I'm conducting dual screening for a systematic review with a colleague. Help me: 1) Calculate Cohen's kappa or other agreement statistics after screening a pilot set

Prompt

ChatGPTOpenAI

I'm conducting dual screening for a systematic review with a colleague. Help me: 1) Calculate Cohen's kappa or other agreement statistics after screening a pilot set

Certainly! When conducting a systematic review and performing dual screening, it's important to measure the level of agreement between the reviewers. One commonly used statistic for this purpose is Cohen's kappa. Here's how to calculate it, as well as some additional agreement statistics you might consider.

Steps to Calculate Cohen's Kappa

Conduct the Screening: Each reviewer independently screens a set of studies. For example, let's say you both screened 50 studies.

Create a Contingency Table: After screening, you will categorize studies as either "included" or "excluded". A 2x2 contingency table would look like this:

| | Reviewer 2: Included | Reviewer 2: Excluded |
|---------------|---------------------|-----------------------|
| Reviewer 1: Included | a (both included) | b (Reviewer 1 included, Reviewer 2 excluded) |
| Reviewer 1: Excluded | c (Reviewer 1 excluded, Reviewer 2 included) | d (both excluded) |

Where:

a = Number of studies both included

b = Number of studies where only Reviewer 1 included

c = Number of studies where only Reviewer 2 included

d = Number of studies both excluded

Calculate Observed Agreement (Po):

\[
P_o = \frac{a + d}{N}
\]
where $ N $ is the total number of studies screened ($N = a + b + c + d$).

Calculate Expected Agreement (Pe):

\[
P_e = \left(\frac{(a+b)(a+c)}{N^2}\right) + \left(\frac{(c+d)(b+d)}{N^2}\right)
\]
This is computed by taking the proportion of included studies by each reviewer and squaring it, as well as doing the same for excluded studies.

Calculate Cohen's Kappa (κ):

\[
\kappa = \frac{Po - Pe}{1 - P_e}
\]

Example Calculation

Suppose after screening you have the following results:

a = 30

b = 5

c = 8

d = 7

Calculating:

Total $ N = a + b + c + d = 30 + 5 + 8 + 7 = 50 $

Observed Agreement $ P_o = \frac{30 + 7}{50} = \frac{37}{50} = 0.74 $

Expected Agreement Calculation:

$ \frac{(30 + 5)(30 + 8)}{50^2} = \frac{35 \cdot 38}{2500} = \frac{1330}{2500} = 0.532 $

$ \frac{(8 + 7)(5 + 7)}{50^2} = \frac{15 \cdot 12}{2500} = \frac{180}{2500} = 0.072 $

Combine these: $ P_e = 0.532 + 0.072 = 0.604 $

Now calculate Kappa:
\[
\kappa = \frac{0.74 - 0.604}{1 - 0.604} = \frac{0.136}{0.396} \approx 0.343
\]

Additional Agreement Statistics

Percentage Agreement: A simpler measure that states the percentage of times the reviewers agree. This is:

\[
\text{Percentage Agreement} = \frac{a + d}{N} \times 100
\]

Fleiss' Kappa: If there are more than two reviewers or if you want to measure agreement for multiple reviewers.

Krippendorff's Alpha: A versatile measure of inter-rater reliability that can be used for different levels of measurement.

Scott’s Pi: Another chance-corrected measure of agreement.

Using Cohen's Kappa is a widely accepted choice for two independent raters. Consider calculating these additional metrics depending on your needs and data structure. If you have further specifics, feel free to ask!

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GeminiGoogle

I'm conducting dual screening for a systematic review with a colleague. Help me: 1) Calculate Cohen's kappa or other agreement statistics after screening a pilot set

This is a crucial step in a systematic review! Calculating agreement statistics after a pilot screening helps ensure your inclusion/exclusion criteria are clear and consistently applied before you screen the full set of articles.

Let's break down how to calculate Cohen's Kappa and other relevant statistics, along with what to do with the results.

1. Calculating Cohen's Kappa (or other agreement statistics)

Cohen's Kappa ($\kappa$) is the most widely used agreement statistic for systematic reviews because it accounts for the agreement that would be expected by chance.

Data Setup

First, you need to record the decisions of both screeners for each article in your pilot set. A simple spreadsheet works best.

Article ID	Reviewer 1 Decision	Reviewer 2 Decision
Article 1	Include	Include
Article 2	Exclude	Exclude
Article 3	Include	Exclude
Article 4	Exclude	Include
Article 5	Exclude	Exclude
...	...	...

You'll categorize each decision as either "Include" (I) or "Exclude" (E).

Step-by-Step Calculation for Cohen's Kappa

Step 1: Create a 2x2 Contingency Table

Count the number of articles that fall into each of these four categories:

Reviewer 2: Include	Reviewer 2: Exclude	Total (Reviewer 1)
Reviewer 1: Include	A (Agreed Include)	B (R1 Incl, R2 Excl)	A + B
Reviewer 1: Exclude	C (R1 Excl, R2 Incl)	D (Agreed Exclude)	C + D
Total (Reviewer 2)	A + C	B + D	N (Total Articles)

A: Both reviewers included the article.

B: Reviewer 1 included, Reviewer 2 excluded.

C: Reviewer 1 excluded, Reviewer 2 included.

D: Both reviewers excluded the article.

N: Total number of articles in your pilot.

Step 2: Calculate Observed Agreement ($P_o$)

This is the proportion of articles where both reviewers agreed, regardless of whether they agreed to include or exclude.

$P_o = (A + D) / N$

Step 3: Calculate Expected Agreement by Chance ($P_e$)

This is where Kappa differs from simple percentage agreement. It accounts for how much agreement you'd expect just by random chance.

$P_e = [((A+B)/N) ((A+C)/N)] + [((C+D)/N) ((B+D)/N)]$

Let's break down $P_e$:

((A+B)/N): Proportion of articles Reviewer 1 included.

((A+C)/N): Proportion of articles Reviewer 2 included.

((C+D)/N): Proportion of articles Reviewer 1 excluded.

((B+D)/N): Proportion of articles Reviewer 2 excluded.

The first part of the sum [((A+B)/N) ((A+C)/N)] is the probability that both reviewers randomly* include an article.
The second part of the sum [((C+D)/N) ((B+D)/N)] is the probability that both reviewers randomly* exclude an article.

Step 4: Calculate Cohen's Kappa ($\kappa$)

Now, plug $Po$ and $Pe$ into the Kappa formula:

$\kappa = (Po - Pe) / (1 - P_e)$

Example Calculation

Let's say your pilot set has 100 articles:

A (Agreed Include): 15 articles

B (R1 Incl, R2 Excl): 5 articles

C (R1 Excl, R2 Incl): 10 articles

D (Agreed Exclude): 70 articles

N (Total): 15 + 5 + 10 + 70 = 100 articles

1. 2x2 Table:

R2: Include	R2: Exclude	Total (R1)
R1: Include	15	5	20
R1: Exclude	10	70	80
Total (R2)	25	75	100

2. Observed Agreement ($P_o$):
$P_o = (15 + 70) / 100 = 85 / 100 = 0.85$

3. Expected Agreement by Chance ($P_e$):

Reviewer 1 Included: $(15+5)/100 = 20/100 = 0.20$

Reviewer 2 Included: $(15+10)/100 = 25/100 = 0.25$

Reviewer 1 Excluded: $(10+70)/100 = 80/100 = 0.80$

Reviewer 2 Excluded: $(5+70)/100 = 75/100 = 0.75$

$P_e = (0.20 0.25) + (0.80 0.75)$
$P_e = 0.05 + 0.60$
$P_e = 0.65$

4. Cohen's Kappa ($\kappa$):
$\kappa = (0.85 - 0.65) / (1 - 0.65)$
$\kappa = 0.20 / 0.35$
$\kappa \approx 0.57$

Interpretation of Cohen's Kappa

Kappa values range from -1 to 1:

1: Perfect agreement.

0: Agreement is no better than chance.

< 0: Agreement is worse than chance (very rare in dual screening).

Commonly cited (though somewhat arbitrary) guidelines for interpreting Kappa values (Landis & Koch, 1977):

< 0.00: Poor agreement

0.00 – 0.20: Slight agreement

0.21 – 0.40: Fair agreement

0.41 – 0.60: Moderate agreement

0.61 – 0.80: Substantial agreement

0.81 – 1.00: Almost perfect agreement

For systematic reviews, a Kappa of 0.60 or higher is often considered acceptable for a pilot screening, indicating substantial agreement. Some protocols may aim for 0.70 or 0.80.

Other Agreement Statistics (and why Kappa is often preferred)

While Kappa is standard, you might also consider:

Percentage Agreement (Observed Agreement $P_o$):

Calculation: $(A + D) / N$ (as calculated for Kappa).

Pros: Very easy to understand and calculate.

Cons: It doesn't account for agreement that would happen purely by chance. If you have a very high prevalence of "Exclude" decisions, even random guessing might lead to high observed agreement for "Exclude," inflating this percentage. This is why Kappa is generally preferred.

Gwet's AC1/AC2:

Description: Gwet's AC1 (for nominal data) is an alternative to Kappa that can be more robust to what's called the "prevalence paradox" and "marginal-probability paradox." These paradoxes can cause Kappa to be low even when observed agreement is high, especially if one category is very rare or very common.

Pros: Can provide a more stable measure of agreement in certain scenarios.

Cons: Less commonly reported than Kappa in systematic reviews, so your audience might be less familiar with it. Calculation is more complex and usually requires software.

Recommendation: Start with Cohen's Kappa. It's the standard for good reason. If you encounter a situation where you have very high observed agreement but a surprisingly low Kappa, Gwet's AC1 might be worth exploring, but for most systematic reviews, Kappa is sufficient.

Tools for Calculation

Excel/Google Sheets: You can set up the 2x2 table and input the formulas directly.

For the example above:

A in cell B2, B in C2, C in B3, D in C3.

N (total articles) in D4: =SUM(B2:C3)

Po: =(B2+C3)/D4

Pe: =( ( (B2+C2)/D4 ) ( (B2+B3)/D4 ) ) + ( ( (C3+B3)/D4 ) ( (C2+C3)/D4 ) ) (Make sure parentheses are correct!)

Kappa: =(Po-Pe)/(1-Pe)

Online Calculators:

Search for "Cohen's Kappa calculator online." Many free options are available where you just input your A, B, C, D values.

Statistical Software (R, Python, SPSS, Stata):

These packages have functions for calculating Kappa and often provide confidence intervals, which are useful.

R: vcd package (Kappa() function), psych package (cohen.kappa() function).

Python: scikit-learn library (cohenkappascore() function).

2. What to do with the results of your pilot screening

Calculating Kappa is just the first step. The real value of a pilot is in improving your process.

If Kappa is Acceptable (e.g., > 0.60):

Briefly Review Discrepancies: Even with good Kappa, review the few articles where you disagreed (cells B and C in your 2x2 table).

Confirm Clarity: Are the criteria robust enough for the full screening?

Proceed to Full Screening: You can now screen the full set of articles with reasonable confidence in your consistency.

If Kappa is Low (e.g., < 0.60): This is a learning opportunity!

A low Kappa indicates that your reviewers are not applying the criteria consistently enough. This is precisely why you do a pilot.

Thorough Discrepancy Analysis:

Discuss ALL disagreements (cells B and C). Go through each article where you disagreed.

Identify the ROOT CAUSE of disagreement:

Ambiguous Criteria: Are your inclusion/exclusion criteria unclear, subjective, or too broad/narrow in specific situations? (e.g., "Relevant population" – what defines "relevant"?)

Lack of Specificity: Do your criteria need more explicit definitions or examples?

Misinterpretation: Did one reviewer simply misunderstand a criterion?

Data Extraction Error: Did one reviewer miss a key piece of information in the abstract/title?

Inconsistent Application: Even with clear criteria, were they applied differently?

Consensus: For each disagreed article, reach a consensus decision and document why that decision was made based on your criteria.

Refine Your Screening Protocol:

Clarify Criteria: Rewrite problematic criteria to be more explicit, objective, and unambiguous. Add bullet points, keywords to look for/avoid, and specific examples.

Update Screening Tool: If you're using a screening form, update it to reflect the refined criteria. Add notes or pop-up text to guide reviewers on common ambiguities.

Develop FAQs/Decision Rules: Create a list of common "edge cases" from your pilot and how they should be handled.

Review Definitions: Ensure everyone understands key terms.

Conduct Another Pilot (Repeat):

Take a new set of articles (or a subset of your full pool that hasn't been screened yet) or re-screen the original pilot set after refining the criteria.

Calculate Kappa again.

Repeat this iterative process until you achieve an acceptable Kappa.

Important Note: The goal of the pilot is not just to get a good Kappa score, but to ensure that the criteria are clear enough for independent, consistent application. Don't be discouraged by a low Kappa initially; it just means you've identified areas for improvement.

Good luck with your systematic review!

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MistralMistral AI

I'm conducting dual screening for a systematic review with a colleague. Help me: 1) Calculate Cohen's kappa or other agreement statistics after screening a pilot set

Certainly! Calculating Cohen's kappa is a common method to assess inter-rater agreement in dual screening for systematic reviews. Here’s a step-by-step guide to help you calculate Cohen's kappa:

Step 1: Create a Contingency Table

First, you need to create a contingency table that shows the agreement and disagreement between you and your colleague. The table will look something like this:

Colleague Includes	Colleague Excludes	Total
You Include	a	b	a+b
You Exclude	c	d	c+d
Total	a+c	b+d	N

a: Number of articles both you and your colleague include.

b: Number of articles you include but your colleague excludes.

c: Number of articles you exclude but your colleague includes.

d: Number of articles both you and your colleague exclude.

N: Total number of articles screened.

Step 2: Calculate Observed Agreement (P_o)

Observed agreement is the proportion of times the raters agree.

\[ P_o = \frac{a + d}{N} \]

Step 3: Calculate Expected Agreement (P_e)

Expected agreement is the proportion of times the raters would agree by chance.

\[ P_e = \frac{(a+b)(a+c) + (c+d)(b+d)}{N^2} \]

Step 4: Calculate Cohen's Kappa

Cohen's kappa is calculated as:

\[ \kappa = \frac{Po - Pe}{1 - P_e} \]

Example Calculation

Let's say you and your colleague screened 100 articles and your contingency table looks like this:

Colleague Includes	Colleague Excludes	Total
You Include	40	10	50
You Exclude	5	45	50
Total	45	55	100

Observed Agreement (P_o):

\[ P_o = \frac{40 + 45}{100} = \frac{85}{100} = 0.85 \]

Expected Agreement (P_e):

\[ P_e = \frac{(40+10)(40+5) + (5+45)(10+45)}{100^2} \]
\[ P_e = \frac{(50)(45) + (50)(55)}{10000} \]
\[ P_e = \frac{2250 + 2750}{10000} \]
\[ P_e = \frac{5000}{10000} = 0.50 \]

Cohen's Kappa:

\[ \kappa = \frac{0.85 - 0.50}{1 - 0.50} \]
\[ \kappa = \frac{0.35}{0.50} \]
\[ \kappa = 0.70 \]

Interpretation

Cohen's kappa values are typically interpreted as follows:

≤ 0: No agreement

0.01 – 0.20: Slight agreement

0.21 – 0.40: Fair agreement

0.41 – 0.60: Moderate agreement

0.61 – 0.80: Substantial agreement

0.81 – 1.00: Almost perfect agreement

In this example, a kappa of 0.70 indicates substantial agreement between you and your colleague.

Other Agreement Statistics

If you are interested in other agreement statistics, you might consider:

Percent Agreement: Simply the proportion of agreements (P_o).

Fleiss' Kappa: Useful for more than two raters.

Krippendorff's Alpha: Useful for nominal, ordinal, interval, or ratio data.

For most dual screening tasks in systematic reviews, Cohen's kappa is sufficient and widely accepted.

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Analysis

This comparison demonstrates the different approaches each AI model takes when responding to the same prompt. Here are the key differences observed:

Response Characteristics

ChatGPT: Provides a direct response with 37 sentences.

Gemini: Provides a direct response with 140 sentences.

Mistral: Provides a direct response with 37 sentences.

Key Takeaways

Each model brings unique strengths to this type of query
Response styles vary significantly between models
Consider your specific use case when choosing between these models

Try This Comparison Yourself

Want to test these models with your own prompts? Visit SNEOS.com to compare AI responses side-by-side in real-time.

This comparison was generated using the SNEOS AI Comparison ToolPublished: October 15, 2025 | Models: ChatGPT, Gemini, Mistral