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)

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

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

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

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

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

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

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.