Useful effect size interpretations for single case research

An obstacle to broader acceptability of effect sizes in single case research is their lack of intuitive and useful interpretations. Interpreting Cohen's d as "standard deviation units difference" and R2 as "percent of variance accounted for" do not resound with most visual analysts. In fact, the only comparative analysis widely supported in single case research (SCR) is "percent of nonoverlapping data." This article explores five alternative interpretations of Cohen's d and R2 effect sizes that may be more acceptable to the SCR field. They are: (a) Cohen's (Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum) "Percent of Nonoverlapping Data" (CPND), (b) Parker et al.'s (Parker, R.I., Cryer, J., Byrns, G., 2006. Controlling trend in single case research. School Psychology Quarterly, 21, 418-440, Parker, R.I., Hagan-Burke, S., Vannest, K., in press. Percent of all non-overlapping data (PAND): An alternative to PND. Journal of Special Education) "Percent of All Nonoverlapping Data" (PAND), (c) Rosenthal et al. (Rosenthal, R., Rosnow, R., & Rubin, D. (2000). Contrasts and effect sizes in behavioral research: A correlational approach. Cambridge: Cambridge University Press.) "Binomial Effect Size Display" (BESD), (d) "Percentile Rank in Control Group" (PR), and (e) McGraw and Wong's (McGraw, K. O., & Wong, S. P. (1992). A common language effect-size statistic. Psychological Bulletin, 111, 361-365) "Common Language Effect Size" (CLES). Each of the five interpretation schemes are applied to a published data set and are evaluated according to (a) intuitive appeal, (b) relevance to visual analysis, (c) ease of calculation, and (d) technical adequacy. Three of the five appear to be improvements over prevailing practice.     

The temporal course of the frustration effect

General activity subsequent to reward (R) and nonreward (N) was monitored at 5-sec intervals with a stabilimeter in the runway goal box. Activity of never-rewarded control Ss was also measured. In Expt 1 it was found that the frustration effect (difference between N- and R-trial activities) disappeared after about 40 sec of goal box confinement. This disappearance of the frustration effect was due to activity increase on R trials rather than activity decrease on N trials as a function of time. Comparison of N-trial activity with control group activity indicated that frustration does not dissipate within 60 sec. Expt 2 investigated activity following reward and nonreward as a function of reward magnitude. Evidence from these experiments suggests that the late R-trial activity increase results from frustration, possibly conditioned to apparatus cues on N trials.     

The effect of failure and frustration on reflective and impulsive children

Failure was hypothesized to be an antecedent of a reflective style of responding and frustration an antecedent of an impulsive style. Failure and frustration were manipulated with an anagrams task and their effect on latency and errors on the Matching Familiar Figures Test (MFF) was assessed. The Failure group increased its latency on the MFF, replicating Messer's (1970) research, while the Frustration group showed a nonsignificant decrease in latency. There was a relation between an increase in latency and a decrease in errors on the MFF. The findings were related to research on the “frustration effect” in children and were interpreted as suggesting the need for research on the effects of the amount and patterning of failure on reflection-impulsivity.     

Reexamining the frustration effect in rats: Aftereffects of surprising reinforcement and nonreinforcement

The reinforcement-omission effect (ROE; also called frustration effect), or greater response strength immediately after nonreinforcement (N) than reinforcement (R), has been traditionally interpreted in terms of one of two factors: transient facilitation after N induced by primary frustration or transient suppression after R induced by postconsummatory processes. Three instrumental lever-pressing experiments with rats demonstrated that the ROE can be caused by either factor in isolation, or by both acting simultaneously. The distribution of trials and the interval between N or R and the target response determine which factor would cause the ROE. Both aftereffects decay in time, but the after-N process decays at a slower rate than the after-R factor.     

The prosodic expression of anger: Differentiating threat and frustration

A theory relating aggression and the pitch of vocalizations [Ohala, 1983, 1984] predicts that the expression of anger in humans should have a low pitch; however, experimentally anger is found to have a high pitch. A possible resolution of this discrepancy is that there are two different prosodic expressions of anger, one with low pitch and one with high pitch. To investigate this possibility, 27 different expressions of the phrase “Don't do that” were tape-recorded. Subjects first rated how angry each utterance sounded and then categorized each utterance as expressing either frustration, threat, disgust, advice, or emotional neutrality. Some utterances were rated as angry and categorized as frustration; other utterances were also rated as angry, but categorized as threat. Frustration correlated with higher fundamental frequency (F₀). Threat did not correlate with lower F₀, but it correlated with lower perceived pitch.     

Capuchin monkeys, inequity aversion, and the frustration effect

Each of 4 female capuchin monkeys ("model") was paired with another female capuchin ("witness") in an adjacent cage. In Phases 1 and 3, a model could remove a grape from the experimenter's hand while the witness watched. The witness was then offered a slice of cucumber, a less preferred food. Trials alternated between subjects 50 times, defining a session. In Phases 2 and 4, both were offered cucumber. Witness rejections of cucumber were infrequent and were not dependent on whether models received grape or cucumber. When models were offered cucumber, they rejected it at higher rates than did witnesses. These results fail to support findings of Brosnan and de Waal. An account based on the frustration effect accommodates these results and those of Brosnan and de Waal.     

The effect of metronome pacing on selected aerodynamic patterns of stuttered speech: Some preliminary observations and interpretations

The purpose of this investigation was to provide some preliminary data regarding the effects of metronome pacing on physiological aspects of speech during stuttering. Five aerodynamic measures were chosen as dependent variables: (a) peak intraoral air pressure, (2) intraoral air pressure onset duration, (3) intraoral air pressure offset duration, (4) total intraoral air pressure duration, and (5) peak air flow rate. Five adult stutterers and five adult nonstutterers read a prose passage containing 12 English consonants, each in three syllable-initial stressed positions, during a control condition and experimental condition. In the experimental condition the subjects read the passage while synchronizing one word per beat at 60 beats per minute. The results demonstrated that both stutterers and normals evidenced lower peak pressures and greater pressure durations during metronome pacing. Air flow rates increased for normal subjects and decreased for stutterers in the experimental condition. Dysfluencies recorded during the control condition were observed to have much more rapid intraoral air pressure onsets when compared with fluent counterparts in the experimental reading. These results were interpreted with reference to Wingate's (1969) modified vocalization hypothesis and Van Riper's (1971) altered timing concept.