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A search for a supersymmetric partner of the top quark (t 1 ) has been performed by the OPAL experiment i n e + e collisions at LEP. The integrated luminosity of the data sample analysed was 69.1 pb 1 , which corresponds to 1.6810 6 produced Z 0 ! q q e v ents. Not 1 candidates have been found. This study excludes the existence of thet 1 with a mass below 45.1 GeV at 95% C.L., where the mixing angle of left-and right-handed partners is smaller than 0.85 rad or greater than 1.15 rad, and the mass dierence between thet 1 and the lightest neutralino is greater than 5 GeV.

The strong coupling constant, s , has been determined in hadronic decays of the Z 0 resonance, using measurements of seven observables relating to global event shapes, energy correlations and jet rates. The data have been compared with resummed QCD calculations, which are combined with the O(2 s) theory. The seven measurements agree to about 10%, and the nal result, based on a weighted average, is: s (M Z 0) = 0 : 120 0:006 ; where the error includes both experimental and theoretical uncertainties. This value corresponds to renormalization scale = M Z 0 and the error includes the uncertainty in this choice of scale. The present measurement complements previous determinations using the O(2 s) QCD matrix elements alone, and yields a compatible result, with comparable errors.

When a theoretical psychometric function is fitted to experimental data (as in the obtaining of a psychophysical threshold), maximum-likelihood or probit methods are generally used. In the present paper, the behavior of these curve-fitting methods is studied for the special case of forcedchoice experiments, in which the probability of a subject's making a correct response by chance is not zero. A mathematical investigation of the variance of the threshold and slope estimators shows that, in this case, the accuracy of the methods is much worse, and their sensitivity to the way data are sampled is greater, than in the case in which chance level is zero. Further, Monte Carlo simulations show that, in practical situations in which only a finite number of observations are made, the mean threshold and slope estimates are significantly biased. The amount of bias depends on the curve-fitting method and on the range of intensity values, but it is always greater in forced-choice situations than when chance level is zero.In many applications, it is necessary to determine the relation between the frequency of an event and the intensity of an independent variable. The psychometric function describing such a relation can be obtained with empirical methods such as the method of constant stimuli, staircase methods, the method of limits, and adaptive methods. If more than simply the threshold value of the psychometric function is required-as, for example, when the slope of the function is of interest-it is necessary to fit a theoretical curve (often a cumulative normal or logistic function) to the data points. The choice of a particular function will depend on the experimenter's hypotheses, but the techniques used to lit the curve remain the same irrespective of the function chosen. The most general curve-fitting method is the method of maximum likelihood, in which the parameters of the psychometric function chosen are such that it is the one most likely to have generated the observed data.Theoretical work on fitting psychometric functions (Berkson, 1955;Wetherill, 1963) has shown that the maximum-likelihood method is reliable and gives unbiased estimates of the psychometric function's parameters. But the work has been limited to situations in which chance level is zero-that is, in which the observable proportions of correct responses vary from 0 to 1.The first part of the present paper recalls these classic conclusions and extends them to the case in which chance level is not zero. This is the case for two-alternative (or Correspondence may be addressed to

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