red is the correct choice (e.g., that responses to green following first- choice-errors to blue are more likely to be reinforced than are responses to red). This hypothesis corresponds to a discrete state model (called the N-state model) which contains one state for each of N sample. (or comparison) stimuli.
The state of the system, at any point in time, depends on the identity of the sample if it is present and on the similarity among the comparison stimuli. While the sample is present the system is most likely to occupy the state corresponding to the correct choice. With some probability, however, it might change to the state corresponding to another stimulus. The probability of such a change depends on the similarity between the stimuli. The more similar the stimuli, the higher the likelihood of a state change between them. These state changes continue without further input from the sample during the retention interval, but, at any point in time, the system is in only one state and is unaffected by any previous state it might have occupied. According to this model, second-choices depend solely on the first-choice-error (more specifically on the state corresponding to the first-choice) and therefore contain no additional information about the sample than did the first-choice ( Clarke, 1964). The pattern of second-choices made following each sample should, according to the N-state model, be fully described by the sequence of transitions from samples to first-choice-errors, and from first-choice-errors to second-choices. Four birds were tested ( Roitblat & Scopatz, 1983) with two sample durations and a number of retention interval durations. Each combination of sample and retention interval duration produced three 3 x 3 matrices, an example of which is presented in Table 5.1. The sample/first-choice matrix enumerates the frequency with which each choice was made following each, sample. The major diagonal of this matrix represents correct first-choices so those cells are set by definition to 0 in the sample/first-choice-error matrix. The sample/second-choice matrix enumerates the frequency with which each second-choice occurred following each sample. The first-choice/second-choice matrix enumerates the number of times each second-choice followed each first-choice. Because a first-choice to a given stimulus caused it to be darkened and therefore, no longer available, the cells along the major diagonal in this matrix are set to 0 by design.
The expected first-choice-error distributions were computed on the assumption that first-choice errors are distributed independently of the sample ( Roitblat, 1980). To generate the expected sample/second-choice distribution, the counts in the sample/first-choice-error and in the first- choice-error/second-choice matrices were each converted to row proportions and the two matrices were multiplied. The resulting matrix, converted back to counts, was then compared with the obtained sample/second-choice distribution. A significant difference between the two indicates that second-choices contained information about the sample that was not contained in the first-choice-errors.
Figure 5.1 displays the results of the comparisons between observed and expected distributions in the form of Phi-prime scores (square root of chi-squared). This figure shows that sample information is present in first-choice-errors, but that amount of information is not sufficient to account for the distribution of second-choices. These data are