Regression analyses for assessing relationships or associations among variables.
Regression analyses for assessing relationships or associations among variables.
Journal of Vocational Rehabilitation 20 (2004) 143–150 143 IOS Press
Perspectives on Scientific Inquiry
Correlational designs in rehabilitation research
Shawn M. Fitzgerald∗, Phillip D. Rumrill, Jr. and Jason D. Schenker Kent State University, Department of Educational Foundations and Special Services, 413 White Hall, PO Box 5190, Kent, OH 44242-0001, USA Tel.: +1 330 672 00583; Fax: +1 330 672 2512; E-mail: firstname.lastname@example.org
Abstract. The article describes correlational research designs as a method for testing relationships between or among variables of interest in the lives of people with disabilities. The authors describe conceptual aspects of correlational research, discuss the methods by which researchers select variables for this type of inquiry, explain the primary purposes of correlational studies, and overview data analytic strategies. These discussions are illustrated with examples from the contemporary vocational rehabilitation literature.
Keywords: Correlational research, research design, data analysis
Investigating relationships among variables in the lives of people with disabilities is one of the most ba- sic and important aspects of rehabilitation research . In fact, gaining a deeper understanding of the connec- tions that exist among human phenomena is an abid- ing impetus for scientific inquiry in all of the social science disciplines, and that impetus transcends even the most polarized paradigmatic distinctions between various research methods (e.g., qualitative vs. quan- titative, descriptive vs. inferential, experimental vs. non-experimental).
Rather than attempting to infer causality by system- atically manipulating the independent variable (as is done in experimental research), correlational studies assess the strength of relationships as they occur or have occurred without experimental manipulation. Based on the observed relationships, statistical significance tests are then applied to determine the predictive or explanatory power of those relationships under study.
In this article, we describe issues related to using and interpreting data from correlational designs in contem- porary rehabilitation research. The purposes, assump- tions, and limitations that inhere to correlational re- search are presented, illustrated with examples from existing literature.
1.1. Purpose of correlational designs
Correlational designs are typically used by re- searchers for the purpose of exploring relationships among variables that are not manipulated or cannot be manipulated. For example, Boschen  used a cor- relational design to study the relationship between in- come and life satisfaction among people with disabili- ties. Capella  used a correlational design to study the relationships among age, case costs, and income within a sample of participants with visual impairments. Cor- relational designs were appropriate in these studies be- cause it is not possible to manipulate variables such as income, life satisfaction, age, and case costs. Although participants in these types of studies are assumed to possess the characteristics of interest prior to the study,
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144 S.M. Fitzgerald et al. / Correlational designs in rehabilitation research
Table 1 Typical data requirements for correlational designs and analysis
Subject Life-Satisfaction Income
1 85 45,000 2 66 32,000 3 42 48,000 4 78 42,000 5 25 22,000
and they are measured on those characteristics dur- ing the study, no attempt is made by the researcher to change them. In correlational research studies, it is important to note that researchers often use terms such as predictor and criterion instead of independent and dependent to discuss variables because this is the ap- propriate terminology to use when conducting studies that do not experimentally manipulate variables under investigation.
Because variables are not manipulated, causation is difficult to infer using correlational designs. Al- though variables may be chosen as predictors because they are theoretically expected to explain differences in the criterion variable, a significant statistical rela- tionship between these variables does not prove causal- ity. However, a statistically significant relationship be- tween variables is a precondition of causality. Research consumers may draw causal inferences based on the total evidence generated in a number of correlational studies. Theory-based hypotheses used in correlational studies propose the direction and/or temporal sequence of variables, which is another necessary but not suffi- cient precondition for establishing causality.
1.2. Interpreting relationships in correlational designs
To understand the nature of various relationships that could be examined in conducting correlational studies, consider the data presented in Table 1. Note that with correlational designs at least two points of data related to variables of interest must be collected for each in- dividual. In this example, every individual has pro- vided data on income level and life satisfaction. To understand how variables co-vary (i.e., are related) re- searchers use scatterplots, which require data from one variable to be plotted against data from another variable for each individual in the study. Scores for one variable are plotted on a horizontal axis, referred to as the x axis, and scores from the other variable are plotted on a vertical axis, called the y axis. To plot a data point on the scatterplot for an individual, a researcher would locate scores on each axis for each variable and then
Table 2 Guidelines for interpreting correlation coefficients
Range of values Interpretation
+0.75 to+1.00 Strong positive relationship +0.50 to+0.75 Moderate to strong positive relationship +0.25 to+0.50 Weak to moderate positive relationship
0.00 to+0.25 Zero to weak positive relationship 0.00 to−0.25 Zero to weak negative relationship
−0.25 to−0.50 Weak to moderate negative relationship −0.50 to−0.75 Moderate to strong negative relationship −0.75 to−1.00 Strong negative relationship
mark a spot on the graph where these two scores would meet. Figures 1, 2, and 3 present scatterplots of three types of relationships that might exist among variables. If there is a positive relationship among two variables, higher scores on one variable would tend to be associ- ated with higher scores on another variable. This type of relationship is illustrated in Fig. 1. If a negative re- lationship exists between two variables, higher scores on one variable would tend to be associated with lower scores on another variable. This type of relationship is illustrated in Fig. 2. If there is no relationship between variables a pattern of scores similar to those illustrated in Fig. 3 would be observed.
Scatterplots are not only useful for understanding the direction of a relationship between two variables; they are also useful for understanding the magnitude or strength of the relationship between two variables. To estimate the strength of a relationship, a researcher would consider the closeness of data points plotted on the scatterplot. Points that cluster closely together indicate strong relationships, such as those illustrated in Figs 1 and 2, whereas points that are not tightly clustered indicate weak or no relationships. Figure 3 presents data representing a weak relationship between two variables.
The calculations for determining correlational statis- tics result in both positive and negative values that range from −1 to +1. Negative values are associated with negative relationships between variables and positive values are associated with positive relationships. The closer the correlational statistic (also known as a coef- ficient) is to−1 or +1, the stronger the relationship. Correlational statistics close to 0 indicate weak rela- tionships. If there were no relationship at all between two variables, a value of 0 would be reported. Al- though there are no binding rules for determining what constitutes a strong, moderate, or weak relationship, Table 2 provides a guide for interpretating corelational statistics.
S.M. Fitzgerald et al. / Correlational designs in rehabilitation research 145
Variable A (X axis)
Fig. 1. Scatterplot of a positive relationship between two variables.
Variable A (X axis)
Fig. 2. Scatterplot of a negative relationship between two variables.
1.3. Variables in correlational designs
Correlational designs are prevalent in the social sci- ences and rehabilitation research primarily because they can be used for any research study in which it is
not necessary (or possible) to manipulate the indepen- dent variable of interest. The versatility of this type of research design is borne in the multitude of correla- tional analyses that exist for investigating relationships between or among variables.
146 S.M. Fitzgerald et al. / Correlational designs in rehabilitation research
Variable A (X axis)
Fig. 3. Scatterplot of no relationship between two variables.
Table 3 A summary of the hierarchy of measurement scales used in the social sciences
Properties Scale Examples
One category is different from another Nominal Gender, race Categories are different and ranked in order Ordinal Supervisor rankings, letter grades Categories are different and ranked in order plus differences between points are equal
Interval Standardized tests
Categories are different, ranked in order, differ- ences between points are equal and a true zero
Ratio Height, weight
As with all statistical analyses, deciding on the ap- propriate correlational analysis is dependent on the measurement properties of the variables under consid- eration . In general, measurement refers to the pro- cess of assigning numbers to the responses of individ- uals according to a specific set of rules . In other words, measurement is a process that involves quan- tifying or assigning numbers to the different charac- teristics or levels of the variables in a research study. Stevens  suggested a four-level hierarchy of mea- surement, and Table 3 summarizes this hierarchy.
It is important to note that the specific rules used in assigning numbers to responses of individuals should not be taken lightly by those conducting research in the social sciences. The types of measurements ultimately determine the mathematical manipulations that could appropriately be applied to the data generated from a variable, thereby limiting the type of statistical tests that might also be applied to those data. For example, mathematically, it is inappropriate to calculate an aver-
age (i.e., mean) score when variables are measured on either the nominal or ordinal scales. This is limiting because most parametric statistics utilize a mathemat- ical average or mean as the basis for analyzing data. However, means can be calculated for variables that are measured on either interval or ratio scales. Be- cause the distances between scale points are equal dis- tances for both of these scales, most mathematical ma- nipulations that are required when applying parametric statistics are possible. Measurements taken using these scales, for example, allow for meaningful calculations of averages, standard deviations, and variances – which form the essential “building blocks” for most paramet- ric statistics, including most correlational analyses.
1.4. Overview of data analytic strategies in correlational designs
Data from correlational designs are often analyzed using a variety of bi-variate correlational statistics, as
S.M. Fitzgerald et al. / Correlational designs in rehabilitation research 147
Measurement of the Variable is Interval/Ratio
Measurement of the Variable is Ordinal
Measurement of the Variable is Nominal
How is the One Variable Measured ?
How is the Other Variable Measured ?
What is the Appropriate Correlational Analysis ?
Phi, Chi-Square, C Coefficient
Interval or Ratio
Interval or Ratio
Interval or Ratio
Fig. 4. Correlational analyses for assessing relationships or associations between variables.
well as both simple regression and multiple regres- sion. Correlational statistics characterize both the na- ture and magnitude of the relationship between two variables . Bi-variate correlation coefficients and simple regression analyses are used to demonstrate the relationship between one predictor variable and one criterion variable. When researchers are interested in determining the relationship of several predictor vari- ables as they relate to one criterion variable, multiple regression analyses are typically used. Data from more complex correlational designs may be analyzed using canonical correlations or path analysis when multiple criterion variables and multiple predictor variables are assessed simultaneously or when complex theoretical models are analyzed. Figure 4 presents various correla- tional analyses that are commonly used in rehabilitation research for investigating relationships, whereas Fig. 5 presents the most commonly used regression analyses.
1.5. Using correlational designs for the purposes of prediction or explanation
Although the two are not mutually exclusive, corre- lational studies can be conducted for either predictive or explanatory purposes [11,12]. In predictive studies, researchers gather data on one or more predictor vari- able and one criterion variable that is hypothesized to
occur after the predictor variable(s). For example, a researcher might investigate the relationship between intelligence and academic success – here, intelligence is hypothesized to predict academic success, not vice- versa. A graduate program in rehabilitation counsel- ing might use Graduate Record Examination (GRE) scores and undergraduate grade-point average to pre- dict graduate-level academic performance. Another researcher might consider the number of disability- related worksite barriers as a predictor of job satisfac- tion.
Explanatory studies make use of theoretically cho- sen predictor variables that are hypothesized to account for the variance in the criterion variable . Here, the emphasis is placed on illuminating the theoretical nature, direction, and sequence of the relationship be- tween or among study variables. Although a researcher who conducts a predictive study would be concerned about choosing variables that accurately predict scores on the criterion variable regardless of their theoretical relevance,a researcher conducting an explanatorystudy would be concerned about choosing predictor variables that are theoretically expected to explain, or account for, variance in the criterion variable. For example, the graduate programmentioned previously would not nec- essarily be concerned about the theoretical relevance of their predictor variables, only their accuracy in predict-
148 S.M. Fitzgerald et al. / Correlational designs in rehabilitation research
Criterion Variable is Interval/Ratio
Criterion Variable is Ordinal
Criterion Variable is Nominal
How is the Criterion Variable Measures ?
How are the Predictor Variables Measured ?
What is the Appropriate Analysis?
Simple/Multiple Linear Regression
Log-Linear Analysis or Multinomial Analysis
Interval or Ratio
Interval or Ratio
Interval or Ratio
Fig. 5. Regression analyses for assessing relationships or associations among variables.
ing graduate-level academic performance. However, if a researcher wanted to conduct an explanatory study of graduate-level academic performance, he or she might include socioeconomic, personality, and motivational variables that previous research has shown to be rele- vant to success in graduate school. Most often, corre- lational studies published in rehabilitation journals are explanatory in nature.
1.6. Issues in interpreting data from correlational designs
Correlational studies present a number of concerns for the researcher as he or she attempts to interpret data. For example, multicollinearity becomes a concern with predictive as well as explanatory studies when multiple predictor variables are included in the regression equa- tion. Multicollinearity occurs when two or more of the predictor variables are highly correlated with one an- other. This presents a problem because the researcher cannot ascertain the unique predictive or explanatory influence of each predicator variable because those variables are too similar as evidenced by their high cor- relation with one another. However, researchers who conduct correlational studies generally wish to achieve the highest degree of accuracy in prediction or expla- nation with the fewest predictor variables. Therefore,
predictor variables that are highly correlated with other predictor variables are considered redundant and often eliminated from the regression equation.
Other concerns that face rehabilitation researchers who use correlational designs include the quality and consistency of data collection and recording activities (especially in ex post facto studies where data have been collected for a purpose other than the research study being conducted), the tendency to rely primarily on self-report data, and the specification of directional aspects of observed relationships (i.e., which comes first, the independent or dependent variable).
1.7. Examples of correlational studies
Bolton et al.  used hierarchical multiple regres- sion analysis to examine the predictive utility of several independent variables vis-à-vis the dependent variables of competitive employment status and weekly salary for successful rehabilitants. Specifically, the authors ex- amined the predictive power of personal history (demo- graphic variables), functional limitations (adaptive be- havior, cognition, physical condition, motor function, communication, and vocational qualification), and re- habilitation services (placement, personal adjustment, training, restoration, maintenance, time in active sta- tus, and total costs). The study included data from
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VR clients (N = 4, 603) from five disability groups: orthopedic, chronic medical, psychiatric, mental retar- dation, and learning disabilities. The authors found that the three independent variables combined to ac- count for approximately one-third of the variability in competitive employment status (25% to 40% depend- ing on disability group) and approximately one-eighth of the variability in weekly salary (9% to 17% depend- ing on disability group). Personal history accounted for approximately five percent of the variability in both competitive employment and weekly salary.
Capella  conducted a correlational study designed to predict the earnings of former VR clients. The au- thor examined the relationship between education, age, services, case costs, and months of services (predic- tor variables) and earnings (criterion variable) among a sample of participants (N = 16, 270) with visual im- pairments. The author found that age had the strongest, although negative, relationship to earnings, followed by education and cost of case services. Number of ser- vices and months the case was open were both found to be significantly related to earnings, but they accounted for little variance beyond that attributable to age, edu- cation, and case costs.
Strauser and Ketz  used multiple regression to test Hershenson’s theory of work adjustment, examin- ing the relationships among job-readiness self-efficacy, work locus of control, and work personality within a sample (N = 104) of participants diagnosed with men- tal retardation, mental illness, or substance abuse dis- orders. Work personality was defined by the authors as the person’s self-concept as a worker, motivation for work, and work-related needs and values. The authors also examined work competencies, which were defined as work habits, physical and mental skills, and inter- personal skills. The authors found that work person- ality (acceptance of work role, ability to profit from instruction and correction, work persistence, and work tolerance combined) significantly predicted internal lo- cus of control and job-readiness self-efficacy. How- ever, only work persistence provided a unique predic- tive contribution beyond the other subscales in the work personality inventory with regard to locus of control. Also, ability to profit from instruction and correction provided a unique contribution to job-readiness self- efficacy. In addition, the authors examined the correla- tions between demographic variables (number of jobs held, number of days since last worked, and number of times fired or asked to leave a job) and work person- ality, locus of control, and self-efficacy. Strauser and Ketz found a significant positive correlation between the number of jobs held and work personality.
Wilson et al.  provided an example of the use of binary logistic regression, using VR acceptance rate as the criterion variable and race, gender, education, work status at application, and primary source of sup- port at application as the predictor variables. The origi- nal sample consisted of 599,444 consumers who sought VR services. The authors then chose 2,476 participants from each of four racial categories, and coded them on whether they were accepted for VR services. The au- thors found that African Americans and Native Ameri- cans were more likely than European Americans to be accepted for VR services, whereas Asians or Pacific Islanders were less likely than European Americans to be accepted for VR services. In addition, participants with more available resources were less likely to be accepted for VR. Finally, the researchers found that as a participant’s education increased, the likelihood that he or she was accepted for VR services decreased.
Numerous other correlational studies can be found in recent rehabilitation research. Horton and Wal- lander  examined the relationship between care- giver disability-related stress, social support, and hope (predictor variables) and distress (criterion variable). Hampton  examined the relationships between (a) various demographic predictor variables and self- efficacy and (b) a quality of life criterion variable among Chinese individuals with spinal cord injuries, finding that self-efficacy, health status, income, educa- tional level, and time spent on voluntary work were sig- nificantly correlated with quality of life. Bellini  ex- amined the relationship between several demographic predictor variables and multicultural counseling com- petencies on the part of VR counselors, reporting that females, members of ethnic minority groups, and those who have attended a greater number of multicultural counseling workshops exhibited greater multicultural counseling competencies. Chase et al.  studied per- ceived control, verbal communication skills, satisfac- tion with personal assistance, marital status, and hand- icap as predictors of life satisfaction among persons with spinal cord injuries. They found that perceived control and marital status were the strongest predictors of life satisfaction. Finally, Mullins et al.  con- ducted a hierarchical multiple regression analysis to ex- amine the relationship between the predictor variables of illness intrusiveness and illness uncertainty and the criterion variable of severity of psychological distress among individuals diagnosed with multiple sclerosis. Results indicated that the two independent variables significantly predicted severity of distress beyond the predictive power of various demographic and illness variables.
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Correlational research investigations comprise a sub- stantial proportionof the empirical literature in the field of vocational rehabilitation. Utilized primarily for the purposes of prediction and explanation, correlational designs enable researchers to test the magnitude and direction of relationships between and among impor- tant variables in the lives of people with disabilities and rehabilitation professionals. These studies test rela- tionships as they occur or as they have occurred, rather than manipulating independent variables or introduc- ing an intervention as is commonly done in experimen- tal research. Therefore, the demonstration or verifi- cation of causal linkages between or among variables is not the objective of correlational research. By un- derstanding the most common applications of correla- tional research, by being able to identify appropriate variables for relationship-testing, and by familiarizing themselves with procedures used to predict or explain outcomes of interest in the field of vocational rehabil- itation, rehabilitation professionals can gain a deeper appreciation of the manner in which variable relation- ships express themselves in the rehabilitation process, as well as in the lives of people with disabilities.
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