Measurement scales

1. Measurement scales

2. Measurement Scales of Variables
• Ratio scale
• Interval scale
• Ordinal scale
• Nominal scale

3. Ratio Scale
• For a variable X, taking two values, X1 and X2, the ratio
X1/X2 and the distance (X2 − X1) are meaningful
quantities. Also, there is a natural ordering (ascending
or descending) of the values along the scale. Therefore,
comparisons such as X2 ≤ X1 or X2 ≥ X1 are
meaningful. Most economic variables belong to this
category. Thus, it is meaningful to ask how big this
year’s GDP is compared with the previous year’s GDP.
Personal income, measured in dollars, is a ratio
variable; someone earning $100,000 is making twice as
much as another person earning $50,000 (before taxes
are assessed, of course!)

4. Interval Scale
• An interval scale variable satisfies the last two
properties of the ratio scale variable but not the first.
Thus, the distance between two time periods, say
(2000–1995) is meaningful, but not the ratio of two
time periods (2000/1995). At 11:00 a.m. PST on August
11, 2007, Portland, Oregon, reported a temperature of
60 degrees Fahrenheit while Tallahassee, Florida,
reached 90 degrees. Temperature is not measured on a
ratio scale since it does not make sense to claim that
Tallahassee was 50 percent warmer than Portland. This
is mainly due to the fact that the Fahrenheit scale does
not use 0 degrees as a natural base

5. Ordinal Scale
• A variable belongs to this category only if it
satisfies the third property of the ratio scale (i.e.,
natural ordering). Examples are grading systems
(A, B, C grades) or income class (upper, middle,
lower). For these variables the ordering exists but
the distances between the categories cannot be
quantified. Students of economics will recall the
indifference curves between two goods. Each
higher indifference curve indicates a higher level
of utility, but one cannot quantify by how much
one indifference curve is higher than the others.

6. Nominal Scale
• Variables in this category have none of the
features of the ratio scale variables. Variables
such as gender (male, female) and marital
status (married, unmarried, divorced,
separated) simply denote categories.
Question: What is the reason why such
variables cannot be expressed on the ratio,
interval, or ordinal scales?

7. Types of Data
• Three types of data may be available for
empirical analysis: time series, cross-section,
and pooled (i.e., combination of time series
and cross-section) data.

8. Time Series Data
• A time series is a set of observations on the values that a
variable takes at different times. Such data may be
collected at regular time intervals, such as daily (e.g., stock
prices, weather reports), weekly (e.g., money supply
figures), monthly (e.g., the unemployment rate, the
Consumer Price Index [CPI]), quarterly (e.g., GDP), annually
(e.g., government budgets), quinquennially, that is, every 5
years (e.g., the census of manufactures), or decennially,
that is, every 10 years (e.g., the census of population).
Sometime data are available both quarterly as well as
annually, as in the case of the data on GDP and consumer
expenditure. With the advent of high-speed computers,
data can now be collected over an extremely short interval
of time, such as the data on stock prices, which can be
obtained literally continuously (the so-called real-time
quote).

9. Cross-Section Data
• Cross-section data are data on one or more
variables collected at the same point in time,
such as the census of population conducted
by the Census Bureau every 10 years, the
household surveys conducted by NSSO.

10. Pooled Data
• In pooled, or combined, data are elements of
both time series and cross-section data.

11. Panel, Longitudinal, or Micropanel
Data
• This is a special type of pooled data in which
the same cross-sectional unit (say, a family, a
firm or a country) is surveyed over time.
• If all the units have the same number of
observations, we have what is called a
balanced panel. If the number of observations
is not the same for each company, it is called
an unbalanced panel

12. Thanks