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Curvilinear Relationship
A curvilinear relationship is a type of relationship between two variables that has a pattern of correspondence or association between the two variables that change as the values of the variables change (increase or decrease). Whereas some relationships are straightforward to understand, explain, and detect statistically (i.e., linear relationships), curvilinear relationships are more complex because the nature of the relationship is different at different levels of the variables. Curvilinear relationships can occur often in communication research, given the complex, socially and contextually dependent phenomena that are the focus of such research. However, researchers may overlook the possibilities of curvilinear relationships in their data and miss the unique and valuable information they can provide. Curvilinear relationships are important to be able to understand and detect in communication research, because they provide information about a relationship between variables that reflects a much more complex process than a simple linear association.
This entry first provides an overview of the broad types of relationships and describes how curvilinear relationships are different from linear relationships. Examples of two different types of curvilinear relationships from communication research are provided for further illustration of the concept. Finally, issues regarding how to statistically detect, account for, and even model curvilinear relationships are discussed.
Types of Relationships
A relationship between two variables represents the degree of correspondence between those two variables. The strength or magnitude of the relationship as well as the direction or pattern of the relationship are vital pieces of information for interpreting a relationship between two variables. The two simplest types of relationships in terms of the direction of the association are positive and negative linear relationships. On one hand, a positive relationship between variables occurs when higher values of one variable are associated with higher values of the other variables. Another way to interpret a positive relationship is that lower values of one variable are associated with lower values of the other variable. One the other hand, a negative relationship occurs when as values of one variable increase, the values of the other variable decrease. Negative relationships are also referred to as inverse relationships.
Both positive and negative relationships are assumed to be linear; however, not all relationships between variables follow a linear pattern. A curvilinear relationship is more complex to explain and detect than linear relationships because the pattern of the relationship between two variables changes over the range of values of those variables. Often, curvilinear relationships can occur when the relationship between two variables is positive (i.e., values of one variable increase as values of the other variable increase) but only up to a certain point in the values of one variable, and then the relationship changes to no longer be positive and may even change to a negative relationship. The slope of these relationships follows the shape of a curved line when plotted on a graph relating values of one variable along the x-axis (e.g., independent or predictor variable) to values of the other variable (e.g., dependent or outcome variable) along the y-axis. Common representations of a curvilinear relationship are a bell-shaped (or upside-down U shaped) curve or a U-shaped curve.
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