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.