SINFA: Multivariate uncertainty analysis for confusion matrices
SINFA: Multivariate uncertainty analysis for confusion matrices
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SINFA：混淆矩阵的多元不确定性分析
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发表时间：
1976
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通讯作者：
Marilyn D. Wang
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作者：
Marilyn D. Wang
刺激-反应混淆矩阵通常用于总结知觉实验的结果，在知觉实验中，受试者必须从一组封闭的刺激中识别出哪一个刺激出现在给定的试验中。受试者的表现通常通过计算所传输的刺激信息的量来评估。在不确定性分析（Garner，1962）的术语中，传输信息是偶然不确定性U（S：R）的特殊情况，其中偶然性介于刺激和响应之间。当刺激是多维的时，可以评估针对单个维度或特征传输的信息量。这是通过组合混淆矩阵的单元格以形成特征混淆矩阵并计算该简化矩阵的偶然不确定性来实现的。如果刺激特征是正交的，并且如果受试者对不同特征的反应是独立的，则U（S：R）只是特征的偶然不确定性的总和。如果刺激特征是冗余的，或者如果对特征的响应不是独立的，则特征偶然不确定性的总和将大于U（S：R），因为没有考虑冗余。对于包含特征F1、F2、.，Fk，U（S：R）可以表示为多个偶然不确定性U（F1，F2，.，Fk：h，f2，.，fk），其中，""字母表示刺激特征，""字母表示响应特征。Garner（1962）已经表明，多重偶然不确定性可以被划分为可加分量，并且有很多方法来执行划分。划分的一种方法涉及k项的计算，k项的形式为：U（FI：（1），UF f（F2：f2），11 UFIF，flf，（Fa：fa），...、UF1F、. fk-lflf，. fk-1（Fk：fk）。第一项是F1的偶然不确定性。第二项是F2的部分偶然不确定性，其中F1的影响已经被部分消除。第三项是Fa的部分偶然不确定性，其中F1和F2的影响都被部分化。k个这样的项的和将总是小于或等于U（S：R），并且，
Stimulus-response confusion matrices are often used to summarize the results of perceptual experiments in which subjects must identify which stimulus, from a closed set of stimuli, has been presented on a given trial. The subject's performance is often assessed by calculating the amount of stimulus information transmitted. In the terminology of uncertainty analysis (Garner, 1962), transmitted information is a special case of contingent uncertainty U(S: R), where the contingency is between stimuli and responses. When the stimuli are multidimensional, it is possible to assess the amount of information transmitted for a single dimension or feature. This is accomplished by combining the cells of the confusion matrix to form a feature confusion matrix and calculating contingent uncertainty for this reduced matrix. If stimulus features are orthogonal and if the subject's responses to the different features are independent, then U(S: R) is simply the sum of the contingent uncertainties for the features. If the stimulus features are redundant or if the responses to the features are not independent, then the sum of the feature contingent uncertainties will be greater than U(S: R) because the redundancy has not been taken into account. For multidimensional stimulus sets containing features FI , F2 , ... , Fk, U(S:R) may be represented as a multiple contingent uncertainty U(FI , F2 , ... , Fk: h, f2 , ... , fk), where uppercase letters designate stimulus features and lowercase letters designate response features. Garner (1962) has shown that the multiple contingent uncertainty can be partitioned into additive components and that there are a great many ways to perform the partitioning. One method of partitioning involves calculation of k terms, k of which are of the form: U(FI :(1), UF f (F2:f2), 1 1 UFIF,flf,(Fa:fa), ... ,UF1F, ... Fk-lflf, ... fk-l (Fk : fk). The first term is the contingent uncertainty for Fl. The second term is a partial contingent uncertainty for F2 in which the effects of F1 have been partialed out. The third term is a partial contingent uncertainty for Fa in which the effects of both FI and F2 have been partialed. The sum of k such terms will always be less than or equal to U(S: R) and, there-