Equivalence tests for comparing correlation and regression coefficients

Equivalence tests are an alternative to traditional difference‐based tests for demonstrating a lack of association between two variables. While there are several recent studies investigating equivalence tests for comparing means, little research has been conducted on equivalence methods for evaluating the equivalence or similarity of two correlation coefficients or two regression coefficients. The current project proposes novel tests for evaluating the equivalence of two regression or correlation coefficients derived from the two one‐sided tests (TOST) method (Schuirmann, 1987, J. Pharmacokinet. Biopharm, 15, 657) and an equivalence test by Anderson and Hauck (1983, Stat. Commun., 12, 2663). A simulation study was used to evaluate the performance of these tests and compare them with the common, yet inappropriate, method of assessing equivalence using non‐rejection of the null hypothesis in difference‐based tests. Results demonstrate that equivalence tests have more accurate probabilities of declaring equivalence than difference‐based tests. However, equivalence tests require large sample sizes to ensure adequate power. We recommend the Anderson–Hauck equivalence test over the TOST method for comparing correlation or regression coefficients.     

The formation of linked perceptual classes

Multiple-exemplar training with stimuli in four domains induced two new fill-based (A1' and A2') and satellite-image-based (B1' and B2') perceptual classes. Conditional discriminations were established between the endpoints of the A1' and B1' classes as well as the A2' and B2' classes. The emergence of linked perceptual classes was evaluated by the performances occasioned by nine cross-class probes that contained fill variants as samples and satellite variants as comparisons, along with nine other cross-class probes that consisted of satellite variants as samples and fill variants as comparisons. The 18 probes were first presented serially and then concurrently. Class-consistent responding indicated the emergence of linked perceptual classes. Of the linked perceptual classes, 70% emerged during the initial serial test. An additional 20% of the linked perceptual classes emerged during the subsequently presented concurrent test block. Thus, linked perceptual classes emerged on an immediate or delayed basis. Linked perceptual classes, then, share structural and fuctional similarities with equivalence classes, generalized equivalence classes, cross-modal classes, and complex maturally occurring categories, and may clarify processes such as intersensory perception.     

The effects of nodality on the formation of equivalence classes

A four-member equivalence class (A → B → C → D) can be formed by training AB, BC, and CD. The nodal stimuli, B and C, mediate all of the derivative (transitive and equivalence) relations in the class. The derivative relations AC, CA, BD, and DB are separated by one node, whereas AD and DA are separated by two nodes. How do the number of nodes that separate the stimuli in a derivative relation influence the induction of stimulus control exerted by that relation? Seven college students learned two four-member classes made up of nonsense syllables. After training, all derivative relations were presented repeatedly without informative feedback. Stimulus control exerted by each derivative relation was assessed concurrently. For the 7 subjects, control exerted by the derivative relations increased gradually with repeated presentations. With 6 of the 7 subjects, the one-node relations exerted more control than the two-node relations during the process. However, the disparity between the one- and two-node relations decreased with repeated presentations. Eventually, all derivative relations exerted complete control. The control exerted by derivative relations during induction was inversely related to the number of nodes separating the terms in the derivative relations. These results demonstrate that nodal distance is a determinant of the relatedness of stimuli in equivalence classes. The findings are discussed in terms of remote association, semantic memory networks, and the study of transitive inference.     

Citations of Murray Sidman's work in JEAB: Evidence of a long and large contribution

We examined citations of Murray Sidman's publications in the Journal of the Experimental Analysis of Behavior from the journal's inception in 1958 through May 2020. On average, he was cited 35.6 times per year. The rate of citation did not change substantially across time and the cumulative citation count was 2,212. His 10 publications cited most often deal with behavior-analytic research methods, stimulus equivalence, and unsignaled free-operant (or Sidman) avoidance. Our data provide clear evidence of the breadth and depth of Sidman's influence on the experimental analysis of behavior across 7 decades. His contributions were both exceptional and praiseworthy and his legacy will long endure.     

Do common elements predict class merger: A test of Sidman's theory of equivalence

The study presented here investigated the effect of common and uncommon elements on class merger as predicted by Sidman in his reconceptualization of stimulus equivalence suggesting that common elements among contingencies can facilitate emergent performances (1994, 1997, 2000). Eight adult participants were exposed to a procedure that arranged for stimulus–reinforcer correlations in Phase 1 and response–reinforcer correlations in Phase 2 of a 3-phase study. In the common element group, the visual images serving as reinforcers were the same in Phase 1 and Phase 2. In the uncommon elements group, the images serving as reinforcers were different in Phases 1 and 2. In Phase 3, participants were given an opportunity to respond but no feedback was programmed. The results showed that participants' responding was well differentiated in the common element group and undifferentiated in the uncommon elements group. These results are predicted by Sidman's revised formulation of the provenance and scope of equivalence relations. Specifically, these data support Sidman's (1994, 1997, 2000) suggestion that elements of a contingency enter into an equivalence class and common elements among contingencies are sufficient to produce class mergers. The findings highlight an emergent simple discrimination and raise some interesting considerations about the definition of equivalence under the new formulation.     

Differential recognition of pitch patterns in discrete and gliding stimuli in congenital amusia: evidence from Mandarin speakers

This study examined whether "melodic contour deafness" (insensitivity to the direction of pitch movement) in congenital amusia is associated with specific types of pitch patterns (discrete versus gliding pitches) or stimulus types (speech syllables versus complex tones). Thresholds for identification of pitch direction were obtained using discrete or gliding pitches in the syllable /ma/ or its complex tone analog, from nineteen amusics and nineteen controls, all healthy university students with Mandarin Chinese as their native language. Amusics, unlike controls, had more difficulty recognizing pitch direction in discrete than in gliding pitches, for both speech and non-speech stimuli. Also, amusic thresholds were not significantly affected by stimulus types (speech versus non-speech), whereas controls showed lower thresholds for tones than for speech. These findings help explain why amusics have greater difficulty with discrete musical pitch perception than with speech perception, in which continuously changing pitch movements are prevalent.