Bear F. Braumoeller and Gary Goertz, “The methodology of necessary conditions”, AJPS 44 (2000), pp. 844-858.

Summary: Braumoeller and Goertz argue that necessary conditions are not rare and are not inapplicable for empirical research. However, it is necessary to establish whether or not a factor is truly necessary, and if it is, whether or not it is trivial. They propose that a variable cannot be assumed necessary “if the lower-bound of the one-sided 95-percent confidence interval around p-hat is greater than the estimated error rate of the data.” They argue that one counter-example is not enough to prove that a condition is not necessary, and neither is the absence of counterexamples a good tool for predicting necessity (especially in small-N situations)

Notes

Provides a methodology for determining

  • Whether X is a necessary condition of Y; and if so
  • Whether X is trivially necessary

The Concept of Necessary Condition

  • X must always be present when Y occurs
  • Y does not occur in the absence of X

Step One: Is X Necessary for Y

  • Normally done through looking for one counterexample, but this is flawed
    • Data are inevitably measured with error
    • Reliability and validity are a concern
    • Coding variables introduces grayness
    • Absence of counterexamples is of no use with a small number of examined cases

Solutions: The P1 Test

  • “Reject the hypothesis of necessity if the lower-bound of the one-sided 95-percent confidence interval around p-hat is greater than the estimated error rate of the data”
  • This guards against Type I errors (rejecting propositions when true)
  • We also need to guard against Type II errors (failing to reject the hypothesis when it is false)

Step Two: Evaluating Trivialness

  • Comparison with those rejected in Step 1

Necessary conditions are NOT rare and are NOT inapplicable for empirical research