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Damian Dupuy

Variables and Data Variable  Characteristic of the population that changes or varies overtime  Examples include temperature, income, education, etc. o Look at the varying income over a period of time, or look at the varying in different neighborhoods, cities, countries, regions o Compare something that happens in one location compared to an another location, ex. Looking at census tracts o Ex. looking at two variables, looking at education and income how those connect and vary in different locations  Observe and measure variables – before you start testing them  Two Key Categories o Quantitative – numerical e.g. number of students who.. o Discrete (1,2,3,4…) or Conitious (1.5, 2.5,6.76, 3.89) o Qualitative – Non Numerical e.g. male/female, plant species  You can count the number of males or females in class Data  Results from measuring variables – set of measurements  Different Categories – Univariate, Bivariate , Multivariate Variables – Scales of Measurement I  Scale defines amount of information a variable contains and what statistical techniques can be used o EXAM: give a statistical problem and ask what statistical tests should be used. Two key pieces: what is the scale of in cremations are the variables measured at and how many sample am I dealing with? These two questions will allow you narrow down which test you can use.  Four Scales o Nominal o Ordinal o Interval o Ratio o ( ^ those are lowest to highest)  lowest has the least amount of information  you collect your data at the highest scale of information , just because you are able to compress them later on, you choose the highest scale based on what you are looking for o Nominal  Lowest scale of measurement , no numerical value attached  Classifies observations into mutually exclusive ( when grouing, they can only fit in one group and only one group alone) and collectively exhaustive ( there must be a group, where the values can fall under) groups  Simply the name or category of the variable – you make categories and give a numerical value , you see the frequency of your observation  E.g. Occupation Type, gender , place of birth ( these are categories, and you just count how many people are in each of those categories )  Ex. for Occupation Type – how many people are in management, how many people are in general labour? o Ordinal  Stronger scale as it allows data to be ordered or ranked  E.g. look at the 12 largest towns in a region, income by group (high, middle, low) – the process of ranking is ordinal level  The counts yield more information , because you are able to weight each value o Interval  Unit distance separating numbers is important  You can have a unit scale , each number has a lot more weight attached to them  E.g. Temperature (C or F)  But does not allow ratios and does not have a “true” Zero . ex. 10 degrees is warmer than 5 degrees , but its not necessary double the temperature. The only time you can have a zero with temperature is when you use the Kelvin Scale – this would not be a interval scale because there is a definite zero. o Ratio  Strongest scale of measurement  Ratios of distances on a number scale – you can say something is double something  Presence of an absolute “Zero”  E.g. how much a individual pay for rent a month, is a ratio scale  Anytime you can have zero as a value, then it’s a ratio scale o In practice, we consider interval/ratio scales together o Ex. You get the value of rent per month from a person that is ratio , and then you can convert to Ordinal by saying what category they fall under Describing Data I Graphs  Pie charts o Circular graphs where measurement are distributed among categories o You slice based on the frequency of the observation o E.g. counting the number of people that use different types of transit – Distribution of Transit Use : cars, bikes, public transit  Bar Graph o Graph where measurements are distributed among categories o Ex. arranging how many students got a A ,B , C etc, in a course Relative Frequency Histogram I  Graphs quantitate, rather than qualitative data  Vertical axis (y) shows “how often” measurements (frequency ) fall into a particular class or subinterval.  Classes are plotted on the horizontal (x) axis  Rules of thumb o 5 to 12 intervals or categories (Anything more, gets too complex) o 1 + 3.3 Log 10 of observations) – to figure out how many groups you need o Must be mutually exclusive and collectively exhaustive (every element in your data set must be able to fit in a class ) – if they don’t fit , then
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