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The search for statistical truth

The search for statistical truth. There is a hierarchy of truths:. Mathematical truth is independent of our perceptions. Examples are facts like ( x + y ) z = xz + yz and (for right triangles) a 2 + b 2 = c 2 .

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The search for statistical truth

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  1. The search for statistical truth

  2. There is a hierarchy of truths: Mathematical truth is independent of our perceptions. Examples are facts like (x + y) z = xz + yz and (for right triangles) a2 + b2 = c2 . Scientific truth is learned from experimental or observational science. We believe these truths, but they are not as eternal mathematical truths.

  3. Political truth is obtained from our social, political, and legal systems. It is illegal to litter. The drill sergeant must be obeyed. The Dear Leader never makes mistakes. Felt truth is what we feel inside. My child is the most beautiful in the world. Love is the most powerful force in the world.

  4. Mathematical truth is at the highest level, but it is problematic. Mathematical statements do not always link easily to our experiences. Mathematics is incomplete in a disturbing way. There are true statements for which no proof exists. (Gödel, 1931)

  5. We have based statistical theory on mathematical truth, the highest level. The search for statistical truth in our lives is at the experimental (second) level. It is not as solid as mathematical truth, and it can be overturned by new insight or by new data. Statistical truth is more profound than political truth or felt truth, but it is not as powerful a force in our lives.

  6. Statisticians work through inference. Facts obtained from data are used to make statements about populations. But….is inference for real? Why do humans think in terms of propositions like A B ?

  7. Why do we order our lives around statements like (earlier event)  (following event) ? For sure, such patterns of thinking had great value in terms of evolutionary survival.

  8. Consider this inferential statement: If you play with the crocodile, then … Evolution dictates that those who value this statement will survive.

  9. Formal inference is a mathematical truth. If it is true that P implies Q and ifP is also true, thenQ is true. This inference is known as “modus ponens.” It’s a critical part of symbolic logic. However, the choices involved in deciding which P and Q we want to discuss are all influenced by the evolutionary history that has created our human consciousness.

  10. So….. does cause-and-effect inference really exist? Maybe inference is just a way of thinking that has evolutionary value. Our entire perception of reality must be filtered through our minds. Our minds are wired to think in patterns that have evolutionary value, and not necessarily to think along lines of truth. Neurobiology is a hot topic at present. We have much to learn. As we advance, we’ll have to think about what exactly it means to be human. And we will also have to think about the essence of truth.

  11. So what’s real? Can the basis for truth ever get beyond what we claim to believe is true? A wonderful insight into the progress of neurobiology and attempts to answer the question above is this book: Why We Believe What We Believe, by Andrew Newberg and Mark Robert Waldman, 2006.

  12. Consider the statistician’s confidence interval. Such a statement might be “I am 95% confident that the true rate of growth for firms in this industry is between 1.80% and 4.42%.” The mathematics behind this is solid. There are however assumptions. These include normal populations, random sampling, and a clean understanding of how to define to problem in the first place. Our minds use confusing and prejudiced techniques to decide which problems are worth our attention.

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