Daily Speculations
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James Sogi
Philosopher, Juris Doctor, surfer,
trader, investor, musician, black belt, sailor,
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(address is not clickable)12/29/2005
Contingency Tables
I have 12 different surfboards, for big, small, medium, glassy, wind conditions. Each fits best in certain conditions. The difficult question is which one to bring to the beach. It's like different golf clubs for different parts of the course. Like surfboards and golf clubs, statistical models each work best in certain conditions. Parametric testing assumes certain models, for example, a normal distribution, exponential distribution, a binomial model. Sometimes it is obvious that a normal distribution and the standard parametric tests might not give an accurate reading, for example when the sample size is small, or is given as ordered, factorial or binomial responses. The difficulty is determining which test and which model is best to determine the needed information. Wrong assumptions can create wrong answers. John Rayner and John Best, A Contingency Table Approach to Nonparametric Testing, describes ideas for testing such situations. A few examples of models they use are related to marketing research, such as which milk tastes better using four different styles of milk container ranked on a scale of one to four, taste testing whiskey by age and grade, and even happiness ranked by years of education and number of siblings. The data are set up in tables, and the columns and rows are summed. Using the formulas and the various tests described, surprisingly accurate results can be obtained from seemingly sparse data. Many of the tests are based on the chi-square approach rather than a log-linear approach. Unfortunately, there are few pictures in the book and it is difficult for the uninitiated to slog through formulas to code these up. The key is to pick the one or two models in the book that apply to market data. Often an entire book might have a few applications that are relevant to markets, as opposed to chocolate tasting in Japan and Australia.
I'm looking at the application to markets, especially at the big ranges since late November, and even the small ranges this week. If a range could be set up as a contingency table, some of the methods could be used. Markets are not dissimilar to marketing products. Set up a contingency table to describe the range. Assume that the speculators/investors are the judges, and the S&P is the product. Divide the range into four areas, high, medium-high, medium-low, and low. The data is order sensitive since prior data affect later data, what I call the second ice cream cone effect. If we count the bars in each level by period, this will give a distribution about the range and reveal some aspect of the data, its distribution, skewness, linearity, etc. that may reveal information or lead to parametric testing with adjustments for the non-normality. The preference for high priced goods might lead to the conclusion of prosperity, spending habits and thus an eventual breakout to the upside. A penurious interest in low priced discounted goods, with no sales at marked-up values, especially at a late time, might indicate a depressed market heading for a drop. This is in progress and comments and corrections are appreciated.
Jim Sogi, May 2005
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