The Irony of Samples
Kahneman observes, “The exaggerated faith in small samples is only one example of a more general illusion-we pay more attention to the content of messages than to information about their reliability, and as a result end up with a view of the world around us that is simpler and more coherent than the data.”
Samples are deemed to be accurate in studies or experiments. However, the confidence ascribed to samples is based on illusions which are not necessarily accurate. Samples may simplify conclusions reading various aspects under study but they are not an accurate representation of reality; in fact, samples encourage the formulation of conclusions that are in agreement with imaginations.
The Irony of “Causal Explanations”
Kahneman explains, “Statistics produce many observations that appear to beg for causal explanations but do not lend themselves to such explanations. Many facts of the world are due to chance, includes accidents of sampling. Causal explanations of chance events are inevitably wrong.”
Causality is founded on sampling errors; accordingly, causal explanations are not a reflection of reality. Excessive faith in statistics is flawed because statics cannot account for the chance that results in conclusions regarding causal explanations. The statistics cannot accurately elucidate how chance events come about; there is no causality between chance and statistics.
“Illusion of Causality”
Kahneman expounds, “Michotte had a different idea: he argues that we see causality, just as directly as we see color. To make his point, he created episodes in which a black square, which immediately begins to move. The observers know that there is no real physical contact, but they nevertheless have a powerful “illusion of causality.” If the second object starts moving instantly, they describe it as having been “launched” by the first.”
Human beings may perceive' 'physical causality' which is unreal. Some perceptions of causality are illusions that are inherent among humanity. Configurations of causality do not necessarily arise from physical actualities. System 1 triggers the illusions which make the mind perceive causalities that are non-existent.
“The 3-D Heuristic”
Kahneman writes, “Have a look at the picture of the three men and answer the question that follows. As printed on the page, is the figure on the right larger than the figure on the left? The obvious answer comes quickly to mind: the figure on the right is larger. If you take a ruler to the two figures, however, you will discover that in fact the figures are exactly the same size. Your impression of their relative size is dominated by a powerful illusion, which neatly illustrates the process of substitution.”
In the text, Kahneman provides three images to elaborate on the implication of illusion. The illusion exploits depth whereby, the three images, of the same size, are placed at different heights. The 3-D interpretation makes the view to perceive that the images are of different sizes. The 3-D heuristic creates an illusion which informs the viewers’ judgment about the sizes of the images. Accordingly, 3-D interpretations are not absolutely exact, they could encourage erroneous conclusions.
“The Law of Small Numbers”
Kahneman states, “In a survey of 1662 schools in Pennsylvania, for instance 6 of the top 50 were small, which is an overrepresentation by a factor of 4. These data encouraged the Gates foundation to make a substantial investment in the creation of small schools, sometimes by splitting large schools into smaller units.”
However, the causality between small schools and excellent performance is flawed. Kahneman confirms that in reality "small schools are not better on average; they are simply more variable." So the Gates Foundation's investment in small schools was based on a flawed heuristic about small numbers' efficiency. The statisticians who made recommendations to the foundations based his recommendations on his bias regarding small numbers. He complied with his intuitions and used statistics to validate his preconceived notions regarding ‘small numbers.’
