Department

GeographyCourse Code

GGR270H1Professor

Damian DupuyStudy Guide

FinalGGR 270 – Lecture 2 – September 22, 2010

Variables and Data

Variable

oCharacteristic of the population that changes or varies over time

oExamples include temperature, income, education, etc...

oObserve and measure variables

oTwo key categories

Quantitative (numerical)

•Discrete or continuous

Qualitative (non-numerical)

•Male/female, species

Data

oResults from measuring variables – set of measurements

oDifferent categories: Univariate, Bivariate, Multivariate

Variables – Scales of Measurement I

Scale defines amount of information a variable contains and what statistical

techniques can be used

Four scales:

Nominal

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oOrdinal

oInterval

oRatio

*It’s easier to go from something complex into something simpler

Variables – Scales of Measurement I I

Nominal

Lowest scale of measurement, no numerical value attached

Classifies observations into mutually exclusive and collectively exhaustive groups

Often called ‘categorical’ data

Ex: occupation type, gender, place of birth

Ordinal

Stronger scale of measurement as it allows data to be ordered or ranked

Ex: 12 largest towns in a region, income by group (high, middle, low)

Interval

Unit distance separating numbers is important

Ex: Temperature (°C, F), taxable income ($)

Ratio

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Strongest scale of measurement

Ratios of distance on a number scale

Presence of an absolute ‘zero’

Ex: Temperature (Kelvin), Income from all sources ($), population in a city

*In practice we consider interval/ratio scales together

*in theory, 4 scales

*In practice, 3 scales

Describing Data I

Pie Charts: Circular graph where measurements are distributed among categories

Bar graphs: Graph where measurements are distributed among categories

Relative Frequency Histogram

Graphs quantitative, rather than qualitative data

Vertical axis (Y) shows “how often” measurements fall into a particular class or

subinterval

Classes are plotted on the horizontal (X) axis

Rules of thumb:

o5-12 intervals or categories

o1+3.3log

10 (# of observations)

oCategories must be mutually exclusive and collectively exhaustive

oIntervals should be the same width (Largest # - Smallest # / # of classes)

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