It is concluded that there are differences between the wines and, in the case of the reds, national differences. It is shown that even skilled tasters can often be out by as much as 3 when judging on a scale from 0 to For the statistician, Bayes factors are contrasted with F-values. DATA This note deals with the analysis of some data from one of the most famous wine-tastings, as reported in the Underground Wine Journal for July
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It is concluded that there are differences between the wines and, in the case of the reds, national differences. It is shown that even skilled tasters can often be out by as much as 3 when judging on a scale from 0 to For the statistician, Bayes factors are contrasted with F-values. DATA This note deals with the analysis of some data from one of the most famous wine-tastings, as reported in the Underground Wine Journal for July The tasting was organized by Englishman Steven Spurrier in Paris in order to introduce Californian wines to experienced, French wine-tasters.
Some French wines were included to add to the interest. There were 11 tasters, one of whom was Spurrier, and another was an American, Patricia Gallagher these two were co-directors of L'Académie du Vin in Paris.
The remaining 9 were French. Table 1 lists them, together with their numerical coding used in other tables and in this text. There were two tastings. One was of Chardonnays; the other of Cabernet Sauvignons, that is, of wines in which that grape was predominant. In both tastings there were 10 wines in all, 6 American and 4 French. The Chardonnays are listed in Table 2, the Cabernets in Table 3, in both cases with their numerical codes.
The American wines were all from the Napa valley. The French Chardonnays were from Burgundy; the French Cabernets from Bordeaux; in both case wines of distinguished pedigrees. Each taster tasted every wine once, giving it a score from 0 to 20 though 19 and 20 were never used. The results are given in Table 4 for the white wines, and in Table 5 for the reds. Thus taster 4 gave Chardonnay E a score of This is virtually all the information available. We do not know in which order the wines were tasted, so that any possible carry-over effects cannot be investigated.
It is not clear whether the tasters compared notes. They differ on the reds. The tastings were all blind. There is a suggestion that some, at least, of the tasters gave their opinion as to the country of origin of a wine, but no record is available.
Of course, in giving a high score to a wine, an experienced taster may be reflecting his preference for the familiar as against the strange. The results surprised the French and delighted the Californians.
Our task is two-fold: to see how far these views are justified; and to explore the possibility of a statistical analysis of a well-organized tasting using modern methods. MEANS Table 6 lists the mean scores over the 11 tasters for each of the 20 wines under the heading 'raw means'. The other values in the table will be discussed later. Also listed are the means for each country and overall, both for red and white wines.
Notice that, unlike those for the tasters, the codes for the wines are in a purposeful order, namely from A, which has the highest mean, to J for the lowest. There are marked differences between the Chardonnay wines, which are confirmed by a statistical analysis provided in Section 5 below.
There are three that do well, with mean scores around 14 A,B,C , one of which is French. One American does badly J. The remainder form a more homogeneous group with mean scores between The French do slightly better than the Americans but the difference is unimportant and could easily arise by chance. If the poorly-performing wine J is removed, the American mean is higher than the French, but again the difference is unimportant. Thc exclusion of wine J has been justified on account of its non-Gallic character, and it is certainly true that the two non-French tasters 4,8 gave it higher scores than any Gallic taster.
Nevertheless, the same argument has been put forward for wine G in the Cabernet tasting, whereas it did not disgrace itself. The first conclusion is that the American Chardonnays did as well as the French, but that there are real differences between some wines.
If the French were expecting to give high marks to their own wines in comparison with those from Napa, they failed. There are similarly marked differences between the Cabernets, that again are confirmed by a statistical analysis in Section 5. The wines do not naturally group themselves, there being a steady trend from the top two A,B at a mean score of Unlike the whites, the French reds are really judged better than the Americans with a mean score that is higher by 2.
Four US wines do rather poorly and only two are up with the French. Presumably in the scoring by the French tasters, they would judge a wine of Gallic type more highly than one of a different style, as the Americans were. The latter were pure Cabernets whilst the familiar French style is not. This national difference is slightly supported by the fact that the non-French tasters 4,8 did tend to give high marks to US wines.
Thus taster 4 gave wine G a score of 17, against an average of On this simple basis of the means, the tasters observed real differences between the wines, both red and white. With the whites, the Americans held their own, but were not so successful with the reds. The claim that the Americans won is presumably based on the fact that both the top wines were from the Napa valley. We will later see why this claim is probably fallacious.
We now turn to the tasters. Their means over the 10 wines for both of the tastings are listed in Table 7. In the case of the Cabernets, the differences are most reasonably due to chance. There are substantial differences with the Chardonnays, but these largely, though not entirely, disappear if the rogue wine J is removed. Whatever variation there is between the tasters is small in comparison with that between the wines. In any case, in comparative tastings it does not matter if a taster is biased.
Another reason for not paying much attention to the apparent difference is that they are not systematic from white wine to red, with the exception of taster 5 who is low on both. This tricky problem is now addressed. The means given for the wines are somewhat misleading for a reason now to be explained. Suppose that there were truly no differences between the 10 wines in each group.
Then, because tasting and scoring are not precise sciences, the means over the 11 tasters will not all be equal, one wine will be at the top, another will be at the bottom in the scale of means. The spread of the observed means is spurious, for the wines are truly the same. To incorporate this observation, the spread needs to be reduced. The same consideration applies when there are as in this tasting real differences between the wines.
The apparently best wine is truly not as good as it looks: the apparently worst one is not all that bad. To correct for this, the means need to be 'shrunk' towards the average over all the wines. Table 6 provides, in addition to the observed means, these shrunk values. Thus the top Cabernet at Chardonnay I rises from The eccentric J has been removed for technical reasons. The revised, shrunk means provide a better reflection of the true worths of the wines than do the raw data.
With these corrected values, it is now possible to compare the wines in pairs. This is done in Table 10 for the whites, and in Table 11 for the reds. Each entry in the table is the probability, expressed as a percentage, that the wine of that row is better than the wine of that column.
Thus, referring to Table 11, the entry of 73 in the row numbered B and column numbered D, means that there is a probability of 0. Thus the first three Cabernets are all better than the last 4. Again wine J has been omitted from the Chardonnay table. It can now be seen why the claim that, since a US wine was the best in each class, the Americans won, is doubtful. It is not until wine A is compared with wine E, another American, that there is substantial probability of a real difference.
Similar remarks apply to the whites. Consequently, if we take the score given by a taster to a wine, it will be affected by the wine and by any bias of the taster.
It will also be affected by the fact, already mentioned, that tasting is not a precise science. It is revealing to see how large this last effect is.
To illustrate, consider taster 4 with Cabernet E. She gave it a score of 16 Table 5. The mean for all Cabernets is E had a mean over all tasters of Taster 4 had a mean over all wines of So taking account of the wine and the taster involved, the score expected would be The observed value of 16 is in excess of this by 1. It is called a residual. Table 8 lists all the residuals for the Chardonnays, and Table 9 does the same for the Cabernets.
A negative entry means that the score given was less than that expected on the basis solely of the wine and the taster. There is no systematic pattern to these residuals but there are a few large values. With the white wines, taster 3 gave an exceptionally low score of 3 to wine A, giving rise to a residual of With the reds, there is a possibility that the tasters confused wines H and I.
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Using this type of simulation enables one to examine the velocity field of galaxies and DM independently without an ad hoc assumption of bias between galaxies and DM. Accepting the fact that the existing peculiar velocity data do not allow us to compute the ideally defined as in OS90 , they defined a modified Mach number that incorporates the observational errors in measured distances due to the scatter in the Tully-Fisher relation. They constructed a mock catalog of the observations using SCDM hydrodynamical simulations similar to those that were used by SCO92 and calculated their modified from them. S93 obtained smaller than did OS90 because they included all velocity components on scales less than the bulk flow into the velocity dispersion, whereas OS90 erased the small-scale dispersion by smoothing. As a consequence, the estimates of S93 on are larger, resulting in a smaller.
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