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Inter-annotator Agreement (IAA) Calculation
Explain how Datasaur turns labelers and reviewers labels into IAA matrix.
In Datasaur, we use Cohen's Kappa Datasaur to calculate the agreement while taking into account the possibility of chance agreement. We will deep dive into how Datasaur collects all labels from labelers and reviewers in a project and process them into an Inter-annotator Agreement matrix.

Sample Data

Suppose there are 2 labelers who labeled the same sentences:
Labeler A
Labeler B
Reviewer

Calculating the Data

Agreement Records

Based on the screenshots above, we map those labels into the agreement records below:
Position in sentence
Labeler A
Labeler B
Reviewer
The Tragedy of Hamlet
EVE
TITLE
TITLE
Prince of Denmark
PER
<EMPTY>
<EMPTY>
Hamlet
PER
TITLE
PER
William Shakespeare
PER
PER
PER
1599
YEAR
YEAR
YEAR
1601
YEAR
YEAR
YEAR
Shakespeare
ORG
ORG
PER
30,557
<EMPTY>
<EMPTY>
QTY

Agreement Table / Confusion Matrix

Then, we construct the records into the agreement table. We use Labeler A and Labeler B data for the simulation.

Calculating the Kappa

From the table above, there are 7 records with 4 agreements.
The observed proportionate agreement is:
To calculate the probability of random agreement, we note that:
  • Labeler A labeled EVE once and Labeler B didn't label EVE. Therefore, the probability of random agreement on the label EVE is:
  • Compute the probability of random agreement for all labels:
The full random agreement probability is the sum of the probability of random agreement for all labels:
Finally, we can calculate the Cohen's Kappa:

Kappa for Labeler A and Reviewer

Kappa for Labeler B and Reviewer

Summary

  • We apply the same calculation for agreement between labelers, and between reviewer and labelers.
  • Missing labels from a single labeler will be counted as having applied empty labels.
  • The percentage of chance agreement will vary depending on:
    • The number of the labels in a project.
    • The number of label options.
  • When both labelers agree but the reviewer rejects the labels:
    • The agreement between the two labelers increases.
    • The agreement between the labelers and the reviewer decreases.