A linear relationship enables psychologists to represent associations between two sets of variables via a straight line on a graph. Oppositely, non-linear relationships employ a curved line to represent relationships between entities. Because linear relationships are represented via a straight line, they can either be positive or negative in nature. Positive linear relationships are characterized by a positively sloping line on a graph while negative relationships have negative slopes. Otherwise, a relationship may also be curvilinear, where an increase in one variable results in an increase of another variable up to a certain threshold, after which one variable starts to decrease. Curvilinear relationships are naturally non-linear and are represented by curved lines on a graph.
In a meta-analysis study by Hanson &Bussiere (1998), where the researchers attempt to predict relapse in sexual offender recidivism studies, the findings report a negative linear relationship between age and sexual recidivism. This implies that when age increases, the degree of recidivism decreases and vice versa. If the curve was curvilinear, the findings would indicate that age influences sexual recidivism positively until a certain age beyond which the influence becomes negative. Nevertheless, sexual recidivism is subject to many factors and age is just a single variable, which could explain the curvilinear relationship. In another study by Brace et al., (2009), researchers found a positive linear relationship between violence and traffic offenses, meaning that the incidence of violent behavior predicts occurrence of traffic offenses. In a curvilinear representation, the former variable would cease to predict the frequency of traffic offenses on its own, requiring researchers to examine other variables at play.
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