Leecture 2 – September 19
Variables and Data
– Charactestics of the population that changes or varies over time
– Where things happen
– ex. Income distribution,
– Space helps us to look at these variables
– Examples include temperature, income, education etc...
– Basically, we are measuring temperature, education level,
– ** Observe and measure variables
– Two Key Categories
– Quantitative – numerical eg. Numbers of students who...
– we can measure by using numbers, we can assing numberrs or we can count
– Discrete (1,2,3,4...) or Continuous (1.5. 2.76, 3.445...)
– Qualitative – Non Numerical e.g MALE/FEMALE, plant species, education type
– sometimes based on what you are doing, qualitative can be assigned to
quantitative, 2 men or 6 women
– Data are always plural , because it is always based on numbers and many things
– Results from measuring variables -set of measurements***
– you have a variable and then after measuring, what it gives you is a set of DATA
– Different Categories
– Univariate (One variable and one set data) ,
– Bivariat (there are two variables at work) ,
– Multivariate (measuring gender, income, level of school, when you have bunch
of measurements, then you have a series of variables)
– Variables and Data can be defined in simple way, however it is more than that, and they
influence how we measure and so on
Variables – Scales of Measurement 1
– Scale defines amount of information a variable contains and what statistical techniques can
– How much informaiton should that variable have for us.
– All variables contain information, so basically how we measure is based on how we get
– Four Scales (Ranges from Lowest to Highest)
--------- – Interval
1) How many samples am i Dealing with, two sets or one set ?
2) What scale of inromation the varibale is measured at?
We always try to measure our variables at the RATIO scale.
– You can decomposed , it is more precise , ZERO is the KEY
– The more information you have the more you can push it all together and make it a nominal
number if you wish.
– You can never go the opposite the way
Variables – Scales of Measurement 2
– Lowest scale of measurement, no numerical value attached
– those numbers that dont carry weight, or information about them
– Classifies observations into mutually exclusive and collective exhausted groups
– every observation must fit into category
– they must be mutually exclusive or different from the groups,
– which means you have one choice and only, and must fit into only ONE
– ex. WE are just assigning names, Male and Female, there is no weight or scale
– Often called “categorical” data
– e.g occupation type, gender, place of birth
– objects placed into a box .
– Stronger scale as it allows data to be ordered or ranked
– ex. categoriziing people into groups
– NOMINAL would ask do you have income, Ordinal would give you option and you
have to pick one, example, which category of income are you,1) 0-1000 2) 2000-3000
– E.g 12 largest towns in a region, income by group (high, middle, low)
(Both of the groups above, USUALLY GO
Variables – Scales of Measurement 3
– Unit distance seperating numbers is important
– it doesnt convey some weighting associated with it
– E.g Temperature (F of C), taxable income ($)
– freezing point can be different
– It is very tricky to find
– Strongest scale of measurement
– Ratios of distances on a number scale – It is meaningfull
– Presence of an absolute 'ZERO'
– You cant have less then ZERO
– The grade you get is example of the RATIO – ex. You got 20% , which is 20x better than 0
– e.g Temperature (Kelvin) I