Measurement Levels (Scales)

Data could be described as qualitative (includes nominal and ordinal levels of measurement) or quantitative (includes interval and ratio levels of measurement).
   
Nominal and Ordinal Levels of Measurement refer  to data obtained from categorical questions. A nominal scale indicates assignments to groups or classes such as gender (male-female), geographic region (Dhaka, Rajshahi, Chittagong, etc), the model of car you own, or simply the yes or no responses to questions such as the ownership of a cellular phone. Nominal data is considered the lowest or weakest type of data, since numerical identification is chosen strictly for convenience.   

The values of nominal variables are words that describe the categories or classes of responses. The values of the gender variable are male and female; the values of “Did you ever visit Oslo, Norway?” are “yes” and “no.” We arbitrarily assign a code or number to each response. However, this number has no meaning other than for categorizing. For example, we could gender responses or yes/no responses as

                      1 = Male                                   1 = Yes
                      2 = Female                                2 = No

Ordinal data indicates rank ordering of items. Whenever observations are not only different from category to category but can be ranked according to some criteria. Examples include product quality ratings (1: poor; 2: average; 3: good) or satisfaction ratings with university food service, academic advising, or your new car (1: very unsatisfied; 2: somewhat unsatisfied; 3: neutral; 4: somewhat satisfied; 5: very satisfied). At the end of the semester you complete questionnaire about your course and your instructor. Often students are asked to respond to a statement such as “The instructor in this course was an effective teacher” with number from 1 to 5 (with 1, strongly disagree; 2, slightly disagree; 3, neutral; 4, slightly agree; and 5, strongly agree). In these examples, the responses are ordinal, or put into a rank order but there is no measurable meaning to the “difference” between responses. That is, the difference between your first and second choices may not be the same as the difference between your second and third choices.  

Interval and Ratio Levels of measurement refer to data on an ordered scale where meaning is given to the difference between measurements. An interval scale indicates rank and distance from an arbitrary zero measured in unit intervals. Temperature is a classic example of this level of measurement, with arbitrarily determined benchmarks generally based on either Fahrenheit or Celsius degrees. Suppose that it is 80 degrees Fahrenheit in Otlando, Florida, only 20 degrees Fahrenheit in St. Paul, Minesota. We can conclude that the difference in temperature is 60 degrees, but we can not that it is four times as warm in Orlando as it is in St. Paul.  

Ratio scale data does indicate both rank and the distance from a natural zero, with ratios of two measures having meaning.  A person who weighs 200 pounds is twice the weight of a person who weighs only 100 pounds; a person who is 40 years old is twice as old as someone who is 20 years of age.

After you have defined the problem of interest, you will need to carefully design an instrument, such as a survey, collect needed information. Or perhaps you will gather information from available data sources. In either case, before you can proceed to summarize or design data, you will first need to classify responses as categorical or numerical, or by measurement scale. Certain graphs and descriptive measures are used for numerical variables. Analysts use different graphs and descriptive measures for categorical data.