Types of VariablesWe can distinguish between two types of variables according to the level of measurement:1. Continuous or Quantitative Variables.2. Discrete or Qualitative Variables.A quantitative variable is one in which the variates differ in magnitude,e.g. income, age, GNP, etc. A qualitative variable is one in which the variates differ in kind rather than in magnitude, e.g. marital status, gender, nationality, etc.Continuous or Quantitative VariablesContinuous variables can be classified into three categories: Interval - scale Variables:Interval scale data has order and equal intervals. Interval scale variables are measured on a linear scale, and can take on positive or negative values. It is assumed that the intervals keep the same importance throughout the scale. They allow us not only to rank order the items that are measured but also to quantify and compare the magnitudes of differences between them. We can say that the temperature of 40C is higher than 30C, and an increase from 20C to 40C is twice as much as the increase from 30C to 40C. Counts are interval scale measurements, such as counts of publications or citations, years of education, etc. Continuous Ordinal VariablesThey occur when the measurements are continuous, but one is not certain whether they are on a linear scale, the only trustworthy information being the rank order of the observations. For example, if a scale is transformed by an exponential, logarithmic or any other nonlinear monotonic transformation, it loses its interval - scale property. Here, it would be expedient to replace the observations by their ranks. Ratio - scale VariablesThese are continuous positive measurements on a nonlinear scale. A typical example is the growth of bacterial population (say, with a growth function AeBt.). In this model, equal time intervals multiply the population by the same ratio. (Hence, the name ratio - scale).Ratio data are also interval data, but they are not measured on a linear scale. . With interval data, one can perform logical operations, add, and subtract, but one cannot multiply or divide. For instance, if a liquid is at 40 degrees and we add 10 degrees, it will be 50 degrees. However, a liquid at 40 degrees does not have twice the temperature of a liquid at 20 degrees because 0 degrees does not represent "no temperature" -- to multiply or divide in this way we would have to use the Kelvin temperature scale, with a true zero point (0 degrees Kelvin = -273.15 degrees Celsius). In social sciences, the issue of "true zero" rarely arises, but one should be aware of the statistical issues involved.There are three different ways to handle the ratio-scaled variables. Simply as interval scale variables. However this procedure should be avoided as it can distort the results. As continuous ordinal scale. By transforming the data (for example, logarithmic transformation) and then treating the results as interval scale variables.Qualitative or Discrete VariablesDiscrete variables are also called categorical variables. A discrete variable,X, can take on a finite number of numerical values, categories or codes. Discrete variables can be classified into the following categories:1. Nominal variables2. Ordinal variables3. Dummy variables from quantitative variables4. Preference variables5. Multiple response variables1. Nominal VariablesNominal variables allow for only qualitative classification. That is, they can be measured only in terms of whether the individual items belong to certain distinct categories, but we cannot quantify or even rank order the categories: Nominal data has no order, and the assignment of numbers to categories is purely arbitrary. Because of lack of order or equal intervals, one cannot perform arithmetic (+, -, /, *) or logical operations (>,