\nLevel<\/strong><\/td>\nPermitted Statistics<\/strong><\/td>\nExample<\/strong><\/td>\n<\/tr>\n\n| Nominal<\/td>\n | Mode, frequency counts, percentages<\/td>\n | Most common blood type in a sample<\/td>\n<\/tr>\n | \n| Ordinal<\/td>\n | Mode, median, percentiles, interquartile range<\/td>\n | Median satisfaction rating on a five-point scale<\/td>\n<\/tr>\n | \n| Interval<\/td>\n | Mode, median, mean, standard deviation, variance, correlation<\/td>\n | Mean IQ score in a population<\/td>\n<\/tr>\n | \n| Ratio<\/td>\n | All of the above, plus ratios, proportions, geometric mean, coefficient of variation<\/td>\n | Mean income ratio between two countries<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n <\/span>Choosing the Right Statistical Test<\/span><\/h2>\nThis is the most practically important application of understanding levels of measurement. Each inferential test rests on assumptions about the data’s scale; violating those assumptions can invalidate conclusions.<\/p>\n \n\n\nLevel<\/strong><\/td>\nCommon Statistical Tests<\/strong><\/td>\nExample Use Case<\/strong><\/td>\n<\/tr>\n\n| Nominal<\/td>\n | Chi-square test<\/a>, Fisher’s exact test, logistic regression<\/td>\n | Testing whether gender affects voting preference<\/td>\n<\/tr>\n | \n| Ordinal<\/td>\n | Mann-Whitney U, Kruskal-Wallis, Spearman correlation, Wilcoxon signed-rank<\/td>\n | Comparing satisfaction scores between two service providers<\/td>\n<\/tr>\n | \n| Interval<\/td>\n | Independent samples t-test, paired t-test<\/a>, ANOVA<\/a>, Pearson correlation, linear regression<\/td>\n | Comparing average IQ scores across school types<\/td>\n<\/tr>\n | \n| Ratio<\/td>\n | All interval tests, plus geometric mean comparisons, ratio analysis, log-linear models<\/td>\n | Analyzing income inequality across regions<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n <\/span>Quick Decision Guide: What Level Is Your Variable?<\/span><\/h3>\nUse these questions in order:<\/p>\n \n- Step 1: <\/strong>Can the values only be placed into named categories with no order? If yes: nominal.<\/li>\n
- Step 2: <\/strong>Can the categories be meaningfully ranked, but are the distances between ranks unknown or unequal? If yes: ordinal.<\/li>\n
- Step 3: <\/strong>Are the distances between values equal and measurable, but does zero not mean the absence of the attribute? If yes: interval.<\/li>\n
- Step 4: <\/strong>Are the distances equal and measurable, and does zero mean the attribute is completely absent? If yes: ratio.<\/li>\n<\/ul>\n
<\/p>\n <\/span>Real-World Examples Across Research Disciplines<\/span><\/h2>\n\n\n\nLevel<\/strong><\/td>\nClinical Research<\/strong><\/td>\nSocial Science<\/strong><\/td>\nEconomics \/ Business<\/strong><\/td>\n<\/tr>\n\n| Nominal<\/td>\n | Blood type, tumor classification, drug treatment group<\/td>\n | Country of birth, religious affiliation, political party<\/td>\n | Industry sector, brand name, payment method<\/td>\n<\/tr>\n | \n| Ordinal<\/td>\n | Pain severity (mild\/moderate\/severe), tumor staging (I-IV)<\/td>\n | Socioeconomic status (low\/medium\/high), Likert-scale survey items<\/td>\n | Customer satisfaction tier, credit rating (AAA to D)<\/td>\n<\/tr>\n | \n| Interval<\/td>\n | Temperature (Celsius), calendar date, IQ score<\/td>\n | Year of survey response, attitude scale scores<\/td>\n | Year of incorporation, index score (e.g., Consumer Price Index baseline)<\/td>\n<\/tr>\n | \n| Ratio<\/td>\n | Blood pressure, dosage in milligrams, patient age, body weight<\/td>\n | Number of years of schooling, household size, annual income<\/td>\n | Revenue, sales volume, profit margin, years in business<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n <\/span>Common Errors and Misconceptions<\/span><\/h2>\n<\/span>Treating Likert-Scale Data as Interval<\/span><\/h3>\nThis is the single most widespread measurement error in social science and business research. A five-point Likert item (strongly disagree to strongly agree) is technically ordinal: there is no guarantee that the psychological distance from “disagree” to “neutral” equals the distance from “neutral” to “agree.”<\/p>\n In practice, many researchers compute means and apply t-tests to Likert items. Norman (2010) and subsequent simulation studies suggest that this often produces acceptable results when scales have five or more points and distributions are roughly symmetric. However, the safer and more theoretically defensible approach is to use ordinal methods (medians, Spearman correlation, Mann-Whitney U) unless parametric assumptions can be justified.<\/p>\n <\/span>Applying the Mean to Ordinal Data in Research<\/span><\/h3>\nCalculating an average rank or an average satisfaction category is statistically unjustified unless the equal-interval assumption holds. For example, reporting the mean of cancer stage scores (I through IV) implies that the clinical difference between Stage I and Stage II is the same as the difference between Stage III and Stage IV, which is biologically false.<\/p>\n <\/span>Confusing Interval and Ratio Scales for Temperature<\/span><\/h3>\nTemperature in Celsius and Fahrenheit is interval, not ratio. Saying that 30 degrees Celsius is “twice as hot” as 15 degrees Celsius is incorrect because zero Celsius is not the absence of heat. Temperature in Kelvin, however, is a ratio scale: 0 Kelvin is absolute zero, the complete absence of thermal energy. This distinction matters in physical sciences and thermodynamics.<\/p>\n <\/span>Assuming Discrete Data Cannot Be Ratio<\/span><\/h3>\nSome researchers confuse continuous versus discrete with interval versus ratio. A variable can be discrete (countable, whole numbers only) and still be ratio. The number of publications an author has produced is discrete and ratio: zero means no publications, and having 20 papers is genuinely twice as many as having 10.<\/p>\n <\/span>Misclassifying IQ Scores<\/span><\/h3>\nIQ scores are interval, not ratio. An IQ of zero does not mean the complete absence of intelligence; it is a statistically impossible score outside any real distribution. Furthermore, a person with an IQ of 140 is not twice as intelligent as a person with an IQ of 70 in any meaningful psychological sense. Accordingly, ratios of IQ scores are not interpretable, and analyses that imply such ratios are methodologically flawed.<\/p>\n <\/p>\n | | | | | | | | | | | | |