What are the levels of measurement? Explain each level so that the reader can understand the description of the level and differentiate each level from other levels.
Write down 10 examples for
each level and further explain one example from each level.
- Course: Introduction to Educational Statistics (8614)
- Level: B.Ed (1.5 Years)
Answer:
Data Levels of Measurement
A variable has one of four
different levels of measurement: Nominal, Ordinal, Interval, or Ratio. (Interval and Ratio levels of measurement
are sometimes called Continuous or Scale).
The researcher needs to understand the different levels of measurement, as these levels
of measurement, together with how the research question is phrased, dictate
what statistical analysis is appropriate.
In fact, the Free download below conveniently ties
In descending order of precision,
the four different levels of measurement variable’s levels to different statistical analyses.t are:
•
Nominal–Latin for name only (Republican, Democrat, Green, Libertarian)
•
Ordinal–Think ordered levels or ranks (small–8oz, medium–12oz,
large–32oz)
•
Interval–Equal intervals among levels (1 dollar to 2 dollars is the same
interval as 88 dollars to 89 dollars)
•
Ratio–Let the “o” in ratio remind you of a zero in the scale (Day 0, day
1, day 2, day 3, …)
The first level of measurement is the nominal level of measurement. In
this level of measurement, the numbers in the variable are used only to
classify the data. In this level of measurement,
words, letters, and alpha-numeric symbols can be used. Suppose there is data about people
belonging to three different gender categories. In this case, the person belonging
to the female gender could be classified as F, the person belonging to the male
gender could be classified as M, and the transgendered classified as T. This
type of assigning classification is the nominal level of measurement.
The second level of measurement
is the ordinal level of measurement.
This level of measurement depicts some ordered relationship among the
variable’s observations. Suppose a
student scores the highest grade of 100 in the class. In this case, he would be assigned the first
rank. Then, another classmate scored
the second highest grade of 92; she would be assigned the second rank. A third student scores 81 and he would be
assigned the third rank, and so on.
The ordinal level of measurement indicates an ordering of the measurements.
The third level of measurement is
the interval level of measurement.
The interval level of measurement not only classifies and orders the measurements, but also specifies that
the distances between each interval on the scale are equivalent along the scale
from low interval to high interval. For
example, an interval level of measurement could be the measurement of anxiety
in a student between the score of 10 and 11, this interval is the same as that
of a student who scores between 40 and 41. A popular example of this level of
measurement is temperature in centigrade, where, for example, the distance
between 94C and 96C is the same as the
distance between 100C and 102C.
The fourth level of measurement
is the ratio level of measurement.
In this level of measurement, the observations, in addition to having
equal intervals, can have a value of zero as well. The zero in the scale makes this type of
measurement, unlike the other types of measurement, although the properties are
similar to that of the interval level of measurement. In the ratio level of
measurement, the divisions between the points on the scale have an equivalent
distance between them.
The researcher should note that
among these levels of measurement, the nominal level is simply used to classify
data, whereas the levels of measurement described by the interval level and the
ratio level are much more exact.
What level of measurement is used for psychological variables?
Rating scales are used frequently
in psychological research. For example, experimental subjects may be asked to
rate their level of pain, how much they like a consumer product, their
attitudes about capital punishment, and their confidence in an answer to a test
question.
Typically these ratings are made
on a 5-point or a 7-point scale. These scales are ordinal since there is
no assurance that a given difference represents the same thing across the range
of the scale. For example, there is no way to be sure that a treatment that
reduces pain from a rated pain level of 3 to a rated pain level of 2 represents
the same level of relief as a treatment that reduces pain from a rated pain
level of 7 to a rated pain level of 6.
In memory experiments, the
dependent variable is often the number of items correctly recalled. What scale
of measurement is this? You could reasonably argue that it is a ratio scale.
First, there is a true zero point: some subjects may get no items correct at
all. Moreover, a difference of one represents a difference of one item recalled
across the entire scale. It is certainly valid to say that someone who recalled
12 items recalled twice as many items as someone who recalled only 6 items.
But the number of items recalled is a
more complicated case than it appears at first. Consider the following example
in which subjects are asked to remember as many items as possible from a list
of 10. Assume that (a) there are 5 easy items and 5 difficult items, (b) half of the subjects can recall
all the easy items and different numbers of difficult items, while (c) the
other half of the subjects are unable to recall any of the difficult items but
they do remember different numbers of easy items. Some sample data are shown
below.
|
Subject
|
Easy Items
|
Difficult Items
|
Score
|
||||||||
|
A
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
2
|
|
B
|
1
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
3
|
|
C
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
0
|
7
|
|
D
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
0
|
1
|
8
|
Let's compare (1) the difference
between Subject A's score of 2 and Subject B's score of 3 with (2) the
difference between Subject C's score of 7 and Subject D's score of 8. The
former difference is a difference of one easy item; the latter difference is a
difference of one difficult item. Do these two differences necessarily signify the same difference in
memory? We are inclined to respond "No" to this question since only a
little more memory may be needed to retain the additional easy item whereas a
lot more memory may be needed to retain the additional hard item. The general
point is that it is often inappropriate to consider psychological measurement
scales as either interval or ratio.
Consequences of the level of measurement
Why are we so interested in the
type of scale that measures a dependent variable? The crux of the matter is the
relationship between the variable's level of measurement and the statistics that
can be meaningfully computed with that variable. For example, consider a
hypothetical study in which 5 children are asked to choose their favorite colors
from blue, red, yellow, green, and purple. The researcher codes the results as
follows:
|
Color
|
Code
|
|
Blue
|
1
|
|
Red
|
2
|
|
Green
|
3
|
|
Yellow
|
4
|
|
Purple
|
5
|
Related Topics
No comments:
Post a Comment
If you have any question related to children education, teacher education, school administration or any question related to education field do not hesitate asking. I will try my best to answer. Thanks.