Variables in the Scholarship of Teaching and Learning

Introduction

In educational research, particularly within the scholarship of teaching and learning (SoTL), understanding the concept of variables is crucial. Variables are the fundamental building blocks of research, representing the characteristics or properties that researchers aim to measure, manipulate, or control. A comprehensive grasp of what constitutes a variable, the different levels of measurement, and their relevance to the research problem is essential for conducting meaningful and rigorous SoTL studies.

The purpose of this section is to introduce the concept of variables, emphasizing their importance in the context of SoTL research. We will explore the definition of variables and the levels of measurement, including nominal, ordinal, interval, and ratio scales. Additionally, we will discuss how variables must be associated with the same unit of analysis, such as the teacher, the student, or the college, to ensure coherence in the study. It is also important to understand how variables should align with the theoretical framework, as this alignment enables the framework to effectively explain the phenomenon under investigation.

Finally, we will discuss the types of descriptive statistics that correspond to each level of measurement, providing insights into how these statistics can be used to summarize and interpret research data. By understanding these concepts, SoTL researchers can better design their studies, ensuring their variables are well-defined and aligned with their research objectives. 

Background

Research variables are the elements that researchers seek to observe and measure. They represent different aspects of the phenomenon being studied. They can vary in type, such as independent variables, dependent variables, predictor variables,  and criterion variables, among other types, depending on the research design. Understanding the different levels of measurement for these variables—nominal, ordinal, interval, and ratio—is fundamental to effectively designing and conducting research, as is being able to describe the data associated with these variables correctly. 

Variable Types

It is crucial to understand the different types of variables and their roles within a study. Independent variables and dependent variables are typically used in comparative research. Independent variables are the factors that researchers manipulate or categorize to determine their effect on other variables, while dependent variables are the outcomes or responses measured to see if they are influenced by the independent variables. For example, in a study examining the impact of teaching methods (independent variable) on student performance (dependent variable), the teaching method is manipulated to observe changes in student performance.

In single-sample studies using regression models, predictor and criterion variables are used. Predictor variables, also known as predictors, are the variables used to predict the value of another variable and explain the variance in the outcome. Criterion variables, or target variables, are the outcomes or responses that are predicted by the predictor variables. For example, in a regression analysis predicting student grades (criterion variable) based on study hours and attendance (predictor variables), the focus is on how well the predictor variables can estimate the criterion variable and explain the differences, or variances, in student grades. Understanding the explanatory power of predictors helps identify which factors significantly influence the outcome and how much variability in the criterion variable they account for. Differentiating between these variable types is essential for designing robust research studies, as it clarifies the relationships and causality being examined. By properly identifying and defining these variables, researchers can ensure that their studies are methodologically sound and their findings are valid.

A variable level of measurement refers to classifying variables based on the nature and type of data they represent. This classification helps determine the appropriate statistical methods for analyzing the data and ensures that the chosen methods are suitable for the type of data being measured (Gravetter & Wallnau, 2013). The levels of measurement define how variables are quantified and categorized, influencing how data can be interpreted and used in research and are described below and summarized in Figure 1.

Levels of Measurement

1. Nominal Variables: These variables represent categories without any intrinsic order. Examples include gender, race, or academic major. Nominal variables are useful for classification and are analyzed using frequency counts and mode.
2. Ordinal Variables: These variables represent categories with a meaningful order but no consistent interval between categories. Examples include class rankings or levels of satisfaction. Ordinal variables are analyzed using median and mode, as well as non-parametric statistics.
3. Interval Variables: These variables have ordered categories with consistent intervals between values but lack a true zero point. Examples include temperature in Celsius or standardized test scores. Interval variables are analyzed using means, standard deviations, and other parametric statistics.
4. Ratio Variables: These variables have ordered categories, consistent intervals, and a true zero point. Examples include age, height, or test scores measured from zero. Ratio variables allow for a full range of statistical analyses, including parametric tests.

Figure 1.

Variable Levels of Measurement

Unit of Analysis

The unit of analysis is the entity being studied, such as individuals, groups, or institutions (Casteel & Bridier, 2021). It is crucial that all variables are characteristics of the same unit of analysis to ensure consistency and coherence in the research. For instance, if the unit of analysis is the student, variables might include GPA, study habits, and class attendance.

Aligning Variables with Theoretical Frameworks

Variables must align with the theoretical framework guiding the research. This alignment ensures that the variables help test the hypotheses derived from the theoretical framework. For example, if the theoretical framework posits that student engagement influences academic performance, the variables must measure aspects of engagement and performance. 

Measuring Variables

Accurately measuring variables is essential in both traditional and online classroom settings. Traditional classrooms might use observational techniques, surveys, and tests, while online classrooms might rely on digital analytics, online assessments, and virtual participation logs. Regardless of the setting, the measurement tools must be reliable and valid to ensure the accuracy of the data collected. For more information about valid and reliable instruments, visit Sources of Data.

Descriptive Statistics and Levels of Measurement

Descriptive statistics serve the critical purpose of summarizing and organizing data about a sample, providing a comprehensive overview of the dataset. They help researchers understand the main features of the data by presenting quantitative descriptions in a manageable form. By employing descriptive statistics, researchers can gain insights into the central tendency, variability, and distribution of the variables in their study. Different levels of measurement require specific types of descriptive statistics

Nominal Variables: Use frequency counts, mode, and proportions to summarize data.

Ordinal Variables: Use median, mode, and percentiles to describe data.

Interval Variables: Use mean, standard deviation, and range to interpret data.

Ratio Variables: Use geometric mean, coefficient of variation, and ratios for analysis.

For example, in a study measuring a student's rating of a course faculty member on an end-of-course survey (ordinal variable), researchers might report the median rating level and the distribution of rating categories. In contrast, for a study measuring exam scores (ratio variable), researchers might report the mean score, standard deviation, and range of scores.