Question

Explain why researchers typically focus on statistical independence rather than statistical dependence.

Answer 1

Researchers focus on statistical independence instead of statistical dependence because in most cases the data for independent samples are collected and compared and statistical dependence is only used where the researchers repeat the measurements.

The reason we so often assume statistical independence is not its real-world accuracy. We assume statistical independence because of its armchair appeal: It makes the math easy. It often makes the intractable tractable.  

Statistical independence splits compound probabilities into products of individual probabilities. (Then often a logarithm converts the probability product into a sum because it is easier still to work with sums than products). And it is far easier to lecture would-be gamblers that successive coin flips are independent than to conduct the fairly extensive experiments with conditional probabilities required to factually establish such a remarkable property. That holds because in general a compound or joint probability always splits into a product of conditional probabilities. The so-called multiplication rule guarantees this factorization. Independence further reduces the conditional probabilities to unconditional ones. Removing the conditioning removes the statistical dependency.