Sampling experiments are reported that show that the uncorrected chi-square test of independence is exceptionally robust with respect to small expected frequencies in ^h R × C ^H contingency tables. In general, error rates that exceed .06 occurred only when both marginal probability distributions were extremely skewed and sample size was small. Nevertheless, the quality of the approximation of chi-square probabilities for exact multinomial probabilities was sometimes poor, although excessive errors in approximation by W. G. Cochran's (1952) criteria usually resulted from actual error rates being smaller, not larger, than the nominal level. A distinction is made between accuracy of approximation and control of the Type I error rate as considerations dictating the advisability of using an approximate test. (38 ref)
Brain electrical potentials evoked by visual stimulation were analyzed to study the neurophysiological mechanism associated with hypnotic hallucination. The visual evoked responses of 6 high-and 6 low-hypnotizable subjects were compared in three hypnotic conditions: stimulus enhancement. stimulus diminution, and stimulus elimination (obstructive hallucination). High-hypnotizable individuals demonstrated significant suppression of the later components of the evoked response (N 2 and P l) while experiencing obstructive hallucinations, indicating a change in information processing. This effect was significantly greater in the right. as compared to the left, occipital region. Hypnosis involves intense concentration (Hilgard, 1965; Spiegel & Spiegel, 1978; Van Nuys, 1973) and can, therefore, be a useful tool for exploring the neural mechanisms involved in focused attention. The hypnotic state can be considered one extreme of a continuum in which focus is accomplished at the exPense of the range of ambient awareness. In animals, neural controls on input processing have been demonstrated (Lassonde. Ptito, & Pribram, 1981; Spinelli & Pribram, 1966, 1967). The nature of these controls suggests that they operate much as does a zoom lens in providing a trade-off between a wide-angle view (ambience) and resolution (focus; Marg & Adams, 1970; Pribram, 1966, 1967). Individuals vary in hypnotizability, and there is some evidence that in hypnotizable individuals the amplitude of the evoked response (ERP) is diminished in response to hypnotic suggestion that the stimulus is attenuated (Clynes, Kohn,
A Monte Carlo program for sampling 2 by 2 contingency tables from a user-specified population is discussed. Applications include computer-assisted instruction (CAl) of statistics, evaluation of actual vs nominal Type I error rates of the chi-square test of independence when expected frequencies are less than 10, and estimation of the power of the chi-square test.In the present paper, we describe a Monte Carlo program, Clll-PHI, which randomly samples 2 by 2 contingency tables from a user-specified population. Figure la presents the symbolic notation used for depicting the population. The parameters requiring specification are the row and column marginal probabilities [P(Ai), P(Bj)] , the degree of association between the two categorical variables (c/» , and the size and number of samples to be drawn (N, K). The marginal probabilities and the phi coefficient uniquely determine the joint probability distribution [P(ABjj)] of the population. 1 These parameters are specified on-line when the program is run (Figure 1b). CHI-PHI then randomly samples N observations for each of the K samples such that the probability of obtaining an observation in Cellij is equal to the joint probability for that cell. In the special case where c/> =0, the variables are independent and the program sets the probability of obtaining an observation in Cellij equal to the product of the corresponding marginal probabilities [P(ABij) = P(Ai)P(B j)] . When tf> '* 0, the program sets the probability of obtaining an observation in Celljj equal to the product of the corresponding marginal probabilities incremented or decremented by whatever amount is necessary to produce the degree of association specified by the user [P(~j) =P(AJP(Bj) ±~p] .For each sample of N observations drawn from the user-specified population, the program computes the chi-square statistic and the phi coefficient, and determines whether or not the observed chi square is significant (p < .05). CHI-PHI then outputs the following information: (1) the theoretical expected frequency of Cellg, assuming independence between the two variables, obtained by multiplying sample sizeThe computer simulations reported in this paper were conducted on the Dartmouth Time-Sharing System, using the recently installed Honeywell66/40 duplex computer system. We wish to express our appreciation to Dartmouth
A computer-automated testing apparatus for monkey and human subjects is described. This dual-computer system generates programmable color video displays and permits on-linecollection of behavioral and electrophysiological data. Video displays are generated by an Apple II minicomputer linked via a serial transmission port to a general-purpose laboratory computer (DEC PDP-1l/34). Control of event sequences is determined by serial interaction between the two computers. Software (programs) for the collection and analysis of event-related brain potentials data is described, and the experimental and clinical applications of this DADTA VI (Discrimination apparatus for discrete-trial analysis, Version 6) for neuropsychology are discussed.
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