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variables and data, scales of measurement

Course Code
Damian Dupuy

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Statistics Lecture
September 21, 2011
Variables and Data
A variable is a characteristic of a population that changes or
varies over time; its something that can be measured over time
oEx. How household income changes in a region or country
over time
oTwo key categories: quantitative and qualitative
Quantitative variables: can be discrete [1,2,3,4,5, etc] or
continuous [1.7, 2.76, 4.45, etc] in continuous data, the
decimals matter
Qualitative data don’t have numbers; ex. Male or female, plant
species, etc.
Data: results from measuring variables [use data as the plural]
oMultivariate, bivariate and univariate
Scales of Measurement
A scale defines the amount of information a variable contains
and what statistical techniques can be used
Four scales: nominal [lowest amount of information], ordinal,
interval and ratio [highest amount of information]
oNominal: lowest scale and no numerical value attached to
it [no weighting]. Classifies observations into mutually
exclusive [an element can only go into one box or another;
only one category] and collectively exhaustive groups. A
nominal variable is simply the name or category of the
variable [ex. Its either male or female]
oOrdinal: allows data to be ordered and ranked. Ex. People
living in large towns, medium towns or small towns and
could then group them by the top 12 cities for example.
oInterval: unit distance separating numbers is important. Ex.
Temperature [F or C] or taxable income [$] In this case,
negative numbers can mean something
oRatio: ratios of distance on a number scale. Most important
way of describing it is the presence of an absolute zero;
you can’t have less than zero on a ratio but zero is
possible. Ex. Temperature [Kelvin], income from all sources
[$], population of a city. In practice, we consider
interval/ratio scales together
Describing Data
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