In: Statistics and Probability
Many researchers have tried to determine whether capital punishment deters murder. Suppose a new study has been published analyzing how death-sentence rates in one year relate to murder rates the following year. The researchers who conducted this study included only the 32 states that authorize the death penalty, and excluded the remaining states. Do you think this is a justifiable approach to studying the possible deterrent effects of the death penalty? Would you trust the results of the analysis and the conclusions the researchers reach on the basis of those results? Explain your answer. These questions are related to the chapter about types of variables and levels of measurement
In order to determine the relative benefit of capital punishment in deterring murder, we need to also consider the murder rate in states where the death penalty has not been authorized. This is to make sure that, for example, a decrease in murder rate isn't mis-conceived as being a result of the death penalty authorization when it was actually a result of another law or social plan or decreasing unemployment across all states, not only those where the death penalty was authorized.
Hence, based on the above reasoning, we cannot trust the results of the analysis done on the applicable states alone. For a proper relative analysis, we need to include all the states in the analysis, where we can use the Death Penalty Authorized flag as a factor taking value of 1 if implemented for a particular state, or 0 if not implemented for a state. In addition to this, we can possibly consider other relevant macroeconomic factors like change in GDP, unemployment rate, inflation, etc to understand if the change in murder rate is actually a resultant of another associated factor.