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Measurement Scales

victoria-briones-headshotBy Victoria Briones, Ph.D.

The first step in designing any quantitative study is to identify the independent (i.e., cause or predictor) and dependent (i.e., effect or criterion) variables. The second step is to define the variables concretely (guided by prior research). Variables can be defined using one of four measurement scales: nominal (i.e., numbers signify categories), ordinal (i.e., numbers signify ranks), interval (i.e., signifies quantity and units are equal), and ratio (i.e., same as interval but with an absolute zero). It is important to know the variables’ measurement scale because this is what determines which statistical test you will need to conduct to test your hypothesis.

Consider for example, a study assessing the relationship between BMI and hypertension. The independent variable would be BMI and the dependent variable would be hypertension. BMI (the independent variable) can be defined in many different ways:
1. Nominal – Not Obese vs. Obese
2. Ordinal – Underweight, Normal, Overweight, vs. Obese
3. Interval/ratio – Actual BMI score

Hypertension (the dependent variable) can be defined in different ways:
1. Nominal – Not Hypertensive vs. Hypertensive
2. Ordinal – Not Hypertensive, Borderline Hypertensive, vs. Hypertensive
3. Interval/ratio – Actual systolic and diastolic numbers

If, for example, a researcher decided to measure BMI and hypertension using a nominal scale of measurement, the researcher would conduct one of two statistical tests:
1. Cross-tabulation with chi-square
2. Logistic regression

If the researcher decided to measure both variables using an ordinal scale, the researcher would conduct one of two statistical tests:
1. Multinomial logistic regression
2. Ordinal regression

Lastly, if the researcher decided to measure both variables using an interval/ratio scale, the researcher would conduct one of two tests:
1. Pearson correlation
2. Linear regression

A researcher can, of course, have various combinations, where the independent variable is measured using a nominal scale and the dependent variable is measured using an interval/ratio scale. In these circumstances, the researcher would conduct one of two tests:
1. Independent t-test (if the independent variable has two categories)
2. One-way ANOVA (if the independent variable has three or more categories)
3. Linear regression

One advantage of measuring variables using an interval or ratio scale is that you can always code the variables (later, once you are analyzing the data) into variables measured using a nominal or ordinal scale. It is thus very important to do an extensive literature review and spend time defining and operationalizing the study variables.

Dr. Briones graduated with a PhD in Organizational Psychology from Columbia University. While completing her graduate studies, she taught applied regression analysis to graduate students in education and psychology. Students enjoyed her regression course because she was able to translate complex statistical concepts into a language that the “stats phobic” students could easily understand. Victoria was also an assistant lecturer in research methods (and received the highest mean evaluation for teaching performance). After graduating, she was a research fellow at Harvard University’s Kennedy School of Government. As a fellow, she conducted statistical analyses and wrote articles on negotiation behavior and conflict resolution with her former dissertation adviser.

In the last two years, Victoria has worked as a statistical consultant, helping graduate students in psychology, education, nursing, biology, and business hone their study hypotheses, arrive at better operational definitions of their study variables, and improve procedures to increase the internal and/or external validity of their study. She also performed general statistical procedures such as reliability analyses, non-parametric tests (e.g., Mann-Whitney, Kruskal-Wallis, and chi-square tests), t-tests, analysis of variance (ANOVA), analysis of covariance (ANCOVA), exploratory factor analysis (EFA), and linear regression. Further, she conducted multivariate tests such as multivariate analysis of variance (MANOVA), logistic regression, and structural equation modeling (SEM; using AMOS, LISREL, and EQS). Victoria also created summary tables and graphs of statistical findings and helped students interpret their study results. More importantly, she enjoyed explaining basic statistical procedures and findings to clients who had a limited understanding of such concepts.

Contact Dr. Briones via HelpWithStatistics.com or DissertationAdvisors.com.

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