S1T11 Section 1 Topic 1 Levels of Measurement Categorical Data

S1T12 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.

S1T13 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.

S1T14 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?

S1T15 Life Expectancy Variables 1. 1.Country 2. 2.Sex 3. 3.Year 4. 4.Life Expectancy 15 countries Notes p.18

S1T16 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

S1T17 Level of Measurement Numbers mean different things in different situations. Numbers mean different things in different situations. Q:“What number did you wear in the race?” A:“5” Q:“What number did you wear in the race?” A:“5” Q:“What place did you finish in?” A:“5” Q:“What place did you finish in?” A:“5” Q:“How many minutes did it take you?” A:“5” Q:“How many minutes did it take you?” A:“5”

S1T18 Level of Measurement nominal scale ordinal scale interval scale ratio scale Notes p.20

S1T19 The Nominal Scale Lowest level of measurement Lowest level of measurement Numbers used to name or nominate and numbers can be interchanged, or changed Numbers used to name or nominate and numbers can be interchanged, or changed Eg: 1= “female”, 2= “male” Eg: 1= “female”, 2= “male” or 1=“male”, 2= ‘female” or 0 = “male”, 1 = “female”

S1T110 The Nominal Scale 10 For example, we might have the variable Location of home, with: 1 = “northern suburbs” 2 = “southern suburbs” 3 = “western suburbs” 4 = “eastern suburbs”

S1T111 Ordinal Data Numbers are used to both label order Numbers are used to both label and order Example: Participants asked to rate a painting Example: Participants asked to rate a painting 1least appealing 2less appealing 3unsure 4more appealing 5most appealing

S1T112 *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

S1T113 The Interval Scale Has properties of ordinal scale plusHas properties of ordinal scale plus Intervals between the numbers are equalIntervals between the numbers are equal Has no true zero pointHas no true zero point Notes p.21

S1T114 Interval: Celsius Scale Intervals on the scale shown represent equal differences of 5 o C in temperature. Intervals on the scale shown represent equal differences of 5 o C in temperature. 0°C does not mean complete absence of heat. 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”. cannot say “a day of 40°C is twice as hot as a day of 20°C”.

S1T115 Interval Scale Example IQ 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: 112Person B: 113Person C: 114

S1T116 Ratio Scale Examples: Height measured in metres, centimetres … Weight measured in kilograms, grams… Reaction time Measure in seconds, minutes … Notes p.22

S1T117 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)

S1T118 *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

S1T119 *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 ordinal

S1T120 Categorical and Metric Data Level of Measurement Measurement Metric IntervalRatio Categorical nominalordinal Notes p.23

S1T121 SPSS Levels of Measurement Notes p.23 Nominal Ordinal Scale – (Interval/ratio)