Levels of Measurement

Levels of Measurement
Introduction:-
• The level of measurement refers to the
relationship among the values that are
assigned to the attributes for a variable.
• What does that mean? Begin with the idea
of the variable, in this example "party
affiliation." That variable has a number of
attributes.

Introduction:-
• Let's assume that in this particular election
context the only relevant attributes are
"republican", "democrat", and "independent".
• For purposes of analyzing the results of this
variable, we arbitrarily assign the values 1, 2
and 3 to the three attributes.
• The level of measurement describes the
relationship among these three values.

Introduction:-
• In this case, we simply are using the
numbers as shorter placeholders for the
lengthier text terms.
• We don't assume that higher values mean
"more" of something and lower numbers
signify "less".
• We don't assume the value of 2 means that
democrats are twice something that
republicans are.

Introduction:-
• We don't assume that republicans are in
first place or have the highest priority just
because they have the value of 1.
• In this case, we only use the values as a
shorter name for the attribute.
• Here, we would describe the level of
measurement as "nominal".

Why is Level of Measurement Important?
• First, knowing the level of
measurement helps you decide how to
interpret the data from that variable.
• When you know that a measure is
nominal (like the one just described),
then you know that the numerical values
are just short codes for the longer names.

Why is Level of Measurement Important?
• Second, knowing the level of
measurement helps you decide what
statistical analysis is appropriate on the
values that were assigned.
• If a measure is nominal, then you know
that you would never average the data
values or do a t-test on the data.

There are typically four levels of measurement
that are defined:
1. Nominal
2. Ordinal
3. Interval
4. Ratio

Incremental
Progress
Measure
Property
Mathematical
Operators
Advanced
Operations
Central
Tendency
Nominal
Classification,
Membership
=, != Grouping Mode
Ordinal
Comparison,
Level
>, < Sorting Median
Interval
Difference,
Affinity
+, - Yardstick
Mean,
Deviation
Ratio
Magnitude,
Amount
*, / Ratio
Geometric
Mean,
Coeff. of
Variation

Nominal level
The nominal type differentiates between
items or subjects based only on their names
or (meta-)categories and other qualitative
classifications they belong to; thus
dichotomous data involves the construction
of classifications as well as the classification
of items.

Examples of these classifications include gender,
nationality, ethnicity, language, genre, style, biological
species, and form. In a university one could also use hall
of affiliation as an example. Other concrete examples are
• in grammar, the parts of speech: noun, verb,
preposition, article, pronoun, etc.
• in politics, power projection: hard power, soft
power, etc.
• in biology, the taxonomic ranks below domains:
Archaea, Bacteria, and Eukarya
• in software engineering, type of faults: specification
faults, design faults, and code faults

Ordinal scale
The ordinal type allows for rank order (1st, 2nd,
3rd, etc.) by which data can be sorted, but still
does not allow for relative degree of
difference between them.
Examples include, on one hand, dichotomous data
with dichotomous (or dichotomized) values such
as 'sick' vs. 'healthy' when measuring health,
• 'guilty' vs. 'not-guilty' when making
judgments in courts,

Ordinal scale
• 'wrong/false' vs. 'right/true' when
measuring truth value, and, on the other hand,
• Non-dichotomous data consisting of a
spectrum of values, such as 'completely agree',
'mostly agree', 'mostly disagree', 'completely
disagree' when measuring opinion.

Interval scale
The interval type allows for the degree of
difference between items, but not the ratio between
them.
Examples include temperature with the Celsius scale,
which has two defined points (the freezing and boiling
point of water at specific conditions) and then separated
into 100 intervals, percentage such as a percentage
return on a stock location in Cartesian coordinates,
and direction measured in degrees from true or magnetic
north.

Ratio scale
•The ratio type takes its name from the fact that
measurement is the estimation of the ratio
between a magnitude of a continuous quantity
and a unit magnitude of the same kind (Michell,
1997, 1999).
•A ratio scale possesses a meaningful (unique and
non-arbitrary) zero value.
•Most measurement in the physical sciences and
engineering is done on ratio scales.

Ratio scale
•Examples include mass, length, duration, plane
angle, energy and electric charge.
•In contrast to interval scales, ratios are now
meaningful because having a non-arbitrary zero
point makes it meaningful to say, for example,
that one object has "twice the length" of another
(= is "twice as long").

Ratio scale
•Very informally, many ratio scales can be
described as specifying "how much" of something
(i.e. an amount or magnitude) or "how many" (a
count). The Kelvin temperature scale is a ratio
scale because it has a unique, non-arbitrary zero
point called absolute zero.

Levels of Measurement

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Levels of Measurement