Section 1 Topic 1
Levels of Measurement
Categorical Data
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Statistics
Descriptive

Purpose to organise,
display and
summarise the data
that have been
collected
Inferential

Purpose is to make
generalisations,
estimates, predictions
or decisions about
some measure of a
population from a
sample.
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Descriptive Statistics
1.
2.
Begin by examining each variable by
itself. Then move on to study the
relationships among the variables.
Begin with a graph. Then add
numerical summaries for specific
aspects of the data.
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Section 1 Topic 1
Displaying and summarising categorical
data

What are the four levels of measurement?

Why do we bother with levels of
measurement?

How do we display categorical data?

How do we summarise categorical data?
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Variables
Life Expectancy
1.
Country
2.
Sex
3.
Year
4.
Life Expectancy
15
countries
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Notes p.18
Variables and Values

Variables



Quantities about which we record
information
Eg: Sex, country, Income level
Values


How is the data recorded or coded?
Sex could be coded



Male, female
M, F
0, 1
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Level of Measurement




Numbers mean different things in different
situations.
Q: “What number did you wear in the
race?”
A: “5”
Q: “What place did you finish in?”
A: “5”
Q: “How many minutes did it take you?”
A: “5”
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Level of Measurement
nominal scale
 ordinal scale
 interval scale
 ratio scale

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Notes p.20
The Nominal Scale



Lowest level of measurement
Numbers used to name or nominate
and numbers can be interchanged, or
changed
Eg: 1= “female”, 2= “male”
or 1=“male”, 2= ‘female”
or 0 = “male”, 1 = “female”
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The Nominal Scale
For example, we might have the
variable Location of home, with:
1 = “northern suburbs”
2 = “southern suburbs”
3 = “western suburbs”
4 = “eastern suburbs”
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Ordinal Data


Numbers are used to both label and
order
Example: Participants asked to rate a
painting





1
2
3
4
5
least appealing
less appealing
unsure
more appealing
most appealing
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*Exercise 3: Ordinal or
Nominal?

religion
nominal (1 = Protestant, 2 = Roman Catholic, 3 =
Other, 4 = None)

ordinal

year of course
(1 = year 1, 2 = year 2, 3 = year 3)
suburb
nominal (1 = eastern, 2 = southern, 3 = central, 4 =
western, 5 = northern)

ordinal
family income
(1 = low, 2 = medium, 3 = high)
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Notes p.21
The Interval Scale
•Has properties of ordinal scale plus
•Intervals between the numbers are equal
•Has no true zero point
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Notes p.21
Interval: Celsius Scale



Intervals on the scale shown
represent equal differences of
5oC in temperature.
0°C does not mean complete
absence of heat.
cannot say “a day of 40°C is
twice as hot as a day of
20°C”.
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Interval Scale Example
IQ Scale
Person A: 112
1.
2.
3.
4.
Person B: 113
Person C: 114
They have different IQ's (nominal property of the
scale)
Person C scored higher on the test than person B
who scored higher than person A (ordinal property
of the scale)
There is the same difference in intelligence (in
theory at least) between person A and B as there is
between B and C.
We cannot say is that a person who scores 0 on an
IQ test has no intelligence, nor that someone with
an IQ of 150 is twice as smart as someone with an
IQ of 75.
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Ratio Scale
Examples:
 Height


Weight


measured in metres, centimetres …
measured in kilograms, grams…
Reaction time

Measure in seconds, minutes …
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Notes p.22
Ratio Scale



All properties of interval scale
But “zero” means absence of the
quantity
Consequently ratio statements such as
Alice (150cm) is “twice as tall” as Ruby
(75cm)
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*Exercise 4: Identify the level
of measurement
nominal 
political party preference
(1 = Labor, 2 = Liberal, 3 = National, 4 =
Other)
ratio

interval

time taken to solve a mental puzzle in
seconds
self-esteem as measured on a
standardised Psychological test
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Notes p.22
*Exercise 4: Identify the level
of measurement
ordinal

health rating
(1 = excellent, 2 = good, 3 =
satisfactory, 4 = poor, 5 = very poor)
ratio

ratio

ordinal

number of children
weight in kilograms
weight
(1 = below average, 2 = average, 3 =
above average)
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Categorical and Metric Data
Level of
Measurement
Metric
Interval
Categorical
Ratio
nominal
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ordinal
20
Notes p.23
SPSS Levels of Measurement

Nominal

Ordinal

Scale – (Interval/ratio)
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Notes p.23