Measurement
Statistical methods are ways of getting sense out of numbers.
The numbers are the result of measuring things. We will
distinguish four types of measurement:
- Nominal measurement:
- Numbers are used as "names";
their size and other arithmetic properties are irrelevant. If I
label females "1" and males "2", I have measured at the
nominal level.
It is worth noting that in this day of sophisticated computer
programs it is not always necessary to measure by using numbers.
We can also accomplish nominal measurement with letters or names; e.g.,
when we code the Boys as B and the Girls as G in a spreadsheet.
- Ordinal measurement:
- The ordering property of
the numbers is used but no other. If I give the tallest child a
rank of 1, the second tallest a rank of 2 and so on, I am engaging
in measurement at the ordinal level.
- Interval measurement:
- In order to accomplish interval
measurement, one must have a conventional unit of measurement
such as a "day" (24 hrs) of time, a Centigrade degree, a Grade
Equivalent Unit (for measuring school achievement). Furthermnore, the
"zero point" on the interval scale does NOT correspond to an
absence of the property measured, e.g., 0 degrees Centigrade is not
the absence of temperature--it is simply the temperature at which
water freezes; and 0.0 Grade Equivalents in Reading does not indicate
illiteracy, it merely indicates the literacy of a child before
entering the first month of Kindergarten.
- Ratio measurement:
- At this level of measurement, there
exists a conventional unit of measurement and the Zero point on the
scale does in fact correspond to an absence of the property measured.
For example, the measurement of height or weight or calories is at
the ratio level.
These considerations of measurement scale imply that certain statements
involving numbers may not apply to the thing measured. For example,
if Joe has a rank in high school class of 10 and Mary has a rank of
20 and Pete has a rank of 30, it can NOT be concluded that Joe and
Mary differ in achievement to the same degree that Mary and Pete do.
For each of the following, indicate whether the statement
about the things measured is Valid or Invalid:
- Political Affiliation is measured on a nominal scale with
Republican = 1, Democrat = 2 and Independent = 3. Independents have
greater political affiliation than do either Democrats or
Republicans:
- Rank in High School Graduating Class is measured by assigning
a 1 to the student with the highest GPA, a 2 to the next highest,
and so on. Sylvia's rank is 41; Arthur's is 64. Sylvia had a better
grade point average in high school than did Arthur.
- The high temperature in Phoenix, AZ on September 12, 1994 was
104 degrees; the high temperature in Minneapolis, MN on the same
day was 52 degrees Fahrenheit. On that day, Phoenix was twice as
hot as Minneapolis.
- When I was 14 years old, I ran a 100 yard dash in 11.1 seconds;
now, at age 60, I can run 100 yards in about 22 seconds (with a tail wind).
I could run twice as fast at age 14 as at age 60.
Return to Lesson 5 on Proportions and Contingencies
|