Errors of the Second Kind in Organoleptic Difference Testing

Abstract

An error of the first kind in difference testing by organoleptic methods is committed if it is said that a difference exists when in fact no difference is present. An error of the second kind is made when actual differences are overlooked. Errors of the first kind in organoleptic difference testing have been discussed by several authors (2, 3, 4, 5, 9, 10, 2 1 ) . I n particular, Lockhart (5) is quite clear on some points overlooked by others.The mathematical model for organoleptic difference testing is the binomial distribution. The probability of errors of the second kind based on the binomial distribution is discussed in detail in the literature (1,7,8). However, all the published discussions assume an unchanging fundamental probability. Thus, the published results might possibly apply t o difference tcsting by one "coinpctent" judge, but even this is doubtful due to psychological factors operating on the individual judge, which are largely beyond the control of the experimenter. When it comes t o the case of panel or general consumer testing the situation is greatly complicated by varying "thresholds," rate of increase of the probability of detecting differences, and direction of preference.It is the purpose of this paper t o present an experiment indicating the importance of varying thresholds and of rates of increase of probability of detecting differences for individuals in panel testing on the probabilities of errors of the second kind. These results will be contrasted with classical results in the literature where it is assumed that all individuals of the panel have identical tasting characteristics. The matter of errors of the second kind are very important because the whole program of flavor improvement is based upon detectable organoleptic differences. PRELIMINARY THEORETICAL CONSIDERATIONSLet us first consider a single taster with a constant probability of detecting a difference at a given level. We shall assume (a) that there is a fixed threshold f o r detecting a difference, and (b) that the probability of detecting a difference is proportional t o the concentration present, the concentration being measured on an appropriate scale above the threshold value up t o a certain point where the probability of detection becomes and remains one. Thus for this one taster there would be a threshold value, say &, and a value for 100% detection, say bl. The factor of proportionality expressing the relationship between concentration and probability of detection can be designated by ?&, but k~ is expressible in terms of CZI and bl in the form 1 kl = ~ (bl -al) I f we have a series or panel of tasters and denote by a l , bi, and ki the constants characterizing the ith taster, then it is readily seen that the situation is more complex since none of the constants a!, bi, and ki need be even approximately equal.We shall set the probability of an error of the first kind equal t o a and indicate the effect of the situations noted above on the probability of errors of the second kind. 206

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