Compute Cohen’s kappa with variance and equal-zero test
Parameters: | table : array_like, 2-Dim
square array with results of two raters, one rater in rows, second
rater in columns
weights : array_like
The interpretation of weights depends on the wt argument.
If both are None, then the simple kappa is computed.
see wt for the case when wt is not None
If weights is two dimensional, then it is directly used as a weight
matrix. For computing the variance of kappa, the maximum of the
weights is assumed to be smaller or equal to one.
TODO: fix conflicting definitions in the 2-Dim case for
wt : None or string
If wt and weights are None, then the simple kappa is computed.
If wt is given, but weights is None, then the weights are set to
be [0, 1, 2, ..., k].
If weights is a one-dimensional array, then it is used to construct
the weight matrix given the following options.
- wt in [‘linear’, ‘ca’ or None] : use linear weights, Cicchetti-Allison
actual weights are linear in the score “weights” difference
- wt in [‘quadratic’, ‘fc’] : use linear weights, Fleiss-Cohen
actual weights are squared in the score “weights” difference
- wt = ‘toeplitz’ : weight matrix is constructed as a toeplitz matrix
from the one dimensional weights.
return_results : bool
If True (default), then an instance of KappaResults is returned.
If False, then only kappa is computed and returned.
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Returns: | results or kappa :
If return_results is True (default), then a results instance with all
statistics is returned
If return_results is False, then only kappa is calculated and returned.
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Notes
There are two conflicting definitions of the weight matrix, Wikipedia
versus SAS manual. However, the computation are invariant to rescaling
of the weights matrix, so there is no difference in the results.
Weights for ‘linear’ and ‘quadratic’ are interpreted as scores for the
categories, the weights in the computation are based on the pairwise
difference between the scores.
Weights for ‘toeplitz’ are a interpreted as weighted distance. The distance
only depends on how many levels apart two entries in the table are but
not on the levels themselves.
example:
weights = ‘0, 1, 2, 3’ and wt is either linear or toeplitz means that the
weighting only depends on the simple distance of levels.
weights = ‘0, 0, 1, 1’ and wt = ‘linear’ means that the first two levels
are zero distance apart and the same for the last two levels. This is
the sampe as forming two aggregated levels by merging the first two and
the last two levels, respectively.
weights = [0, 1, 2, 3] and wt = ‘quadratic’ is the same as squaring these
weights and using wt = ‘toeplitz’.
References
Wikipedia
SAS Manual