Variables and Measurement (2.1)

1. Variables and Measurement (2.1) • Variable - Characteristic that takes on varying levels among subjects • Qualitative - Levels are unordered categories (referred to as nominal scale) • Quantitative - Levels vary in magnitude (referred to as interval scale) • Combination - Levels are ordered categories (referred to as ordinal scale)

2. Statistical Methods (2.1) • Statistical methods apply to the various variable types • When conducting research it is important to identify what variable type(s) are being observed so that proper methods are used to describe the data and make inferences • Ordering of variable types from highest to lowest level of “magnitude differentiation”: • interval > ordinal > nominal

3. Interval Scale Variables (2.1) • Discrete - Variable can take on only a finite (or countably finite) set of levels • Continuous - Variable can take on any values along a continuum • Discrete variables with many possible outcomes are often analyzed as if continuous • Continuous variables often reported as if discrete

4. Randomization • Quality of inferences depends on how well a sample is representative of a population • Simple Random Sampling: All possible samples of n items from a population of N items are equally likely. Makes use of random number tables or statistical software that can quickly generate long lists of random numbers. • Frame (or listing) of all items in population must exist to truly implement simple random sampling

5. Probability & Non-Probability Samples • Probability Samples: Probability of given samples being selected can be computed. • Non-probability Samples: Probability of possible samples cannot be specified: • Volunteer samples: Mail-in questionnaires, internet click on responses, Call-in surveys • Street corner surveys • Inferential methods valid only for probability samples

6. Experimental Designs • Experimental Studies: Researcher assigns subjects to experimental conditions. • Subjects should be assigned at random to the conditions, and preferably blinded to the specific treatment when possible (e.f. Clinical trials) • Randomization in long trials will “balance” treatment groups with respect to other demographic risk factors • Sample surveys that identify subjects by naturally occurring groups are Observational

7. Sampling & Non-sampling Variation • Sampling Error: Difference between a statistic computed on a sample and the true population parameter. • Typically unknown except in academic examples • Methods exist to predict magnitudes (margin of error) • Non-sampling Error sources: • Undercoverage: Frame may not contain all individuals of certain groups (e.g. telephone books) • Nonresponse: Individuals who complete surveys may differ from those who don’t • Response Bias: Taboo questions/”Politically correct answers

8. Probability Sampling Methods • Alternatives to Simple Random Sampling (need adjustments to some formulas): • Systematic Random Sample: Choose an item at random at top of frame, then select every kth item • Stratified Random Sample: Identify groups of individuals by some characteristic (strata), and take simple random samples within each strata. • Cluster Sample: Identify individuals by clusters (typically locations) and randomly sample clusters of individuals.