Are There a Few Magic Numbers for Describing Complex Systems?
Can we understand all (fine-scale) patterns from a massive data set? If you were a genius, you may keep track of all the patterns. But, it is (almost) impossible to analyze all. That’s is why we employ statistics to understand and analyze a large data set and predict/estimate the future from statistical results (e.g. population, economic growth, the unemployment rate, or stock price).
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For example, to make a business model for kids, it is much easier to see the average birthrate in some regions rather than count the number of children in my neighborhood. Statistical approaches always provide just a few numbers to describe the complex systems. This simplification enables us to make a simple (predictive) model, leading to an efficient and optimized analytics.
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I agree that a few numbers make the complex system simple and I have experienced that this simple representation gives us the proper direction to make a better decision. Then, what is the good “number (statistic)” for massive data in our hands? The average? well, but the book also said: “there is no substitute for simply looking at data properly.”
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Hence, we should be careful to understand the complex system using only a few statistics. Some statistics are venerable to outliers such as average.
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Framing: Statistics Can Manipulate Our Thought
There are many examples of positive or negative framing. For example, pharmaceutical companies want to say that a new medicine has a 95% survival rate rather than a 5% mortality rate (positive framing). Investigative journalists want to say that 3,000,000 people are suspected of tax evasion every year rather than 1% of people (negative framing).
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This framing also appears in the graph. Assume that we need to draw a bar chart with two bars whose values are 95 and 98, respectively. If we draw a bar chart from 0 to 100, the two bars look similar. However, if we draw a bar chart from 90 to 100, we see totally different bars on the graph.
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How can we escape from this framing? Information providers should provide alternative data representations (different graphs, law data, tables) so that we can get a balanced view of the data by examining raw data.
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Also, we always should be skeptical when we see data. First, we should check who (and why) published statistical data; data do not lie, only presenters may lie.
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However, this argument does not refer to that statistics are totally crafty tricks. Statistics is still powerful to understand, analyze, and visualize data effectively.
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Moreover, in the age of Big Data, statistical knowledge is fast becoming the main tool to deal with big data correctly. That is, statistics are a double-edged sword; the power of statistics depends on us.
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