Question

Match the following variables with the measurement scale (Nominal, Ordinal, or Interval/Ratio), and whether the measurement is Discrete or Continuous.

Number of text messages received daily.    Socail Security Number Reaction time on a task    Grades assigned in a class (A, B, C, D, F) Score on an IQ test

A. Interval/Ratio; Discrete B. Nominal; Discrete C. Interval/Ratio; Continuous D. Ordinal; Discrete E. Nominal; Continuous F. Ordinal; Continuous

Answer 1

a) The number of text messages cannot be decimal, but they are clearly numerical and can range from 0 to infinity ( any whole number). As the difference between two values here for example between 5 and 2 is same as the difference between 8 and 5, therefore it is an interval variable. Also as we are finding the values of the variable here by counting, therefore this is a discrete variable. As this variable cannot have values between two integers, therefore this is not a continuous variable. Therefore, the required mapping here is given as:

Interval / Ratio ; Discrete

b) Social security number is a categorical variable, it does not have an order here. Therefore it is a nominal variable and as it is not numerical, it has to be a discrete variable. Therefore Nominal ; Discrete variable is the correct answer here.

c) Reaction time is something which is measured, and is numerical and continuous, its value can have infinite possibilities between any two time points. Therefore this is a Interval/Ratio ; Continuous variable.

d) Grade on assignment is categorical but it does have an ordinal behaviour to it:
For example A > B > C > D > F

Therefore this is an ordinal variable and discrete variable here.

e) Score on an IQ Test is again like number of text messages ( it has limited number of possible values here )

Therefore Interval / Ratio ; Discrete is the required answer here.