Introduction
Ordinal data, a type of data that indicates the ordering of items through the application of a rank, represents an intermediate classification from an age-old concept of statistical analysis. They are related to categories, but with an understanding of a hierarchy or a sequence of the highest level at one end and the lowest level at the other end (the middle portion being a distinction among different response patterns situated between the highest and lowest ordering). When you collect ordinal data, you can rank the values or put them in some kind of order. In this sense, the ordinal data reflect or order the classification without specifying the nature of the difference between the ranks. Ordinal data can also be classified as a sub-array of ordered data.
The most common examples of ordinal data are groups in a ranking system, stages in the CBD staging system for cancer, levels of satisfaction or importance using a 5 or 7-point Likert scale, the grouping system in disabilities, job ranks (specialist, associate, assistant, and intern), and ranks that reflect a socio-economic level of inequality. Ordinal data is not based on any standard interval or ratio; it is only based on the order of the options. Therefore, interpreting ordinal data is limited due to the lack of an exact measurement scale of data but is based only on the order such as greater than, less than, more, less, etc. It cannot be used to make a clear-cut conclusion. In addition, complexity lies in the fact that there is no zero value because there is no physical size present. The same difficulty is encountered if we compare metal to air or skin to touch. A further illustration reflects the level of severity such as in accident injuries compared to satisfaction levels. Also, ordinal scales further allow non-equal desired space placed between two levels of measurement; for instance, the size between stages of cancers might not be equal along the CBD scale. Accurately, moving from 1 to 2 might not be the same as from 2 to 3 due to differences in size. Therefore, it is important to operationalize in such conditions and hence must be used in all scientific fields to ensure reliability and consistency within research respondents. Some commonly noted ordinal measurement examples used in medical research newspapers and reports include Travis scores of Disease Severity in asthma (1: mild, 2: moderate, 3: severe, 4: very severe), WHO scores of Pain (1: no pain, 2: moderate, 3: severe), and Adelaide scores of Insulinemia or Metabolic Syndrome (1: not at all, 2: mild, 3: moderate, 4: severe, 5: numerous).
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Methods for Analyzing Ordinal Data
There are several methods that can be employed to analyze ordinal data, including nonparametric and parametric techniques. Nonparametric methods are often advantageous when the data are ordinal because the parametric assumptions, such as homogeneity of variance, are not met when applying techniques such as the t-test or ANOVA. Additionally, nonparametric methods make fewer assumptions about the nature of the underlying population distribution. Two nonparametric techniques specifically designed for analyzing ordinal scales are the Mann-Whitney U test and the Kruskal-Wallis test. By contrast, the most frequently used parametric technique is the one-way ANOVA with the assumption of homogeneity of variance and the Welch or Brown-Forsythe tests as alternatives when this assumption is not met. Finally, ordinal data can also be assessed using log-linear modeling, specifically Poisson regression, although outcomes may not always be easy to interpret.
Nonparametric analyses are advantageous over parametric tests, particularly for ordinal data, as they do not assume a normal distribution and are more resistant to the presence of outliers. However, nonparametric analyses may have less power or be less sensitive than their parametric counterparts. When selecting whether to use a parametric or nonparametric test, the primary consideration will be the underlying data scale, i.e., nonparametric techniques are more suited to ordinal data or data that are non-normal, whereas parametric techniques are more powerful and are suitable for normal data. A comparison of the various methods and when they are appropriate is provided. Statisticians also have the ability to test ordinal data using numerical methods or log-linear modeling and can analyze data with specially designed software. Practical advice on the use of each technique is described. Additionally, it is important to ensure a rigorous investigation into the reliability and validity of any test as part of the test selection. Ensuring the validity and reliability of data helps to ensure that decisions are made on sound data.
Application of Ordinal Data Analysis
3. Case Study: Application of Ordinal Data Analysis. In order to demonstrate the broad application and usefulness of ordinal data analysis, as well as to provide a practical case study of how to apply these methods in a statistical research context, we now turn to an example from a recent project. We detail the example including the research question, analysis methodology, results, and a practical application and corresponding discussion. This case study serves as a bridge connecting theory and practical application.
3.1. Objective, Research Question, and Methodology. Throughout the following example, we propose to uncover an answer to the long-debated research question in statistical meta-analysis: whether or not there is substantial heterogeneity in effect sizes of individual studies that benefit from these analyses. Through this case study, we justify the selection of a particular analysis method given a set of ordinal data. More specifically, we wish to estimate the percentage of variance unexplained by a crucial moderator of suicide and exposure elasticity (the strength of the association between exposure and risk) within the empirical literature. Effect sizes coded into the meta-analysis were based on response categories—'yes', 'no', 'maybe', 'unsure'—which reveal the degree of association between the two main constructs. The results from these questions are reflective of ordinal rather than interval data. We propose that one can, and should, utilize ordinal analysis to explore the differential impact of the level of a moderator across ordinal levels (response categories) of a dependent variable. As we discuss in Section 3.2, the selection of the analysis method—robust linear mixed modeling—was based on the characteristics of ordinal data.
Challenges and Considerations
Once a set of responses has been categorized on the basis of an intensity ordering, there are numerous challenges and considerations for researchers seeking to analyze the data. First, because the intensities on an ordinal scale do not carry equidistant metrics in terms of the underlying variable being measured, it is difficult to establish whether a change in one of the items on the ordinal scale is comparable to a change in another item on the same scale. Furthermore, researchers must balance the limitations of traditional statistical methods assuming interval-level measurement being applied to ordinal data with the reality that there are seldom processes, institutions, or actors that can be measured on anything approaching a true interval or ratio level.
In trying to navigate these interpretative difficulties, a further consideration that should be kept in mind at all times is the potential for biases to arise through, inter alia, (a) the question wording and/or sequence, (b) the validity and reliability of the concepts being measured, and (c) the analysis process itself. While there are no limitations to the application of either descriptive or inferential statistics to ordinal data, such outputs should be treated with caution and the fundamental basis of the interpretation and admissibility as ordinal in nature should be noted. This approach would also benefit from the principles of openness and accountability, setting out explicitly the choices made in the analysis process and the potential consequences thereof. Given the numerous issues with the collection and analysis of ordinal data, researchers working with them should therefore strive to plan their process 'from collection to analysis' in order to maximize the 'validity and utility' of their results. When labeling aggregated findings in any sort of final analysis, researchers should be transparent and accountable about the possible origins of a result, given the measurement being ordinal in nature, as well as the fundamentals of the 'big picture' story being told.
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