SW388R6

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Level of Measurement Problems

• Sources of Information
• Sample Problems

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Level of measurement

• Level of measurement is one of the key
  determinants for selecting the correct statistic
  to use.
• Level of measurement determines whether the
  numeric data value can be treated as representing
  a numeric measure of a characteristic,
  representing the rank or order within the
  distribution of data values, or is simply a
  short-hand substitute for a category.

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Level of measurement

• If the numeric data value represents a numeric
  measure of a characteristic, e.g. age, height,
  GPA, etc., we call it interval level.
• If the data value represents the rank or order
  within the distribution of data values,e.g. level
  of satisfaction, social class, student status,
  etc., we call it ordinal level.
• If the data value simply represents a short-hand
  substitute for a category, e.g. sex, race,
  marital status, etc., we call it nominal level.

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Multiple ways to measure a characteristic

• The name or title of a variable is usually not
  sufficient information to determine level of
  measurement.
• For example, the characteristic of "education"
  can be measured in multiple ways
• The number of years of education completed
• The degree awarded at last graduation
• Did or did not attend college
• To know how a variable is measured in a data set,
  we look at the data itself and at the codebook.

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Data in the SPSS data editor
Data is represented by numbers. Sometimes we may
be able to look at a column of data and guess its
type, e.g. hrs1 and prestg80 are probably
interval level. Most of the time, the numbers
will not be an adequate indicator of level of
measurement.
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The SPSS variable view
SPSS includes codebook information in a data set
on the tabbed page titled "Variable View." Some
of the items in this help us determine level of
measurement.
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SPSS support for level of measurement
SPSS includes a "Measure" column in the "Variable
View" as a spot for recording level of
measurement, but there is no guarantee that is
has been used accurately. In fact, nothing in
SPSS data analysis uses the information in this
column. In our dataset, the "Measure" column has
been deliberately left to the default setting of
"Scale, though we clearly have variables at
other levels of measurement.
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Variable labels
The variable "Labels" column gives us a better
idea of the characteristic that a variable is
measuring than does the variable "Name" column,
but it is little help in determining level of
measurement.
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Value labels
The "Values" column usually provides us with the
best information about level of measurement.
Click on the button with the ellipsis on it to
open the Value Labels dialog box.
The Value Labels Dialog shows the numeric code
values that have been entered for a variable and
the label that is associated with each code value.
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Missing values
SPSS also has a column for "Missing" values.
Missing values are data values or codes that
stand for reasons why a question was not answered
with one of the valid choices. Cases with these
values will not be included in SPSS calculations.
0 and 9 represent missing data for LABOR FRCE
STATUS.
The missing value codes are often included in the
list of value labels, but we should ignore them
when we are determining level of measurement. 0
NAP is a value label that we should ignore.

• Three common missing data indicators in the GSS
  are
• DK dont know
• NA no answer
• NAP not applicable

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Value labels and level of measurement

• Value labels will usually provide us with enough
  information to determine the level of
  measurement.
• First, if there are no value labels, the variable
  is probably interval level (which SPSS calls
  "Scale").
• Second if there are code labels, the variable is
  probably nominal or ordinal. To determine which,
  we study the pattern of the labels and code
  values.

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Nominal versus ordinal

• To determine that a variable is ordinal, we look
  for a pattern that implies a ranking or order, by
  which each higher code value and label represents
  more (or less) of the characteristic or trait
  being measured by the variable.
• If all of the labels are ordered in the same
  direction, the variable is ordinal level.
• Ordinal variables may be ranked from low to high
  or high to low. Either way they are ordinal.
• If the labels and codes for a variable do not
  follow any order, the variable is nominal.

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Problem 1
Answer the following questions based on
information in the dataset GSS2000.SAV. The
level of measurement of the variable "LABOR FRCE
STATUS" is 1. Nominal 2. Ordinal 3.
Interval
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Solution 1
The data values show a narrow range of possible
values, which might lead us to suspect that the
variable is not interval level.
The first two values are ordered by amount of
work, but that ordering breaks down when the
third category changes to reasons for not
working. The value label 0NAP stands for
missing data NAP means not applicable.
The variable is nominal level.
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Problem 2
Answer the following questions based on
information in the dataset GSS2000.SAV. The
level of measurement of the variable "CONFID. IN
UNITED STATES SUPREME COURT" is 1. Nominal 2.
Ordinal 3. Interval
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Solution 2
The data values show a narrow range of possible
values, which might lead us to suspect that the
variable is not interval level.
The code values are ordered in decreasing order
by level of confidence.
The value labels 0NAP and 8DK stand for
missing data NAP means not applicable and DK
means dont know.
The variable is ordinal level.
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Problem 3
Answer the following questions based on
information in the dataset GSS2000.SAV. The
level of measurement of the variable "RS
OCCUPATIONAL PRESTIGE SCORE (1980)" is 1.
Nominal 2. Ordinal 3. Interval
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Solution 3
The data values show a wide range of possible
values, which might lead us to suspect that the
variable is interval level.

• The only value labels for any values are
  associated with missing data
• DK dont know
• NA no answer
• NAP not applicable

The variable is interval level.
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Problem 4
Answer the following questions based on
information in the dataset GSS2000.SAV. The
level of measurement of the variable "TOTAL
FAMILY INCOME" is 1. Nominal 2. Ordinal 3.
Interval
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Solution 4
Income might lead us to jump to the conclusion
that the variable is interval level.
After the missing data category (NAP which means
not applicable, the categories appear to be
ordinal. If the categories were the same width
(e.g. 1000 each), the variable might even be
considered interval. However, we note that
category 2 is 2000 wide, while categories 3 and
4 are 1000 each.
The data values show a wide range of possible
values, which might lead us to suspect that the
variable might be interval level.
The variable is ordinal level.
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Problem 5
Answer the following questions based on
information in the dataset GSS2000.SAV. The
level of measurement of the variable "IS R LIKELY
TO LOSE JOB" is 1. Nominal 2. Ordinal 3.
Interval
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Solution 5
If we only looked at the first four categories,
we might be misled into thinking that the
variable is ordinal level. We need to inspect
all of the value labels for a variable before
drawing a conclusion.
The variable is nominal level.
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Problem 6
Answer the following questions based on
information in the dataset GSS2000.SAV. The
level of measurement of the variable "NUMBER OF
CHILDREN" is 1. Nominal 2. Ordinal 3.
Interval
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Solution 6
The data values show a narrow range of possible
values, which might lead us to suspect that the
variable is not interval level.
There is only one category label, an open-ended
category for eight or more children. Some
purists might treat the variable as ordinal
because of this last category, but most would
regard it as interval on the assumption that very
few cases would have more that eight children, so
the open-ended category would not really affect
an analysis of this variable.
The variable is interval level.
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Additional information

• If additional information about variables in the
  GSS is needed, try the codebook web site at
• http//www.icpsr.umich.edu/GSS/

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When in doubt

• There are times when you can narrow the level of
  measurement down to two categories, and you can
  make an argument that the variable could
  legitimately be treated as either level.
• In this case, the rule of thumb is to treat the
  variable at the highest level of measurement that
  you can justify, i.e. interval rather than
  ordinal and ordinal rather than nominal.
  Statistics for higher levels of measurement are
  more powerful at detecting differences in our
  data.