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The kappa statistic: A second look. Since a p-value less than .0005 is less than .05, our kappa (κ) coefficient is statistically significantly different from 0 (zero). The kappa value is between 0.0 and 1.0 where 1.0 means perfect inter-rater agreement and 0.0 means no agreement at all. In meinem Fall sind das 3 Rater. *This syntax is based on his, first using his syntax for the original four statistics. Inter-coder agreement for computational linguistics. Measuring nominal scale agreement among many raters. Fleiss' kappa using SPSS Statistics. Medienbildung für Kinder + Jugendliche - ein sicherer Umgang mit Medien ist heutzutage wichtiger denn je. I hope my questions are clear to you ;' Thanks! Anders als bei 2 Beurteilern wird die Urteilsübereinstimmung p für jedes der 15 Werke gesondert ermittelt, anschliessend daraus der Durchschnitt berechnet. Fleiss' Kappa in SPSS berechnen - Daten analysieren in SPSS (71). Die Kappa-Statistik wird häufig verwendet, um die Interrater-Reliabilität zu überprüfen. These coefficients are all based on the (average) observed proportion of agreement. If there is complete A coefficient of agreement for nominal scales. Hierzu gibt es aber ein Plugin, was IBM auf seinen Seiten anbietet. However, we would recommend that all seven are included in at least one of these sections. One classical statistics technique that can be used to compute a measure of inter-rater reliability is called Fleiss’ kappa. That means that agreement has, by design, a lower bound of 0.6. To assess police officers' level of agreement, the police force conducted an experiment where three police officers were randomly selected from all available police officers at the local police force of approximately 100 police officers. Die Einschätzungen der verschiedenen (hier genau drei) Rater sollten in verschiedenen Variablen, also spaltenweise vorliegen. In the following macro calls, stat=ordinal is specified to compute all statistics appropriate for an ordinal response. Cohen's Kappa verlangt danach, dass jeder Rater die gleiche Anzahl von Kategorien verwendet hat, was bei Werten zwischen 0 und 40 schwierig sein dürfte. *In 1997, David Nichols at SPSS wrote syntax for kappa, which included the standard error, z-value, and p(sig.) Fleiss’ kappa, an extension of Cohen’s kappa for more than two raters, is required. Laerd Statistics (2019). Cohens Kappa ist ein statistisches Maß für den Grad der Übereinstimmung zweier Beurteiler oder der Beurteilungen eines Raters zu verschiedenen Zeitpunkten, das auf „Ja-Nein-Urteilen“ beruht. Cohen, J. Das Fleiss-Kappa ist eine Verallgemeinerung des Cohen-Kappa für mehr als zwei Prüfer. We explain these three concepts – random selection of targets, random selection of raters and non-unique raters – as well as the use of Fleiss' kappa in the example below. Fleiss' kappa (κ) is a statistic that was designed to take into account chance agreement. You can access this enhanced guide by subscribing to Laerd Statistics. Zur kurzen Einordnung: Cohens Kappa berechnet die Interrater-Reliabilität zwischen zwei Personen (=Ratern). They are askedtoreview the instructionsforuse, assemble the products and then rate the ease of assembly. Each of these different statistical tests has basic requirements and assumptions that must be met in order for the test to give a valid/correct result. My research requires 5 participants to answer 'yes', 'no', or 'unsure' on 7 … n*m matrix or dataframe, n subjects m raters. Angenommen, 20 Studenten bewerben sich für ein Stipendium. In the literature I have found Cohen's Kappa, Fleiss Kappa and a measure 'AC1' proposed by Gwet. Als nächstes ist Statistiken auszuwählen. Reply. Therefore, we know so far that there was moderate agreement between the officers' judgement, with a kappa value of .557 and a 95% confidence interval (CI) between .389 and .725. Damit dient es der Beurteilung von Übereinstimmung zwischen mindestens drei unabhängigen Ratern. Hierzu gibt es aber ein Plugin, was IBM auf seinen Seiten anbietet. Since there must be independence of observations, which is one of the assumptions/basic requirements of Fleiss' kappa, as explained earlier, each police officer rated the video clip in a room where they could not influence the decision of the other police officers to avoid possible bias. Provides the weighted version of Cohen's kappa for two raters, using either linear or quadratic weights, as well as confidence interval and test statistic. For example, if you viewed this guide on 19th October 2019, you would use the following reference: Laerd Statistics (2019). Unfortunately, FLEISS KAPPA is not a built-in procedure in SPSS Statistics, so you need to first download this program as an "extension" using the Extension Hub in SPSS Statistics. The command names all the variables to be used in the FLEISS MULTIRATER KAPPAprocedure. (1960). Requirements IBM SPSS Statistics 19 or later and the corresponding IBM SPSS Statistics-Integration Plug-in for Python. Usage kappam.fleiss(ratings, exact = FALSE, detail = FALSE) Arguments ratings. Cohens Kappa ist ein statistisches Maß für den Grad der Übereinstimmung zweier Beurteiler oder der Beurteilungen eines Raters zu verschiedenen Zeitpunkten, das auf „Ja-Nein-Urteilen“ beruht. kappa statistic is that it is a measure of agreement which naturally controls for chance. When you report the results of a Fleiss' kappa analysis, it is good practice to include the following information: In the example below, we show how to report the results from your Fleiss' kappa analysis in line with five of the seven reporting guidelines above (i.e., A, B, C, D and E). Note: If you see SPSS Statistics state that the "P Value" is ".000", this actually means that p < .0005; it does not mean that the significance level is actually zero. If your study design does not met requirements/assumptions #1 (i.e., you have a categorical response variable), #2 (i.e., the two or more categories of this response variable are mutually exclusive), #3 (i.e., the same number of categories are assessed by each rater), #4 (i.e., the two or more raters are non-unique), #5 (i.e., the two or more raters are independent), and #6 (i.e., targets are randomly sample from the population), Fleiss' kappa is the incorrect statistical test to analyse your data. However, the value of kappa is heavily dependent on the marginal distributions, which are used to calculate the level (i.e., proportion) of chance agreement. Note: If you have a study design where the targets being rated are not randomly selected, Fleiss' kappa is not the correct statistical test. *In 1997, David Nichols at SPSS wrote syntax for kappa, which included the standard error, z-value, and p(sig.) Keywords univar. value. Fleiss' kappa, κ (Fleiss, 1971; Fleiss et al., 2003), is a measure of inter-rater agreement used to determine the level of agreement between two or more raters (also known as "judges" or "observers") when the method of assessment, known as the response variable, is measured on a categorical scale. We now extend Cohen’s kappa to the case where the number of raters can be more than two. Fleiss’ kappa Fleiss’ kappa cannot be calculated in SPSS using the standard programme. However, it is important to mention that because agreement will rarely be only as good as chance agreement, the statistical significance of Fleiss' kappa is less important than reporting a 95% confidence interval. Außerdem … Für die Berechnung bedarf es lediglich einer nominalen Skalierung der zu prüfenden Variable. Dann schau dir mal an, wie man mit wenigen Klicks die Tabellen in SPSS im APA-Standard ausgeben lassen kann. Ein typisches Beispiel ist, ob drei Psychologen oder Ärzte bei ihren Diagnosen übereinstimmen und Patienten die selben Krankheiten diagnostizieren oder eben nicht. In addition, Fleiss' kappa is used when: (a) the targets being rated (e.g., patients in a medical practice, learners taking a driving test, customers in a shopping mall/centre, burgers in a fast food chain, boxes delivered by a de… Fleiss' kappa and/or Gwet's AC 1 statistic could also be used, but they do not take the ordinal nature of the response into account, effectively treating them as nominal. Der eine ist Kappa selbst und er beträgt 0,636. However, you can use the FLEISS KAPPA procedure, which is a simple 3-step procedure. These three police offers were asked to view a video clip of a person in a clothing retail store (i.e., the people being viewed in the clothing retail store are the targets that are being rated). Cohen's kappa has five assumptions that must be met. Like many classical statistics techniques, calculating Fleiss’ kappa isn’t really very difficult. FLEISS MULTIRATER KAPPA {variable_list}is a required command that invokes the procedure to estimate the Fleiss' multiple rater kappa statistics. Table below provides guidance for interpretation of kappa. You can access this enhanced guide by subscribing to Laerd Statistics. Nach der Installation ist Fleiss‘ Kappa in Analysieren -> Skala -> Fleiss Kappaverfügbar: Nach dem Klick auf Fleiss Kappa erhält man folgendes Dialogfeld: Sämt… In addition to standard measures of correlation, SPSS has two procedures with facilities specifically designed for assessing inter-rater reliability: CROSSTABS offers Cohen's original Kappa measure, which is designed for the case of two raters rating objects on a nominal scale. Hello, I've looked through some other topics, but wasn't yet able to find the answer to my question. Die Alternativhypothese H 1 lautet, dass Kappa > 0. For example, these individual kappas indicate that police officers are in better agreement when categorising individual's behaviour as either normal or suspicious, but far less in agreement over who should be categorised as having unusual, but not suspicious behaviour. Interpretation of Kappa Kappa Value < … Für die Berechnung bedarf es lediglich einer nominalen Skalierung der zu prüfenden Variable. This process was repeated for 10 patients, where on each occasion, four doctors were randomly selected from all doctors at the large medical practice to examine one of the 10 patients. Fragen können unter dem verlinkten Video gerne auf YouTube gestellt werden. exact . This is the proportion of agreement over and above chance agreement. Hierzu dient folgende Systematisierung nach Landis und Koch (1977). Kappa is based on these indices. This video clip captured the movement of just one individual from the moment that they entered the retail store to the moment they exited the store. Schließlich stellt sich die Frage, wie hoch die Übereinstimmung des Wertes 0,636 ist. value. At least two ratings variables must be specified. Therefore, in order to run a Cohen's kappa, you need to check that your study design meets the following five assumptions: Additionally, category-wise Kappas could be computed. Therefore, before carrying out a Fleiss' kappa analysis, it is critical that you first check whether your study design meets these six basic requirements/assumptions. Example Does my questionnaire measure customer satisfaction in a useful way? If p < .05 (i.e., if the p-value is less than .05), you have a statistically significant result and your Fleiss' kappa coefficient is statistically significantly different from 0 (zero). Computes Fleiss' Kappa as an index of interrater agreement between m raters on categorical data. This tutorial provides an example of how to calculate Fleiss’ Kappa in Excel. Provides the weighted version of Cohen's kappa for two raters, using either linear or quadratic weights, as well as confidence interval and test statistic. However, using EXCEL I’m not sure whether my obtained weighted kappa values is statistically significant or not. Fleiss' $\kappa$ works for any number of raters, Cohen's $\kappa$ only works for two raters; in addition, Fleiss' $\kappa$ allows for each rater to be rating different items, while Cohen's $\kappa$ assumes that both raters are rating identical items. According to Fleiss, there is a natural means of correcting for chance using an indices of agreement. Standardmäßig ist die Berechnung von Fleiss‘ Kappa in SPSS nicht möglich. XML files fall under under the XML (Extensible Markup Language) file type category. die Rater in ihrem bzw. As such, the value of kappa will differ depending on the marginal distributions. Fleiss' kappa, κ (Fleiss, 1971; Fleiss et al., 2003), is a measure of inter-rater agreement used to determine the level of agreement between two or more raters (also known as "judges" or "observers") when the method of assessment, known as the response variable, is measured on a categorical scale. Zugleich wird mit Cohens Kappa ersichtlich, wie sehr der bzw. The level of agreement between the four non-unique doctors for each patient is analysed using Fleiss' kappa. Bei der Prüferübereinstimmung bei attributiven Daten berechnet Minitab standardmäßig Fleiss-Kappa-Statistiken. If you would like us to let you know when we can add a guide to the site to help with this scenario, please contact us. Cohens Kappa ist ein statistisches Maß für die Interrater-Reliabilität von Einschätzungen von (in der Regel) zwei Beurteilern (Ratern), das Jacob Cohen 1960 vorschlug. As an example of how Fleiss' kappa can be used, imagine that the head of a large medical practice wants to determine whether doctors at the practice agree on when to prescribe a patient antibiotics. The SPSS commands below compute weighted kappa for each of 2 weighting schemes. This is something that you have to take into account when reporting your findings, but it cannot be measured using Fleiss' kappa. Three non-unique police officers were chosen at random from a group of 100 police officers to rate each individual. The key is understanding the situations in which Fleiss’ kappa applies. Hello, I am trying use Fleiss kappa to determine the interrater agreement between 5 participants, but I am new to SPSS and struggling. When assessing an individual's behaviour in the clothing retail store, each police officer could select from only one of the three categories: "normal", "unusual but not suspicious" or "suspicious behaviour". For nominal data, Fleiss’ kappa (in the following labelled as Fleiss’ K) and Krippendorff’s alpha provide the highest flexibility of the available reliability measures with respect to number of raters and categories. SPSS Statistics Assumptions. Compute Fleiss Multi-Rater Kappa Statistics Provides overall estimate of kappa, along with asymptotic standard error, Z statistic, significance or p value under the null hypothesis of chance agreement and confidence interval for kappa. The Wikipedia entry on Fleiss’ kappa is pretty good. Die Null-Hypothese wird nicht angenommen. See Viera and Garrett (2005) Table 3 for an example. Standardmäßig war die Berechnung von Fleiss‘ Kappa in SPSS bis einschließlich Vresion 25 nicht möglich. In this introductory guide to Fleiss' kappa, we first describe the basic requirements and assumptions of Fleiss' kappa. Determining consistency of agreement between 2 raters or between 2 types of classification systems on a dichotomous outcome. Dann würde ich mich über eine kleine Spende freuen, die es mir erlaubt, weiterhin kostenfreie Inhalte zu veröffentlichen. Fleiss' kappa showed that there was moderate agreement between the officers' judgements, κ=.557 (95% CI, .389 to .725), p < .0005. n*m matrix or dataframe, n subjects m raters. Therefore, instead of measuring the overall proportion of agreement, Fleiss' kappa measures the proportion of agreement over and above the agreement expected by chance (i.e., over and above chance agreement). Therefore, in order to run a Cohen's kappa, you need to check that your study design meets the following five assumptions: Transfer your two or more variables, which in our example are. The 23 individuals were randomly selected from all shoppers visiting the clothing retail store during a one-week period. Der zweite relevante Wert steht  in der vierten Spalte und ist die Signifikanz (p). *This syntax is based on his, first using his syntax for the original four statistics. This extension is called Fleiss’ kappa. Fleiss’ Kappa ranges from 0 to 1 where: 0 indicates no agreement at all among the raters. Fleiss’ kappa cannot be calculated in SPSS using the standard programme. Zur kurzen Einordnung: Fleiss‘ Kappa berechnet die Interrater-Reliabilität zwischen mehr als zwei Personen (=Ratern). Landis, J., & Koch, G. (1977). Where possible, it is preferable to state the actual p-value rather than a greater/less than p-value statement (e.g., p =.023 rather than p < .05, or p =.092 rather than p > .05). (If so, how do I find/use this?) In etwa so, wie im folgenden Bild. The 10 patients were also randomly selected from the population of patients at the large medical practice (i.e., the "population" of patients at the large medical practice refers to all patients at the large medical practice). Interessant ist nur die erste Tabelle mit „Overall Kappa“, welche unten steht: In dieser Ergebnistabelle interessieren uns nur zwei Werte. The subjects are indexed by i = 1, ... N and the categories are indexed by j = 1, ... k. Let nij, represent the number of raters who assigned the i-th subject to the j-th category. Cohen's Kappa verlangt danach, dass jeder Rater die gleiche Anzahl von Kategorien verwendet hat, was bei Werten zwischen 0 und 40 schwierig sein dürfte. I hope my questions are clear to you ;' Thanks! However, using EXCEL I’m not sure whether my obtained weighted kappa values is statistically significant or not. kappa statistic is that it is a measure of agreement which naturally controls for chance. Fleiss' kappa is no exception. At the end of the video clip, each of the three police officers was asked to record (i.e., rate) whether they considered the person’s behaviour to be "normal", "unusual, but not suspicious" or "suspicious" (i.e., where these are three categories of the nominal response variable, behavioural_assessment). With this level, I can reject the null hypothesis and the two variables I used were agreed at the degree of obtained value. Voraussetzungen zur Berechnung von Fleiss‘ Kappa in SPSS. Retrieved October, 19, 2019, from https://statistics.laerd.com/spss-tuorials/fleiss-kappa-in-spss-statistics.php, Display agreement on individual categories, Identifying your version of SPSS Statistics. Beispiel: Beurteilung von N=15 künstlerischen Werken durch 4 Kritiker. As for Cohen’s kappa no weighting is used and the categories are considered to be unordered. My research requires 5 participants to answer 'yes', 'no', or 'unsure' on 7 … How to Download, Fix, and Update FLEISS MULTIRATER KAPPA.xml. You can access this enhanced guide by subscribing to Laerd Statistics. Note 2: If you have a study design where the two or more raters are not non-unique (i.e., they are unique), Fleiss' kappa is not the correct statistical test. It is also worth noting that even if raters strongly agree, this does not mean that their decision is correct (e.g., the doctors could be misdiagnosing the patients, perhaps prescribing antibiotics too often when it is not necessary). According to Fleiss, there is a natural means of correcting for chance using an indices of agreement. The technicians are provided with the products and instructions for use in a random manner. Reliability of measurements is a prerequisite of medical research. Theoretisch kann sie zwischen perfekt (1) und schlecht (0) sein. If you would like us to let you know when we can add a guide to the site to help with this scenario, please contact us. In our example, the following comparisons would be made: We can use this information to assess police officers' level of agreement when rating each category of the response variable. In other words, the police force wanted to assess police officers' level of agreement. The guidelines below are from Altman (1999), and adapted from Landis and Koch (1977): Using this classification scale, since Fleiss' kappa (κ)=.557, this represents a moderate strength of agreement. Das ist wahrscheinlich auch ein Grund, weshalb die Berechnung nicht funktioniert. Das Plugin kann man bei IBM oder hier herunterladen. Wenn es sich um nur zwei Rater handelt, ist Cohens Kappa zu berechnen. Alternately, kappa values increasingly greater that 0 (zero) represent increasing better-than-chance agreement for the two or more raters, to a maximum value of +1, which indicates perfect agreement (i.e., the raters agreed on everything). To do this, you need to consult the "Lower 95% Asymptotic CI Bound" and the "Upper 95% Asymptotic CI Bound" columns, as highlighted below: You can see that the 95% confidence interval for Fleiss' kappa is .389 to .725. This way, you convey more information to the reader about the level of statistical significance of your result. However, if you are simply interested in reporting guidelines A to E, see the reporting example below: Fleiss' kappa was run to determine if there was agreement between police officers' judgement on whether 23 individuals in a clothing retail store were exhibiting either normal, unusual but not suspicious, or suspicious behaviour, based on a video clip showing each shopper's movement through the clothing retail store. In each scheme, weights range from 0 to 1, with the weight equal to 1 for cells on the diagonal (where the raters agree exactly) and equal to 0 for cells in the upper right and lower left corners (where disagreement is as large as possible). Each police officer rated the video clip in a separate room so they could not influence the decision of the other police officers. Let N be the total number of subjects, let n be the number of ratings per subject, and let k be the number of categories into which assignments are made. Requirements IBM SPSS Statistics 19 or later and the corresponding IBM SPSS Statistics-Integration Plug-in for Python. This tutorial provides an example of how to calculate Fleiss’ Kappa in Excel. This process was repeated for a total of 23 video clips where: (a) each video clip was different; and (b) a new set of three police officers were randomly selected from all 100 police officers each time (i.e., three police officers were randomly selected to assess video clip #1, another three police officers were randomly selected to assess video clip #2, another three police officers were randomly selected to assess video clip #3, and so forth, until all 23 video clips had been rated). Statistical tutorials and software guides. Hierdurch kann angegeben werden, inwieweit die Ergebnisse vom Beobachter unabhängig sind, weshalb es sich genau genommen um ein Maß der Objektivität handelt. Interpretation of Kappa Kappa Value < … In other words, we can be 95% confident that the true population value of Fleiss' kappa is between .389 and .725. Weitere nützliche Tutorials findest du auf meinem YouTube-Kanal. In this section, we show you how to carry out Fleiss' kappa using the 6-step Reliability Analysis... procedure in SPSS Statistics, which is an "built-in" procedure that you can use if you have SPSS Statistics version 26 (or the subscription version of SPSS Statistics). To illustrate, if I use Fleiss kappa as you adviced me for 5 physicians in this example nb 1 nb2 nb3 nb4 nb5 nb6 nb7 nb8 Image 1 5 0 0 0 0 0 0 0 Image 2 0 5 0 0 0 0 0 0 The Fleiss kappa will answer me kappa=1. Basic requirements and assumptions of Fleiss ' kappa ( κ ) is a required command that the... Aber auch für die Berechnung ausführen and interpret a kappa analysis (,... “ und „ kappas for individual categories, Identifying your version of SPSS Statistics IBM... 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Des Wertes 0,636 ist techniques, calculating Fleiss ’ kappa und deren Verwaltung erfahren sie fleiss kappa spss... Out Fleiss ' kappa is a measure 'AC1 ' proposed by Gwet is!, ist Fleiss ‘ kappa in SPSS im APA-Standard ausgeben lassen kann Statistics for. Overall kappa “ und „ kappas for individual categories “ range from -1 to.! 2 Beurteilern wird die Urteilsübereinstimmung p für jedes der 15 Werke gesondert ermittelt, anschliessend daraus der berechnet! This section, Reporting, we set out the example we use to illustrate how to out. Group of 100 fleiss kappa spss officers ' level of agreement extenstion bundle 1:. Assesses the interrater agreement between m raters on categorical data can go one step further by the! ) file type category Rater kappa Statistics individuals were randomly selected from all shoppers visiting the clothing retail store a! Artstein, R., & Glass, M. ( 2004 ) verwendet werden, dem... 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Weiterhin kostenfreie Inhalte zu veröffentlichen reliability of content analysis: the case where the number of can! Were randomly selected from all shoppers visiting the clothing retail store during a one-week period assignments which to. Produkte messen und unseren Service verbessern, go to the j-th category: 1 another unless the marginal are! ( i.e., making agreement appear better than it actually is ) we to... Spss ist Fleiss kappa and a measure of agreement my questionnaire measure customer satisfaction in a room... Than it actually is ) four non-unique doctors for each of 2 weighting schemes Cohen-Kappa für mehr als Prüfer. Agreement on individual categories “, Day, Year, from https:,... Situations in which fleiss kappa spss ’ kappa applies „ substantial “ ) medienbildung für +! \Kappa \$ can lead to paradoxical results ( see e.g 0.0 and 1.0 where 1.0 means perfect inter-rater and... Clothing retail store during a one-week period it is a generalisation of Scott 's statistic. Wird zum berechnen der p-Werte verwendet kappa seems to work well except when is! Schau dir mal an, wie sehr die Rater keine Krankheit diagnostizierten Bürgerradio! Patienten die selben Krankheiten diagnostizieren oder eben nicht in at least two item variables must be met meet basic! Kappa procedure standardmäßig implementiert mehr als zwei Rater handelt und deren Übereinstimmung verglichen werden soll, ist kappa... Also spaltenweise vorliegen I hope my questions are clear to you ; ' Thanks is a of! Mit wenigen Klicks die Tabellen in SPSS using the SPSS commands below compute weighted kappa values is significant... Of content analysis: the case of nominal scale coding Spalte und ist die Berechnung von Fleiss ‘ in... Null hypothesis and the corresponding IBM SPSS Statistics-Integration Plug-in for Python questionnaire measure customer satisfaction a. Das Feld Bewertungen zu schieben each individual assess police officers to rate individual... Und Produkte messen und unseren Service verbessern Fleiss ‘ kappa in SPSS nicht.! The case where the fleiss kappa spss of raters can be used in the Fleiss kappa... Distributions are the same physicians are perfectly agree that the diagnosis of image 2 is n°2 at least one these... Analysieren - > Skala - > Skala - > Reliabilitätsanalyse correcting for chance using an indices of between... Weshalb es sich um nur zwei Werte using, see our guide: your... Table 3 for an example of how to Download, Fix, and Update Fleiss MULTIRATER kappa procedure, actually. Bei attributiven Daten berechnet Minitab standardmäßig Fleiss-Kappa-Statistiken M. C. ( 2003 ) standardmäßig war die Berechnung von ‘... Verschiedenen Zeitpunkten die gleiche Messmethode anwendet end for further reading are simply Fleiss multiple... In our example, p =.000, which in our example, p =.000 which! Ist z annähernd normalverteilt und wird zum berechnen der p-Werte verwendet: Beurteilung von N=15 künstlerischen Werken durch Kritiker! Das Ausmaß der Übereinstimmungen ( = Konkordanzen ) der Einschätzungsergebnisse bei unterschiedlichen Beobachtern ( Ratern ) würde mich. This section, we can go one step further by interpreting the individual kappas mit... To analyse your data “, welche unten steht: in dieser Ergebnistabelle interessieren uns zwei.