Descriptive Statistics: Levels of Measurement Explained
This paper provides a concise overview of descriptive statistics as used in research, focusing on the four levels of measurement — nominal, ordinal, interval, and ratio — and explaining how each level shapes the type of statistical analysis that can be applied. It also distinguishes between univariate and bivariate frequency distributions and illustrates how statistical methods are applied in practice, referencing a study on collinearity by Dormann et al. (2012). The paper concludes by addressing tests of statistical significance, including chi-square tests and t-tests, and the steps required to interpret them meaningfully.
- Introduction to Descriptive Statistics: Defines descriptive statistics and their core purpose
- Levels of Measurement: Explains nominal, ordinal, interval, and ratio levels
- Frequency Distributions: Distinguishes univariate from bivariate frequency distributions
- Statistical Methods in Research: Applies statistical methods using a collinearity study example
- Tests of Statistical Significance: Covers chi-square tests, t-tests, and hypothesis testing steps
✍️ How to write this paper — guide, tools & examples ▾
What makes this paper effective
- Each level of measurement is introduced with a concrete, relatable example (e.g., runners ranked by finish position for ordinal data), making abstract concepts accessible.
- The paper moves logically from foundational definitions to applied examples, ending with inferential techniques, creating a coherent progression.
- Brief but precise citations (Polit & Beck, 2017; Dormann et al., 2012) anchor the discussion in peer-reviewed literature without overwhelming the explanatory prose.
Key academic technique demonstrated
The paper consistently pairs each statistical concept with a practical illustration before connecting it to a specific analytical tool (e.g., nominal and ordinal levels → frequencies and percentages; interval and ratio levels → means and standard deviations). This concept-then-application structure is an effective technique for explaining quantitative methods to readers who may be unfamiliar with statistics.
Structure breakdown
The paper opens with a definition of descriptive statistics drawn from a nursing research text, then systematically addresses all four levels of measurement. A dedicated section on frequency distributions distinguishes univariate from bivariate analysis. A real study (Dormann et al., 2012) is then cited to show statistical methods in action. The final section covers significance testing, completing the movement from descriptive to inferential statistics.
Introduction to Descriptive Statistics
Descriptive statistics are used "to synthesize and describe data" by supplying parameters commonly based on averages and percentages that are "calculated with data from a population" (Polit & Beck, 2017, p. 215). While descriptive statistics essentially describe the characteristics of data, there are levels of measurement that can be implemented to aid in that description. These levels include nominal, ordinal, interval, and ratio. Nominal level offers the least amount of detail, while interval and ratio levels offer the most. At the nominal level, variables are categorized without any obvious meaning in the relationship: for instance, age and religious affiliation would be considered nominal-level variables. In descriptive statistics, nominal-level data is commonly used to measure frequencies and percentages.
Levels of Measurement
With ordinal-level variables, there tends to be more order or meaning in the grouping, based on hierarchical arrangement. For instance, runners in a race might be ranked according to where they finished. Such rankings are not used at the nominal level; at the ordinal level they are applied as labels to help establish a sense of order among the data. As with nominal-level data, ordinal-level data is commonly used to describe frequencies and percentages.
Interval and ratio-level variables provide more detail. Variables that have numeric values which may be added, divided, subtracted, or multiplied are used at the interval and ratio levels. In descriptive statistics, the interval and ratio levels are used to describe means (averages) and/or standard deviations (Data Levels and Measurement, 2017).
Frequency Distributions
Frequency distributions represent the number of occasions that a variable holds any of its potential values within a sample. The difference between univariate and bivariate frequency distribution is that with univariate frequency distribution, data is based on a single variable, with the goal of describing that one variable — for instance, the weight of children in a specific age group. Bivariate frequency distribution occurs when data is based on two variables, with the goal of identifying the relationship between them — for instance, the weight and gender of children in an age group. Thus, if only one variable is being examined in a data set, univariate frequency distribution would be used; if two variables are being examined, bivariate frequency distribution would be used.
References
Data Level and Measurement. (2017). Statistics Solutions. Retrieved from http://www.statisticssolutions.com/data-levels-and-measurement/
Dormann, C. et al. (2012). Collinearity: a review of methods to deal with it and a simulation study evaluating their performance. Ecography, 35, 1–20.
Polit, D. F., & Beck, C. T. (2017). Generating and assessing evidence for nursing practice (10th ed.). Philadelphia, PA: Wolters Kluwer.
Create your account
Always verify citation format against your institution’s current style guide requirements.