Interpreting Kappa in Observational Research:

Baserate Matters

Cornelia Taylor BrucknerVanderbilt University

Acknowledgements

• Paul Yoder• Craig Kennedy• Niels Waller• Andrew Tomarken• MRDD training grant• KC Quant core

Overview

• Agreement is a proxy for accuracy• Agreement statistics 101

Chance agreement Agreement matrix Baserate

• Kappa and baserate, a paradox• Estimating accuracy from kappa• Applied example

Framing as observational coding

• I will be framing the talk today within observational measurement but the concepts apply to many other situations e.g., Agreement between clinicians on

diagnosis Agreement between reporters on child

symptoms (e.g. mothers and fathers)

“Rater accuracy”: A fictitious session

• Madeline Scientist writes a script for an interval coded observation session where the Presence or absence of target behavior in interval

• Two coders (Eager Beaver and Slack Jack), blind to the script, are asked to code the session.

• Accuracy of each coder with the script is calculated

Accuracy of Eager Beaver (EB) with session (interval data)

OccurrenceEager Beaver

NonoccurrenceEager Beaver

occurrences True

.90 .10

nonoccurrence True

.01 .99

Accuracy of Slack Jack (SJ) with session (interval data)

occurrenceSlack Jack

nonoccurrenceSlack Jack

occurrence True

.50 .50

nonoccurrence True

.30 .70

Who has the best accuracy?

• Eager Beaver of course.• Slack Jack was not very accurate • Notice that accuracy is about

agreement with the occurrence and nonoccurrence of behavior.

We don’t always know the truth

• It is great when we know the true occurrence and nonoccurrence of behaviors

• But, in the real world we deal with agreement between fallible observers

Agreement between raters

• Point by point interobserver agreement is achieved when independent observers : see the same thing (behavior, event) at the same time

Difference between agreement and accuracy

• Agreement can be directly measured.• Accuracy can not be directly measured.

We don’t know the “truth” of a session.

• However, agreement is used as a proxy for accuracy

• Accuracy can be estimated from agreement The method for this estimation is the focus of

today’s talk

Percent agreement

• Percent agreement The proportion of intervals that were agreed

upon Agreements/agreements+disagreements Takes into account occurrence and

nonoccurrence agreement Varies from 0-100%

Occurrence and Nonoccurrence agreement

• Occurrence agreement The proportion of intervals that either coder

recorded the behavior that were agreed upon Positive agreement

• Non-occurrence agreement The proportion of intervals that either coder

recorded a nonoccurrence that were agreed upon

Negative agreement

Problem with agreement statistics

• We assume that agreement is due to accuracy

• Agreement statistics do not control for chance agreement

• So agreement could be due only to chance

Chance agreement and point by point agreement

Value of IOA statistics when true accuracy is 80%

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10% 20% 30% 40% 50% 60% 70% 80%

% of intervals during which the behavior occured

value of IOA statisticOccurrence agreement

Nonoccurrence agreement

Agreement matrix

Slack Jack

EagerBeaver

happy sad angry puzzled other

happy 60 5 1 1 3 70

sad 1 40 4 2 0 47

angry 0 3 12 0 7 22

puzzled 5 5 4 30 6 50

other 0 0 0 1 10 11

73 53 21 34 19 200

Using a 2x2 table to check agreement on individual codes

• When IOA is computed on the total code set it is an omnibus measure of agreement

• This does not inform us on agreement on any one code.

• To know agreement on a particular code the confusion matrix needs to be collapsed into a 2x2 matrix.

Eager Beaver

Slack Jack

happy sad angry puzzled other

happy 60 9 1 0 0 70

sad 6 40 0 1 0 47

angry 0 7 12 2 1 22

puzzled 0 4 3 30 13 50

other 1 0 0 1 10 11

67 60 16 39 24 200

Eager Beaver

Slack Jack happy All other emotions

happy 60 10 70

All other emotions

7 123 130

67 133 200

Baserate in A 2x2 table

20067

1237All other emotions

701060Happy

All other emotions

HappySlackJack

Eager Beaver

(67+70)/(2*200)= .34

Review

• Defined accuracy• Described the relationship between

chance agreement and IOA• Creating a 2x2 table• Calculating a best estimate of the

base rate

Kappa

• Kappa is an agreement statistic that controls for chance agreement

• Before kappa there was a sense that we should control for chance but we did not know how

• Cohen’s 1960 paper has been cited over 7000 times

Definition of Kappa

• Kappa is the proportion of non-chance agreement observed out of all the non-chance agreement

K = Po-Pe

1 - Pe

Definition of Terms

• Po= The proportion of events for which there is observed agreement. Same metric as percent agreement

• Pe= The proportion of events for which agreement would be expected by chance alone Defined as the probability of two raters

coding the same behavior at the same time by chance

Agreement matrix for EB and SJ with (chance

agreement)HappyEager Beaver

All other emotionsEager Beaver

HappySlack jack

.36 (.33) .36 .72

All other emotionsSlack Jack

.09 .18 (.15) .28

.46 .54

Po = .36+.18; Pe = .33 + .15; k = (.54-.48)/(1-.48)=.12

What determines the value of kappa

• Accuracy and base rate• Increasing accuracy increases

observed agreement therefore: kappa is a consistent estimator of accuracy if base rate is held constant

• If accuracy is held constant, kappa will decrease as the estimated true base rate deviates from .5

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baserate

obtained kappa

Obtained kappa, across baserate, for 80% accuracy

Accuracy 80%

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Obtained kappa

Obtained kappa, across baserate, for 80% and 99% accuracy

Accuracy = 80%

Accuracy = 99%

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obtained kappa

Obtained kappa, across baserate, from 80% to 99% accuracy

Accuracy=80%

Accuracy=85%

Accuracy=90%

Accuracy=95%

Accuracy=99%

Bottom line

• When we observe behaviors that are High or Low baserate our kappa’s will be low.

• This is important for researchers studying low baserate behaviors Many of the behaviors we observe in

young children with developmental disabilities are very low baserate

Criterion values for IOA

• Cohen never suggested using criterion values for kappa

• Many professional organizations recommend criterions for IOA

• e.g., The Council for Exceptional Children: Division for Research Recommendations 2005 “ Data are collected on the reliability or inter-observer

agreement (IOA) associated with each dependent variable, and IOA levels meet minimal standards (e.g., IOA = 80%; Kappa = .60)”

Criterion accuracy?

• Setting a criterion for kappa independent of baserate is not useful

• If we can estimate accuracy And I am suggesting that we can

• We need to consider what sufficient accuracy would be

Criterion accuracy cont.

• If we consider 80% agreement sufficient than Would we consider 80% accuracy

sufficient?• If we used 80% accuracy as a

criterion Acceptable kappa could be as low as .19

depending on baserate

Why it is really important not to use criterion kappas

• There is a belief that the quality of data will be higher if kappa is higher.

• This is only true if there is no associated loss of content or construct validity.

• The processes of collapsing and redefining codes often result in a loss of validity.

Applied example

• See handout for formulas and data

Baserate Kappa Accuracy.5 .81.9 .39.3 .48.7 .2.1 .7

Use the table on the first page of your handout to determine the accuracy of raters from baserate and kappa

    Observer 2        Intervals Intervals not      engaged Engaged or other   Intervals .8 .1 .9Observer 1 engaged               Intervals not .05 .05 .1  Engaged or other          .85 .15 1

P0 .85Pe .78Bas e ra te .88KappaAccu rac y (s ee t ab lePg 1 )Ca lcu la ti on s for Exa m ple 1

 Kap p a = ( . 85- .78 ) /( 1 - .78)

.32.85

Recommendations

• Calculate agreement for each code using a 2x2 table

• Use the table to determine the accuracy of observers from baserate and obtained kappa

• Report kappa and accuracy

Software to calculate kappa

• Comkappa, Developed by Bakeman to calculate kappa, SE of kappa, kappa max, and weighted kappa.

• MOOSES, Developed by Jon Tapp. Calculates kappa on the total code set and individual codes. Can be used with live coding, video coding, and transcription.

• SPSS

Challenge

• The challenge is to change the standards of observational research that demand kappa's above a criteria of .6 Editors PI’s Collaborators