There are four basic types of scales of measurement – nominal, ordinal, interval, and ratio. Since each scale is better suited to specific types of variables, it limits or enables us to perform specific statistical operations or tests. Let’s look at the most appropriate statistical tests for different scales of measurement. A word of caution – these suggestions are not without controversy. For example, certain guidelines state that more complex tests like t-test should be limited to interval and ratio scales only. However, in practice, many researchers make a composite scale (converting ordinal scale to interval scale) and apply such statistical tools to ordinal data. There is no right or wrong answer here, but one should choose an appropriate statistical test based on the assumptions of a particular test that they want to use, the nature of the construct being measured, and the distribution of the data.
Nominal – Appropriate statistical tests
Since the scale is used to classify observation into different categories, it makes sense to arrange the data. A frequency distribution is a good way to start and then we can graph the data by making histograms or polygons. The central tendency is a good way to visualize the classification. Another analysis that can be performed is the chi-square correlation. When we want to compare more than two categorical (nominal) variables, we can use the chi-square test. For example, if we classify a population into several categories with respect to two attributes (for example age and job performance), we can then use a chi-square test to determine whether the two attributes are independent of each other. When we want to compare two groups the chi-square test allows the researcher to determine whether there is a statistically significant relationship between the experimental and control groups based on frequency counts. The Kappa Statistic (κ) or Cohen’s Kappa is another statistical measure used to measure chance corrected agreement between two independent raters.
Ordinal – Appropriate statistical tests
All calculations that you can perform on a nominal scale can also be performed for ordinal scales (frequency, central tendency, chi-square). Percentile calculations are another logical test for this type of scale. By extension, quartiles can also be calculated. The measure of central tendency can be calculated by a median. Spearman’s rank-order correlation is another useful measure to find a correlation between variables when the data is non-numeric and sufficient to rank the data.
Interval – Appropriate statistical tests
Most statistical operations can be performed for interval scales. Mean, standard deviation (which is a measure of central tendency), and variability are available at this level opening up a range of statistical procedures that can be applied to this scale of measurement. The only statistical tests that cannot be applied are ones that require the use of ratios, such as the coefficient of variation. Interval data are usually analyzed using parametric tests such as ANOVAs and t-tests.
Ratio – Appropriate statistical tests
This type of measurement scale is the most versatile as all statistical tools can be applied to this scale. Most common of these tests are the parametric test regression, t-tests, ANCOVA, MANOVA, Pearson correlation etc.
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Cite this article (APA)
Trivedi, C. (2020, December 4). Statistical tests for different scales of measurement. ConceptsHacked. Retrieved from: https://conceptshacked.com/statistical-tests-for-different-scales-of-measurement/
