Elaboration is a statistical analysis process that is used to learn more information about the relationship between two variables (Frankfort-Nachmias & Leon-Guerrero, 2015). Elaboration requires that one introduces control variables in order to control for the new, control variable’s effects on the two variables that are being studied (Frankfort-Nachmias & Leon-Guerrero, 2015).

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Elaboration is useful in establishing a causal relationship and ensuring that the causal relationship cannot be attributed to some other factor or variables (Frankfort-Nachmias & Leon-Guerrero, 2015). For example, in studying recidivism rates of criminal offenders convicted of burglary and violent crimes, one may use elaboration to ensure that socioeconomic status, age, and gender are controlled for and do not contribute to the causal relationship.

A control variable is a variable that is added to the consideration of a relationship between two other variables (Frankfort-Nachmias & Leon-Guerrero, 2015). In the above example, a researcher may say that criminals who have committed non-violent burglaries are more likely to reoffend than violent criminals after controlling for age, socioeconomic status, and gender. In this example, age, socioeconomic status, and gender are the control variables. These are controlled for to ensure that only the relationships between burglary criminals, violent criminals, and recidivism are examined.

An intervening variable is a variable that helps to explain the relationship between two other variables (Frankfort-Nachmias & Leon-Guerrero, 2015). For example, if a researcher was studying the relationship between education and crime, income may be an intervening variable. Individuals with lower education may be more likely to commit crimes. However, that does not mean that getting a higher education necessarily prevents crime. What is more likely the case is that individuals with higher education levels likely have more income and therefore do not need to commit crimes to fulfill criminogenic needs such as not having enough food, housing, or material possessions. Therefore, one’s income (the intervening variable) explains the relationship between lower education and increased rate of crime.

A causally prior variable is a variable that is introduced to a relationship between two variables before the second variable meets the first (Frankfort-Nachmias & Leon-Guerrero, 2015). For example, there is a positive correlational relationship between the number of firefighters that arrive at a fire and the amount of property damage (Frankfort-Nachmias & Leon-Guerrero, 2015). However, the causally prior variable is the size of the fire (Frankfort-Nachmias & Leon-Guerrero, 2015). The size of the fire dictates how many firefighters are needed as well as how much damage is likely to occur. This variable happens before the other two variables are correlated and is required in order for the observed correlation to occur.

A partial relationship determines the degree to which two variables are associated after controlling variables are removed (Frankfort-Nachmias & Leon-Guerrero, 2015). For example, the relationship between height and weight may be studied while controlling for age. All three of these variables – height, weight, and age – are linear and continuous. Another example may be the relationship between height and language skills. The intervening variable is age. As one’s age increases, so does one’s height until adulthood. Language skills also tend to increase until plateauing in adulthood. Therefore, there is a partial relationship between height and language skills that is mitigated by age.