Do these 3 things before closing this tab:
1Scan for outdated or missing drivers - takes under a minute2Clear out junk files and repair common Windows errors3Fix the driver behind crashes, sound loss and screen glitchesA week-to-week change in Cohen’s kappa does not, by itself, show that raters have become better or worse. Kappa depends both on how often the raters agree and on the agreement expected from their category distributions. A change in either input—or a change in which cases were rated—can move the statistic. Start by comparing the counts, raw agreement, and case mix; interpret kappa only after that.
Why Cohen’s kappa changes
For two raters assigning nominal categories, Cohen’s kappa is κ = (Po − Pe) / (1 − Pe). Po is the observed proportion of matching ratings. Pe is the proportion of agreement expected from the raters’ marginal category frequencies. Because both terms affect the result, kappa can change even when raw agreement does not.
As an Amazon Associate I earn from qualifying purchases.
For example, if two weeks have the same proportion of matching ratings but the raters use the categories in different proportions, Pe may differ and kappa may move. If the pattern of matching and disagreeing ratings changes, Po changes. Both can shift at once. The foundational discussion of kappa recommends reporting observed agreement and information about prevalence and bias alongside the coefficient (Byrt, Bishop, and Carlin, 1993).
Category prevalence and rater marginals
Compare how often each rater used each category. A change in the overall prevalence of a category, or a difference between the two raters’ marginal distributions, affects the chance-agreement adjustment. That influence is important context, not automatically a flaw in kappa: interpretation depends on the population and the question being asked. Vach’s discussion emphasizes the composition of the sample and distinguishes observed marginal prevalence from latent prevalence (Vach, 2005).
#1 Best Overall
Case mix and difficulty
Weekly batches may contain different proportions of straightforward and ambiguous cases. Those cases need not produce the same agreement behavior, even if the raters and protocol have not changed. Treat a case-mix shift as a possibility to investigate, not as proof that a kappa change is harmless. The importance of the subjects’ ease or difficulty of agreement is discussed in Vach’s review (Vach, 2005).
Small batches and uncertainty
Smaller weekly samples generally make estimates noisier, but the sources cited here do not establish a universal weekly sample-size cutoff or one confidence-interval method for every repeated-week design. Report an appropriate uncertainty interval for each estimate and consider uncertainty in the difference between weeks. Do not treat a small change in point estimates as meaningful just because the displayed decimals differ. Sample-size determination is part of the broader agreement-methods literature (Wiley’s description of Measuring Agreement).
Rank #2
- This guide is a perfect overview for the topics covered in introductory statistics courses.
Diagnose the change before interpreting it
- Verify that the weeks are comparable. Check that category definitions, inclusion rules, rater pairing, treatment of missing or duplicate ratings, and the kappa variant are consistent.
- Compare denominators and case mix. Record the number of jointly rated cases in each week. Check whether case types, sources, or difficulty mix changed.
- Set the contingency tables side by side. Inspect every cell, the number and location of disagreements, and the total number of matches. A single kappa value conceals this pattern.
- Compare the ingredients of kappa. Report Po, Pe, and each rater’s category proportions for both weeks. This shows whether movement tracks changed observed agreement, changed marginals, or both.
- Quantify uncertainty. Give each weekly estimate an appropriate confidence interval and assess the uncertainty in the between-week difference. Avoid declaring a meaningful change from point estimates alone.
- Investigate operational changes if the counts point to them. Look for rater turnover, retraining, revised instructions, altered tools, or a new kind of borderline case when observed agreement or particular disagreement cells have shifted.
- Check that the statistic fits the design. Use a method suited to the number of raters and the category scale; consider an alternative coefficient only when it answers the question appropriately.
How to report weekly results
For each week, present the number of jointly rated cases, the two-rater contingency table, observed agreement, Cohen’s kappa with an uncertainty interval, and both raters’ category proportions. When relevant, include the distribution of case types and a concise note of protocol or rater changes.
Quick wins for a faster PC:
Scan for outdated or missing drivers - takes under a minuteDriver Scan →Clear out junk files and repair common Windows errorsFree Scan →In the comparison, state which quantities changed. For example, distinguish a change in observed agreement from a change in the marginals that altered expected agreement. Avoid reducing the result to “reliability improved” or “reliability declined” until the underlying counts and context support that interpretation. Recommendations to report prevalence and bias information with kappa are discussed by Byrt, Bishop, and Carlin (1993).
Rank #3
What a low kappa does—and does not—tell you
A low kappa can coexist with high raw agreement, particularly when category prevalence and rater marginals make the chance-agreement adjustment large. Kappa is a chance-corrected agreement coefficient; it is not a diagnosis of why raters disagree, nor is there one universal “good” threshold that applies regardless of context. Report it alongside observed agreement and the data needed to interpret it.
Gwet’s AC1 can be a useful sensitivity comparison when prevalence-related interpretation is central. An article examining the high-agreement, high-prevalence paradox argues that AC1 is more robust under the scenarios it considers; that is not evidence that AC1 is always preferable (High Agreement and High Prevalence: The Paradox of Cohen’s Kappa, 2017). Explain why an alternative fits the design and what it estimates rather than switching coefficients simply to obtain a more favorable number.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Choose an agreement measure for the rating design
| Rating design | Measure to consider | Why |
|---|---|---|
| Two raters, nominal categories | Cohen’s kappa | Corrects observed agreement using the raters’ marginal category frequencies. |
| Two raters, ordered categories where disagreement severity matters | Weighted kappa | Can assign different weights to near and larger disagreements. |
| More than two raters | A measure designed for multiple raters | Cohen’s kappa is for two raters; a method suited to the actual design is needed. |
| Prevalence-related interpretation is a key concern | AC1 as a sensitivity comparison, where justified | Provides another view under stated assumptions; it should not be treated as a universally superior replacement. |
Reference material on kappa describes its scope and related agreement measures (Wiley reference entry, 2010).
What’s actually slowing this PC down?
Pick the symptom - the matching free tool is one click away.
Quick Recap
Best Value
Product prices and availability are accurate as of the date/time indicated and are subject to change. Any price and availability information displayed on Amazon at the time of purchase will apply.
