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Types of Variables:. Numerical vs. non-numerical Discrete vs. continuous A very special variable = “binary” variables What is a “binary variable? Why are they interesting or important? What are their important characteristics? What statistics apply to binary variables?.
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Types of Variables: Numerical vs. non-numerical Discrete vs. continuous A very special variable = “binary” variables What is a “binary variable? Why are they interesting or important? What are their important characteristics? What statistics apply to binary variables?
What is a “binary variable?” A dichotomy only two possible values Exhaustive Mutually exclusive Expressed in binary numbers 0 & 1 as only values (base-2 numbers) Examples: Yes - No Present - Absent Happened - Didn’t happen Action – Inaction Pass - Fail
Why do they matter?” The world consists of LOTS of dichotomous events Outcomes Decisions Binary numbers are very well-defined and handy (in both mathematical & practical terms) Modern digital computers Almost modern computing machines
What are their important features for statistics? Level of measurement? All four levels (nominal, ordinal, interval, ratio) apply to binary variables! All levels of statistics can be applied to binary variables, although interpretations may be a little different Central tendency: mean = p Variability: variance = p (1-p) (where p indicates the proportion of 1s in the distribution)
Note possible differences between true & contrived binary variables: Natural dichotomies/binaries Computed dichotomies where another type of variable has been recoded or converted into a dichotomy for specific purposes Collapsed variables (multiple into two categories) Threshold or bifurcated coding (use a cutoff point to convert into pass-fail) With an underlying interval or ratio variable hidden inside “Dummy coding” of a multi-category variable