Interdependent Factors in Statistics

Yesterday, we considered the wise saying, “Figures don’t lie, but liars figure.” We said that one problem with statistical arguments is that they often don’t include all the variables. A second problem with statistical arguments is that they don’t ensure that all of their variables are independent. Therefore, we must consider the interdependent factors.

For a trivial example, let’s suppose I ask, “What are the odds that I will buy my grandson a BMW for his birthday?” The first question we should ask is, “Is he old enough to drive?” A second question might be, “Can he get insurance?” A third variable would be, “Do I have enough money to buy the car?” Finally, a fourth variable might be, “Would he be happy with a used BMW?”

Since I love my grandson, I might say that the odds of me buying a car for him are 100%. However, as we consider each of those variables (plus many more), the probability becomes less. Are these variables independent, or are they interdependent factors? If he is not old enough to drive, he is also not old enough to get insurance. The probability of him being able to drive and being able to get insurance are not independent because both depend on his age. His being happy with a used BMW is not independent of my having enough money to buy a new one.

If we look at the question of life on Mars, we might be inclined to say that the odds are very high that life does exist on that planet. It has a mass similar to Earth. Mars has an atmosphere, volcanic eruptions, and water. Mars is tilted on its axis, it has a magnetic field, and the length of a day is roughly 24 hours. Are all of these variables independent? The answer is no because if the planet has volcanic eruptions, it will have an atmosphere, and volcanic eruptions always involve some amount of water. Both the water and the atmosphere are interdependent factors that depend upon volcanic eruptions.

The tricky part of this subject for both believers and atheists is knowing what is dependent and what is independent. As our knowledge of a topic improves, we are likely to find more dependent factors. For example, we recently discussed the importance of hydroxyl radicals in cleaning Earth’s atmosphere of pollutants. What are the odds of hydroxyl radicals being in a planet’s atmosphere? What may appear to be a separate and independent variable is the presence of lightning. Science has known for a long time that lightning helps produce nitrates which are essential for plant growth. In June of 2021, scientists announced a recent discovery that lightning produces hydroxyl radicals. Any planet that has lightning will have hydroxyl radicals, so the presence of hydroxyl radicals is not independent but is dependent on lightning.

This discussion has practical value in today’s world. Yesterday we said that we would examine some other statistical issues involving God’s existence. Think about this. Considering the millions of interdependent factors that must be in place to allow us to exist, could they all have come together by chance? Consider it on various levels—the creation of a universe from nothing—the creation of a life-supporting planet—the creation of the first life from inert matter—the creation of advanced life. We could go on. But considering all of the interdependent factors at each level, is it more logical to assume they came together by mere chance or guided by an intelligent Designer?

— John N Clayton © 2021