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Lecture 2

Lecture 2 - September 19.odt

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University of Toronto St. George
Damian Dupuy

Leecture 2 – September 19 Variables and Data – Variable – 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 – 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 be used – How much informaiton should that variable have for us. – All variables contain information, so basically how we measure is based on how we get that information – Four Scales (Ranges from Lowest to Highest) – Nominal – Ordinal --------- – Interval – Ratio 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 Nominal – 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 . Ordinal – 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 Interval – 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 Ratio – 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
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