# Methodological Notes

Interpretation of Krippendorff's Alpha Values

Below is a brief overview of the values of Krippendorff's Alpha, tailored for most of the research and data analysis scenarios. The following values are valid in numerous contexts, as suggested by Krippendorff (2019, p. 356).

Alpha = 1: Indicates perfect agreement among raters. It is the scenario where all raters have provided the exact same ratings for each item evaluated.

Alpha ≥ 0.80: This value is generally considered a satisfactory level of agreement, indicating a reliable rating. In many research contexts, a Krippendorff's Alpha equal to or above 0.80 is acceptable for drawing triangulated conclusions based on the rated data.

Alpha [0.67 - 0.79]: This range is often considered the lower bound for tentative conclusions. A Krippendorff's Alpha in this range suggests moderate agreement; thus, outcomes should be interpreted with concern, questioning the roots of such diverging ratings.

Alpha < 0.67: This is indicative of poor agreement among raters. Data with a Krippendorff's Alpha below this threshold are often deemed unreliable for drawing triangulated conclusions. It suggests that the raters are not applying the coding scheme consistently or that the scheme itself may be flawed.

Alpha = 0: Indicates no agreement among raters other than what would be expected by chance. It is similar to a random rating pattern.

Alpha < 0: A negative value of Krippendorff's Alpha indicates systematic disagreement among raters. This situation might arise in cases where raters are systematically inclined in opposite rating directions.

Methodological Template

Below, we propose a concise template to help researchers develop effective methods sections for studies using Krippendorff's Alpha across various contexts. The template guides the justification and the reporting of Krippendorff's reliability coefficient.

The template is structured to be filled with context-specific details. Green sections in italics, enclosed in [brackets], represent areas designated for user customization.

A group of [Number] raters with backgrounds in [Pertinent fields] took part in this study [Here, the raters themselves may be the authors of the study]. Before coding, they underwent a training session that included familiarising them with the coding scheme, practicing coding exercises, and discussing to clarify any ambiguities.

The coding scheme was developed based on [Here, the authors should delineate the theoretical framework or scholarly literature that informed the development of their coding scheme]. It consisted of [Number] categories, each with a defined set of attributes [Here, authors could describe in detail the characteristics of each category].

Krippendorff's Alpha was employed to assess the inter-rater reliability of the rating scheme (Krippendorff, 2019). This statistical measure is particularly suited for studies with multiple raters and different levels of measurement. It is a measure that accommodates different numbers of raters, sample sizes, and missing data, making it appropriate for numerous study designs (Krippendorff, 2019).

In the present case, each rater independently provided ratings. The rated data were then input into the web-based statistical package K-Alpha Calculator (Marzi et al., 2024). The analysis provided a reliability coefficient for the coding scheme, indicating the extent of agreement among raters beyond chance. The resulting Krippendorff's Alpha coefficient is [Insert the Krippendorff's Alpha value calculated with K-Alpha Calculator, eventually including the Confidence Intervals (CI)], recalling that the threshold for a satisfactory level of this coefficient is 0.80, as suggested by Krippendorff (2019).

References for the Methodological Template

Krippendorff, K. (2019). Content Analysis: An Introduction to Its Methodology (4th Ed.). SAGE Publications. https://doi.org/10.4135/9781071878781

Marzi, G., Balzano, M., & Marchiori, D. (2024). K-Alpha Calculator —Krippendorff's Alpha Calculator: A User-Friendly Tool for Computing Krippendorff's Alpha Inter-Rater Reliability Coefficient. MethodsX, 12, 102545. https://doi.org/10.1016/j.mex.2023.102545

A Brief Methodological Note on Inter-Rater Reliability

Inter-rater reliability, also known as inter-coder reliability in the qualitative studies domain, is essential in research for ensuring triangulated ratings across different evaluators, especially when subjective assessments are involved. This triangulation is crucial for the robustness and credibility of research outcomes (Hayes & Krippendorff, 2007). Commonly used statistical measures to assess rating reliability include Cohen’s Kappa, Fleiss' Kappa, and Krippendorff's Alpha (Cohen, 1960; Fleiss, 1971; Krippendorff, 2019).

Krippendorff's Alpha is particularly notable for its adaptability across various data types and measurement levels, making it suitable for a wide range of disciplines (Zapf et al., 2016). It is effective in content analysis, where interpretations of themes may vary (Hayes & Krippendorff, 2007), qualitative research and ethnographic studies, ensuring consistent interpretation of observed behaviours and phenomena (O’Connor & Joffe, 2020). Its utility also extends to systematic literature reviews, aiding in consistently selecting and rating relevant studies.

The theoretical foundation of Krippendorff's Alpha lies in its ability to quantify agreement among raters by using coincidence matrices to track raters' agreement and disagreement (Krippendorff, 2019). The measure ranges from -1 to 1, with 1 indicating perfect agreement and values below 0 suggesting less than random agreement. This scale helps researchers understand the degree of convergence/divergence in their rating (or coding) process, which is crucial for different types of analysis where researchers' judgement is involved. As such, inter-rater reliability, which can be assessed by Krippendorff's Alpha, is a cornerstone of rigorous research in different fields, fostering triangulated methodological choices and triangulated interpretations of data across various contexts.

References

Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37-46. https://doi.org/10.1177/001316446002000

Fleiss, J. L. (1971). Measuring nominal scale agreement among many raters. Psychological Bulletin, 76(5), 378. https://doi.org/10.1037/h0031619

Hayes, A. F., & Krippendorff, K. (2007). Answering the call for a standard reliability measure for coding data. Communication Methods and Measures, 1(1), 77-89. https://doi.org/10.1080/19312450709336664

Krippendorff, K. (2019). Content Analysis: An Introduction to Its Methodology (4th Ed.). SAGE Publications. https://doi.org/10.4135/9781071878781

O’Connor, C., & Joffe, H. (2020). Intercoder reliability in qualitative research: debates and practical guidelines. International Journal of Qualitative Methods, 19. https://doi.org/10.1177/1609406919899220

Zapf, A., Castell, S., Morawietz, L., & Karch, A. (2016). Measuring inter-rater reliability for nominal data–which coefficients and confidence intervals are appropriate? BMC Medical Research Methodology, 16(93), 1-10. https://doi.org/10.1186/s12874-016-0200-9

A Brief and Simplified Methodological Consideration on the Use of Nominal Data

Using nominal data to calculate the agreement between authors could sometimes lead to counterintuitive results. The present clarification comes from a discussion with Jihad Diab, Rachel Webb, and Geoff Tordzro-Taylor from the Risk Management Authority (RMA) - Research, to whom we are grateful.

Let us consider the following two examples, namely Example 1 and Example 2.

Notably, in Example 1, Item 5 has been categorized as “1,” while in Example 2, the same item has been categorized as “2.” At first glance, one might assume that the agreement in Example 1 and Example 2 is the same, and thus, they should have identical Krippendorff's Alpha values. However, let us recall the general formula for Krippendorff's Alpha where Do is the observed disagreement and De is the expected disagreement:

If we consider Example 1, the expected disagreement (De) is very low due to the extremely low overall variability of the matrix. Consequently, even minimal deviations in coding yield 'disastrous' results because these deviations are amplified. For example, changing the other '2' in Example 1 to '1' tends to worsen rather than improve Krippendorff's Alpha.

Now, let us consider Example 2. Here, the expected disagreement (De) is high because the overall variability of the matrix is greater than in Example 1. Despite converging in their assessments, the coders introduced variation in their coding (a value of “2” for Item 5). As a result, despite the high variability, the coders still achieved a degree of convergence, and the value of Krippendorff’s Alpha improved, indicating this convergence.

It is, therefore, crucial to consider the overall potential for disagreement in the coding exercise. When the expected disagreement is low, even minimal variations can reduce Krippendorff’s Alpha to a minimal value. For instance, removing some (but not all) “2”s from Example 1 decreases Krippendorff’s Alpha (rather than increasing it) because the overall variability is reduced, and the minimal variations introduce an even more pronounced disagreement.

This raises an important methodological consideration: when asking coders to evaluate complex items, such as reports, where potential variability could be high, nominal evaluations may often be suboptimal. For instance, if one asks, 'What is the colour of the sky?', full convergence on 'blue' is expected. Thus, any minimal variation in this assessment signals a coding issue warranting further investigation. In such cases, switching to ordinal evaluations could help researchers. However, the coding exercise should be readapted, for example: 'Rate on a scale from 1 to 5 [....]'.