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Section 1 Topic 1

Levels of MeasurementCategorical 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. Begin by examining each variable by itself. Then move on to study the relationships among the variables.

2. Begin with a graph. Then add numerical summaries for specific aspects of the data.

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Section 1 Topic 1Displaying 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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Life Expectancy

Variables1. Country

2. Sex

3. Year

4. Life Expectancy

15 countries

Notes p.18

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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 Numbers mean different things in

different situations. different situations. Q:Q: “What number did you wear in the“What number did you wear in the

race?”race?”A:A: “5”“5”

Q:Q: “What place did you finish in?”“What place did you finish in?”A:A: “5”“5”

Q:Q: “How many minutes did it take “How many minutes did it take you?”you?”A:A: “5”“5”

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Level of Measurement

nominal scale ordinal scale interval scale ratio scale

Notes p.20

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The Nominal Scale

Lowest level of measurementLowest level of measurement Numbers used to name or Numbers used to name or

nominate and numbers can be nominate and numbers can be interchanged, or changedinterchanged, or changed

Eg: 1= “female”, 2= “male”Eg: 1= “female”, 2= “male”

or 1=“male”, 2= ‘female”or 1=“male”, 2= ‘female”

or 0 = “male”, 1 = “female”or 0 = “male”, 1 = “female”

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The Nominal Scale

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For example, we might have the For example, we might have the variable variable Location of homeLocation of home, with:, with:

1 = “northern suburbs”1 = “northern suburbs”

2 = “southern suburbs”2 = “southern suburbs”3 = “western 3 = “western suburbs”suburbs”4 = “eastern 4 = “eastern suburbs”suburbs”

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Ordinal Data Numbers are used to both label Numbers are used to both label and

orderorder Example: Participants asked to rate a Example: Participants asked to rate a

paintingpainting 1 least appealing 2 less appealing 3 unsure 4 more appealing 5 most appealing

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*Exercise 3: Ordinal or Nominal? religion

(1 = Protestant, 2 = Roman Catholic, 3 = Other, 4 = None)

year of course(1 = year 1, 2 = year 2, 3 = year 3)

suburb(1 = eastern, 2 = southern, 3 = central, 4 = western, 5 = northern)

family income(1 = low, 2 = medium, 3 = high)

nominal

ordinal

nominal

ordinal

Notes p.21

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The Interval Scale

•Has properties of ordinal scale plusHas properties of ordinal scale plus

•Intervals between the numbers are Intervals between the numbers are equalequal

•Has no true zero pointHas no true zero point

Notes p.21

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Interval: Celsius Scale

Intervals on the scale shown Intervals on the scale shown represent equal differences represent equal differences of 5of 5ooC in temperature.C in temperature.

0°C does not mean 0°C does not mean complete absence of heat.complete absence of heat.

cannot say “a day of 40°C is cannot say “a day of 40°C is twice as hot as a day of twice as hot as a day of 20°C”.20°C”.

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Interval Scale ExampleIQ Scale

1. They have different IQ's (nominal property of the scale)

2. Person C scored higher on the test than person B who scored higher than person A (ordinal property of the scale)

3. There is the same difference in intelligence (in theory at least) between person A and B as there is between B and C.

4. 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.

Person A: 112 Person B: 113 Person C: 114

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Ratio Scale

Examples:Examples: Height

measured in metres, centimetres … Weight

measured in kilograms, grams… Reaction time

Measure in seconds, minutes …

Notes p.22

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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

political party preference(1 = Labor, 2 = Liberal, 3 =

National, 4 = Other) time taken to solve a mental

puzzle in seconds self-esteem as measured on a

standardised Psychological test

nominal

ratio

interval

Notes p.22

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*Exercise 4: Identify the level of measurement health rating(1 = excellent, 2 = good, 3 =

satisfactory, 4 = poor, 5 = very poor) number of children weight in kilograms weight(1 = below average, 2 = average, 3 =

above average)

ordinal

ratio

ratio

ordinal

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Categorical and Metric Data

Level ofLevel of

MeasurementMeasurement

MetricMetric CategoricalCategorical

IntervalInterval RatioRatio nominalnominal ordinalordinal

Notes p.23

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SPSS Levels of Measurement

Notes p.23

Nominal

Ordinal

Scale – (Interval/ratio)