p. First, we assessed reliability between evaluators within and between rating subgroups. Reliability between evaluators, expressed as intraclass correlation coefficients (ICC), measures the extent to which the instrument used is able to distinguish between participants reported by two or more evaluators who reach similar conclusions (Liao et al., 2010; Kottner et al., 2011). Therefore, reliability between evaluators is a criterion of the quality of the scoring tool and the accuracy of the scoring process, rather than a criterion that quantifies the correspondence between evaluators. It can be thought of as an estimate of the reliability of the instrument in a specific study population. This is the first study to assess the cross-evaluator reliability of the ELAN questionnaire. We report high inter-evaluator reliability for the mother-father as well as for parent-teacher evaluations and for the entire study population.

No systematic differences were found between the subgroups of evaluators. .