{"product_id":"v4113letbyte","title":"V. 4:1 (13-13): Letters by Technical Analysis","description":"Letters by Technical Analysis\u003cbr\u003e\u003cbr\u003eEditor:\nClifford Sherry's article on the Gambler's Paradox (better known as the Gambler's Fallacy) in the October\nissue contains a serious error. In using Chi square to test the independence of price changes, Dr. Sherry\ngives the probability of obtaining a sequence of '+,+' or one of '-,-'as 0.1666 and the probability of\nobtaining a sequence of '+,-' or of a ',+' as 0.3333. In any random and independent sequence of events,\neach of which has any probability of 0.5, the probability of obtaining any one of the four possible\nsequences is simply 0.25.\u003cbr\u003e\u003cbr\u003eIn the sample of 270 days of soybean-meal prices, using the correct probabilities yields a total Chi square\nvalue of 3.88 rather than 51.73, which changes the conclusion of the study completely. Since 3.88 is not a\n\"significant\" Chi square, there is no reason to conclude that these price changes were non-random. The\nsame correction also applies to the lagged-time Chi square value.\u003cbr\u003e\u003cbr\u003eA finer point should also be made. In using Chi square to test for dependencies within sequences, the\noverall trend of the date should be adjusted for. Using 0.5 as the probability of a price increase in the\nsoybean-meal data ignores the fact that there are more price increase days than price-decrease days in the\ndata and confounds the test for dependencies with a test for overall trend. In the soybean-meal data, the\ntotal Chi square is only 0.61 when adjusted for trend.\u003cbr\u003e\u003cbr\u003eFinally, traders should note that since Chi square only considers nominal changes in price and ignores the\nmagnitude of those changes, a sequential dependency uncovered by a Chi square analysis may or may not\nbe exploited as a profitable trade.\u003cbr\u003e\u003cbr\u003eSincerely,\nGaylon L. Oswalt, Ph.D.\nOmaha, NE","brand":"store-traders-com","offers":[{"title":"Default Title","offer_id":52134012649841,"sku":"\\V04\\C01\\LETTER.PDF","price":2.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0900\/3843\/6209\/files\/unnamed_290d2da4-5357-4fce-978b-9b5ab086f412.jpg?v=1739662298","url":"https:\/\/shop.traders.com\/products\/v4113letbyte","provider":"Stocks \u0026 Commodities","version":"1.0","type":"link"}