[Book] Hot hand fallacy

 Hot hand fallacy states that if performing well in last consecutive trials, a person might perform well in the next trials. In fact, the streak (of well-performance) may just be because of pure chance. If this is the case, the results in the few consecutive trials infer nothing about the next trials.


Hot hand fallacy is perceived in various fields such as sport or business. We usually judge people (e.g., basketball players or companies) by statistics. But we usually misled by a hot hand fallacy. When a good player makes several baskets consecutively, we tend to think that his hand is “hot”, and that his teammates should give him the ball. So if an average player makes several baskets consecutively, does is mean that his is better than a good player? No, because if he is better, his statistics would have been better. The fact that he makes a lot of baskets consecutively implies that he might miss a lot of baskets too. We just don’t know when it will happen.

[Book] People, Perception, Perfection, and Randomness

 Perfection requires perfect perception. It is hard to achieve perfection, since the data we perceives is rarely perfect. So how do we determine whether what we perceive is true. In a more technical term, how do we accept or reject the hypothesis based on what we perceived? In this respect, statisticians resort to "Significant Testing" in order to make decision based on observations.

"Human perception is very narrow. There is only about 1 degree of visual angle around the retina center which has high resolution. Outside this region, the resolution drops off sharply. Therefore, we tend to move our eyes a lot to compensate for the narrow visual area."

[Book] The Dawn of Statistics

Statistics began as early as 1066, when William the conqueror, the Duke of Normandy, conquered and became the King of England. He would like to find out what exactly he did conquer and how much tax he can collect. So he sent out two groups of inspectors to men to do some survey on land and livestock. At that time, people believed that it is the God’s will to let people live or die. So, a survey of people as well as how they born and die were forbidden. As time changes, people changes. In later time, people began to believe that study of population is not against the God’s will, but is the way to understand him better. In the 16th century, the London Bill of Mortality was drafted. It was the first attempts to record people’s birth and death.

"Statistics can provide insights into the system from which the statistics are derived."

Source: The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow, Chapter 8 [Read the Book Review] [Read the Previous Part] [Read the Next Part].

[Book] Measurement and the Law of Errors

Ancient Experiment: Science or Art
In the old time, scientists perform experiment, and make the best intuitive guess of what the result should be. And, if they were to repeat the experiment, they could get totally different results. They just lacked a standard for measurement.
In other words, they use feeling rather than scientific method. Is this science? Or, is it art? “Any variation within a margin of error should be ignored.”

[Book] False Positives and Positive Fallacies

Conditional Probability

We learned earlier that more details can lead to more restriction and reduce the corresponding probability. More specifically, the probability of event A is always greater than the probability of events A and B.

But details do not always reduce the probability. It can increase the probability by shrinking the sample space. We can be more sure that a specific outcome will occur if we can cross off some of the sample space. This is known as “Bayes’ Theorem”.

Probability, Ratio, and the Law of Large Numbers

Probability and Ratio

You probably know about probability and ratio. Suppose I put 70 of black balls and 30 of white balls in an urn. General statements would be

• The Ratio of black balls (when comparing to all the balls in the urn) is 7:10
• If I draw a ball from the urn, the Probability that I would draw a black ball would be 7 in 10

A new blogspot test message no. 5 on Sept. 18