| Subject | : | Significance of "Size" |
| Author | : | R. John Howe |
| Date | : | 10-08-2000 on 04:33 p.m. |
| Mr. Farber - Congratulations on having selected a focused area for your collecting. You appear also to have been skillful and fortunate in your acquisitions. I do not know of many collections with Mughal pieces. I also admire your attention to the pieces themselves and the empirical approach that you take. In your introductory essay you treat size as quite important and of course at some levels it is, since size is often implicated in function. But I notice that you treat quite small differences in size as potentially important. For example, you say: "Textile Arts currently has a djoinamas with the measurements of 155 x 114 cm. This is slighty outside the parameters suggested, but I will stay with the 120-160 cm x 80-110 cm approximation until a large database is assembled, because some limiting categorization which is close to including all the examples is necessary to understand any media discussed. A size definition of too large a range might be less effective or even meaningless." Would you say a little more about your decision here? Is your concern simply a more general one, to define a group of similarly sized textiles so as to make comparisons between them more defensible, or do you have some specific suspicions about pieces of different types that might be included if stricter size boundaries are relaxed? Four centimers on one dimension does not seem to me to be much of a difference. Congratulations on a well-organized and presented salon. Regards, R. John Howe |
| Subject | : | RE:Significance of |
| Author | : | Richard+Farber |
| Date | : | 10-08-2000 on 05:44 p.m. |
| Dear Mr. Howe, Thank you for your kind words. The question of size was treated in the introduction as an indication of the need to deepen study in this area. I believe that we need a broader base of reference. Question of design, origin, and age are more difficult and I only touched on them concerning one piece in the second part of the essay. As to the question of whether a few centimeters in important in including a piece within a group I would answer of course not. But I still thought it might reasonable to start with an hypothetical definition of the area discussed and then, over the months or years, when a larger base of reference is established to reevaluated the definition. The functional role of the wedding night embroidery in the Ottoman Area and in Central Asia - which often has an arch form although sometimes just a sheet embroidered on three sides with or without some embroidery in the corners - determined a larger sized embroidery with a different proportion between the embroidered borders, the arch and the open field to the pieces we are discussing. Since we reallty dont know much about the function[s] of these smaller embroideries I don't really think that at this stage we can think that smaller ones had one use and slightly larger ones another. I am looking foward to your further comments and help in solving some of the puzzles in part two. Sincerely Richard Farber |
| Subject | : | RE: Significance of size |
| Author | : | Steve Price |
| Date | : | 10-16-2000 on 08:41 a.m. |
| sprice@hsc.vcu.edu Dear Richard, I wonder if it might be useful to approach classification based on size from the other direction. Instead of trying to decide what the size limits are for a category, use a statistical estimation of the sizes within the total population from the distribution of sizes in pieces that you consider to be related. For example, the "prayer suzani" group in your collection includes 20 embroideries. The mean and (standard deviation) of the length, width and ratio of length to width are 136.7 (14.4) cm, 91.3 (9.7) cm and 1.51 (0.16), respectively. The population in your collection appears to have sizes more or less normally distributed, so 95% of the complete population from which the sample is drawn would be expected to be 107.9 to 165.5 cm long, 71.9 to 110.7 cm wide, and 1.19 to 1.83 times a long as wide. One of the things that's useful about this kind of analysis is that you can then measure any other prayer suzani and calculate the probability that it belongs to the same global population as yours. If it's more than 2 standard deviations from the mean for your sample, there is at most a 5% probability that it belongs to the same group; if it's more than 3 standard deviations away, the odds drop to 2%; more than four standard deviations brings it down to 1%, and so forth. Since we almost always work with implicit probability statements in making attributions, being able to do so explicitly ought to be a step forward. It at least allows us to specify the limits to which we can be confident about our statements. Regards, Steve Price |
| Subject | : | RE:Significance of |
| Author | : | Richard+Farber |
| Date | : | 10-16-2000 on 09:55 a.m. |
| Dear Mr. Price, Thank you very much for the "statistical" input. One of my hopes of this salon was finding other pieces that people throughout the world know about. I mentioned creating a data base in the essay and what you suggest is great. I also think that a numerical relationship of the borders of the embroidery to the size of the under arch field both widthwise and lengthwise might be included in the statistical base -- any other ideas out there as to relevant proportions. [angle of arch?] Aslo included should be design features such as types of secondary borders and closure or non closure of the "bottom". Number of elements in the design. -- any other ideas as to design elements that should be included? Thanks again Richard Farber NB I trust that the convention was a success. |
| Subject | : | RE:Significance of |
| Author | : | Yon Bard |
| Date | : | 10-16-2000 on 09:57 a.m. |
| I think a more useful appreoach would be to plot the width vs. height of each known piece on a piece of graph paper, and see whether the points form clusters. Of course there are mathematical techniques for determining clusters automatically, but simple eyeballing should suffice for starters. Regards, Yon |
| Subject | : | RE:Significance of size |
| Author | : | Steve Price |
| Date | : | 10-16-2000 on 11:29 a.m. |
| sprice@hsc.vcu.edu Dear Yon, I did the graphical exercise you suggest. There is an obvious clustering around the mean value for length and width, as you might expect, but nothing that would convincingly imply anything other than a unimodal distribution. That isn't to say that a larger sample size couldn't change things, although 20 is a reasonable number for most purposes. Regards, Steve Price |
| Subject | : | RE:Significance of |
| Author | : | Yon Bard |
| Date | : | 10-16-2000 on 03:04 p.m. |
| Steve, glad you cleared up the question of whether there were more than one clusters. I would like, however, to point out that your conclusion "If it's more than 2 standard deviations from the mean for your sample, there is at most a 5% probability that it belongs to the same group..." is not quite right. The only inference that you can make is "the probability that a given sample from a group is more than two standard deviations from the mean is 5%." Once, however, you do have such a sample, you cannot say anything about the probability of its belonging to this or any other group in the absence of knowledge about the existence and statistical parameters of other groups. To give simple examples: 1. If in fact all embroideries do belong to the same group (as seems to be the case here), then any new one belongs to the same group with 100% probability, regardless of its measurements. 2. Suppose there are two groups with the same standard deviations, but with means separated by four standard deviations. Then a sample falling exactly halfway between them, i.e., two standard deviations from each mean. would belong to either group with 50% probability. Of course, if a significant number of new samples came to light with measurements far from the mode of any known group, this would be strong statistical evidence for the existence of other groups. Regards, Yon |
| Subject | : | RE:Significance of size |
| Author | : | Steve Price |
| Date | : | 10-16-2000 on 04:19 p.m. |
| sprice@hsc.vcu.edu Dear Yon, Thanks for unscrambling my garbled rendition of probability and statistics. Steve Price |