Relationships Between Variables

Types of Relationships

Relationships between variables can be described as null, covariant, or influential. The null predicts no relationship between variables. The variables function independently of each other. Covariant relationships exist when a change in one variable is associated with a change in the other. An influential relationship describes how one variable affects another. To identify an influential relationship three criteria must be met. First, two variables must co-vary in a predictable way. Second, one variable (the independent, influential variable) must produce a change in the other (i.e., the value of a dependent variable “depends” on, or is influenced by, changes in an independent variable). This means that the value change in the independent variable must occur prior to the change in the dependent variable. Thus, a time-order effect is necessary to claim influence. Third, there must be a logical connection between the two variables. That is, the two variables must be related and the potential influence must make logical sense. If these three criteria are met, a researcher may claim an influential relationship between the variables.

Analyzing Relationships Between Variables

To analyze these relationships between variables, a researcher must choose an appropriate statistical test. This choice is made according to the measurement level of the variables involved. Variables can have one of four measurement levels. A nominal level describes a variable that has categories, such as female, male. An ordinal-level variable has categories with an identifiable order, [Page 1413]such as socioeconomic status of families (e.g., high, middle, low). An interval-level variable has rank-order categories with equal intervals. Examples of interval-level variables are those measured on Likert or semantic differential scales. Ratio-level variables have rank-ordered, equal-interval categories with zero as a possible value, such as the number of spoken words per minute.

Testing Relationships Statistically

Three broad types of statistical tests examine relationships between these variables. These are tests of difference, tests of relationship, and analyses of variable loadings on underlying dimensions called components, factors, or functions.

Tests of difference, such as the chi-square, t-test, and analysis of variance (ANOVA), analyze the statistical probability that a difference occurs because of the influence of independent variables upon a dependent variable. For a chi-square test both independent and dependent variables are nominal, or categorical. For t-tests, the independent variable has two categorical levels and the dependent variable has continuous, interval, levels. The ANOVA test compares the influence of three or more categorical independent variables on an interval-level dependent variable. These statistical tests identify patterns in the variance of the dependent variable due to the effect of the independent one. These identified patterns of influence are compared to the amount of variance that remains unaccounted for and assumed to be due to chance or error.

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