Science of statistics is not about certainty

science-of-statistics-is-not-about-certaintyForecasting the future is a very tricky business. It is so difficult that statisticians can only give a guide on the occurrence of future events. Thus if asked about the chances of it raining the next day, most statisticians will give a probability forecast rather than a definite ‘yes’ or ‘no‘ answer. The 75 per cent probability referred to above means that during the rainy season, it is likely to rain in three days out of four or the statistician may say that there is a strong chance that it will rain during the rainy season.

Please note that this probability forecast does not mean that it will rain for three days then stay sunny for one day. Nor does it mean that it will definitely rain three days out of every four throughout the rainy season. It could well turn out that it rains throughout for 22 days then it will be sunny for 8 days during a rainy month (assuming that the month is 30 days in length) or the other way round or any one of many possible patterns. It does not even mean that there will definitely be 22 days of rain during a rainy month. There could well be 25 days or 30 days or even 5 (though the last case is extremely unlikely). You may well ask what then is the use of statistical forecast if it cannot give us a straight answer. The statisticians will tell you whilst their forecast may not be very useful in predicting the occurrence of rain from day to day, over a long period of time, their probability forecast can be used in several ways.

Firstly, the probability forecast of the meteorologist can be used to plan your activities better. If we know that there is a 75 per cent chance of rain in October, any outdoor functions we intend to have should be postponed to another month. Thus, if December has only a 25 per cent chance of raining, we would most certainly prefer to hold our outdoor function in December . But we may prefer to hold our garden festival in October when the heavy rain will keep the plants green and fresh.

Secondly, knowing the probability in advance, we are prepared for the worst possible situation. Meteorologists are able to tell in advance that every year in January there is, say, a 50 per cent chance of floods occurring in a Location in Asia. Based on this forecast, the Social Welfare Department is warned in advance to have enough places and food

ready before the rainy season starts because there is a very strong chance of flood occurring in any one year. On the other hand, because

there is only, say, a 5 per cent chance (once in 20 years event) of “oak l occurring in Asia, there is much less need for places and food to be kept ready.

Thirdly, while meteorologists cannot say with certainty whether it will rain tomorrow, over one season, their prediction is not likely a; be very far out. An occurrence which is very different from the prediction is not very likely to occur. Thus we can be reasonably certain that the number of rainy days in a single rainy season will vary, say, between 35 days and 55 days but it is very unlikely that the number of rainy days he 10 or 60. The range of possible error is therefore 45 days +/10 days (or 20 per cent).

Exactly the same principle applies to statistical forecasting used in share price prediction. Share prices are also extremely uncertain such that one can never give a precise forecast. But a good stock market analyst can provide you with some expectation of the likelihood of the price going up or going down. For example, he can tell you what are the approximate chances of making money on a certain share or class of share. But like the meteorologists, he cannot give you an exact prediction. Because prices are uncertain, we should only go for those situations in which we have a good ‘chance of winning. Thus, if a stock analyst warns you that there is only a 10 per cent chance that prices would rise above this level, we should avoid buying shares at that level. On the other hand, if he says that there is a 90 per cent chance that share prices would not fall further, we should certainly grasp the opportunity and buy. Later in the book, we shall see how we can determine the chances of making money.

Statistical forecasting is so uncertain that perhaps, we ought to end this section with a story about my professor of statistics in my under graduate days. He was such a careful man that tried as we might, we could not get him to admit that the probability of a coin turning out either head or tail is 100 per cent. He used to say that there was a chance, however small it might be, that the coin could land on its edge (for example, by falling into a cleft in the floor). The furthest he would go was to say that the probability was very close to 100 per cent but not 100 per cent. Please bear this in mind when you next hear rumours that XXXX is sure to go up to $10.00. Forecasting is such a tricky thing, we must protect our capital by being ultra conservative and maximize the odds in our favour. The next section will explain how we can improve the odds in our favour.

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