Choosing the appropriate statistical treatment will depend on the kind of data involved in the study. The level of measurement is the process of observing and recording observations that are collected as a part of a research effort. The type of data may be nominal, ordinal, or interval. You need to have a knowledge of what type of data you have in order to apply the appropriate statistical test.
1.
Nominal or categorical data is the basic level of
measurement. Examples of nominal data are gender, blood type, religion, marital
status, young or old. The nominal data uses numbers to label
discrete, but it does not imply order. The number or code is used for the
purpose of a label or description. The numeric codes assigned in
nominal data do not convey information. If we classify male as 1 and female as
2, the numbers have no inherent meaning. The number 2 clearly does not mean
‘more than 1’. The numbers are merely symbols that represent two different
values of the gender attribute.
Nominal
data must have categories that are mutually exclusive and collectively
exhaustive. For example, if we are to obtain ethnicity, we may use the
following codes:
1 = American
2 =
AfricanAmerican
3 = Hispanic
4 = Asian
To
present a nominal data you may use piechart, bar chart, or column
chart. Moreover, to summarize, we use Frequency/Percentage. We
cannot use Mean or Average in this type of measurement. The
numbers used in nominal data cannot be treated mathematically. For example,
calculating the average race of a sample. We can, however, count the elements
in the categories based on the frequency of occurrences. For example, in a
sample of 50 employees, we can say that 5 out of 50 or 10% are Asian, 15 out of
50 or 30% are Hispanic, 20 out of 50 or 40% are American, and 10 out of 50 or
20% are AfricanAmerican. No further mathematical operations would be
meaningful with the nominal level of measurement.
2.
Ordinal data involves sorting the objects on the
basis of their relative standing on an attribute. The attributes are
ordered according to some criterion. If a researcher rankorders subjects
from heaviest to lightest, ordinal measurement has been used. Other examples
are:
Rank in a class test (first, second or third)
Rank in a class test (first, second or third)
Customer satisfaction ratings (On a scale of 010)
Socioeconomic status
Education qualification
Unlike
nominal data, ordinal data's information concerns not only equivalence but
relative standing among objects is involved. For example, this scheme is for
coding a client’s ability to perform daily activities:
(1) Completely
dependent
(2) Needs
assistance
(3) Completely
independent
In
this case, the order is ordinal. The numbers are not arbitrary they signify
incremental ability to perform daily activities. Individuals assigned a value
of three is equivalent to each other with regard to functional
ability. Ordinal data provide information regarding the greater than or
less than status, but not how much greater or lesser. We do
not know if being completely independent is twice as good as need
assistance. Nor do we know if the difference between needing assistance is the
same as that of being completely independent. Ordinal level of measurement
tells us only the relative ranking of the attribute’s levels.
To
present ordinal data, you may use a column or bar
chart. Averages are usually meaningless with rankorder
measures. Frequency and percentages are
usually used to summarize an ordinal data.
3.
Interval/Ratio is the most precise level of measurement. It
is also known as scale measurement.
It can be discrete (whole
numbers, i.e., customers, siblings, employees, etc.) or continuous (i.e.,
temperature, weight, height, etc.) It can be measured rather than
classified (ordered). Thus, interval/ratio level of measurement provides not
only information regarding greater than or less than status but also
information as to how
much greater or lesser.
Most psychological and educational tests are based on interval
scales. The Scholastic Assessment Test (SAT) is an example of this level of
measurement. A score of 550 on the SAT is higher than a score of 500, which in
turn is higher than 450. In addition, a difference between 550 and 500 on the
test is presumably equivalent to the difference between 500 and 450.
Interval level of measurement is most informative than ordinal measures.
Many widely used statistical procedures require measurements on at least an
interval scale.
To present an interval/ratio data, we use a bar chart,
histogram, boxplot, or line chart. To summarize this data,
we use Mean, Standard Deviation, or Median.
Note: You
cannot scaleup, but you can scaledown. This means that if the type of data
you have is interval/ratio, you can assign them into ordinal or
nominal form. Such as in this example, ‘What is your current age
in years?’, given the exact age (which is interval/ratio type), you can
classify them into ordinal, for example, assign them to ‘18 – 35 years
old’, or nominal, ‘Young or old” form. However,
you cannot assign a nominal data into an ordinal and interval/ratio form. If
your data is only categorized into ‘Young or Old’, there is
not enough information to assign them to ordinal, nor can you get the exact
age.
Sample questionnaire reflecting the different levels of measurement:
Level of Measurement and Statistical Tests
Figure 1. Nominal Data and Application of Statistical Analysis

Figure 2. Ordinal Data and Application of Statistical Analysis

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