Fleiss' Kappa - Introduction

Introduction

Fleiss' kappa is a generalisation of Scott's pi statistic, a statistical measure of inter-rater reliability. It is also related to Cohen's kappa statistic. Whereas Scott's pi and Cohen's kappa work for only two raters, Fleiss' kappa works for any number of raters giving categorical ratings (see nominal data), to a fixed number of items. It can be interpreted as expressing the extent to which the observed amount of agreement among raters exceeds what would be expected if all raters made their ratings completely randomly. It is important to note that whereas Cohen's kappa assumes the same two raters have rated a set of items, Fleiss' kappa specifically assumes that although there are a fixed number of raters (e.g., three), different items are rated by different individuals (Fleiss, 1971, p.378). That is, Item 1 is rated by Raters A, B, and C; but Item 2 could be rated by Raters D, E, and F.

Agreement can be thought of as follows, if a fixed number of people assign numerical ratings to a number of items then the kappa will give a measure for how consistent the ratings are. The kappa, can be defined as,

(1)

The factor gives the degree of agreement that is attainable above chance, and, gives the degree of agreement actually achieved above chance. If the raters are in complete agreement then . If there is no agreement among the raters (other than what would be expected by chance) then .

An example of the use of Fleiss' kappa may be the following: Consider fourteen psychiatrists are asked to look at ten patients. Each psychiatrist gives one of possibly five diagnoses to each patient. The Fleiss' kappa can be computed from this matrix (see example below) to show the degree of agreement between the psychiatrists above the level of agreement expected by chance.