Transcript Lect 4_Oct 25_Measurement_on line

Research Methodology and Methods of Social Inquiry
GSSR
October 25, 2011
Measurement – Definitions; Indicators; Error
MEASUREMENT
- the process of assigning numbers or labels to units of
analysis to represent the properties of concepts
(variables).
Operationalization
In scientific inquiry we rely on operational definitions to specify
concepts.
An operational definition is a description of the “operations” that
will be undertaken in measuring a concept.
As a result of operational definitions we postulate variables.
Theory informs operationalization: why you decide to measure
the variable in that way and not in any other.
A variable (age) is a measurable characteristic that differs
across the units of observation (individuals).
The observations (years) are the values of the variables for each
unit.
Each variable assumes a set of some definite values.
A full measurement procedure specifies values for each variable
across all observation units.
Levels of Measurement
Nominal, ordinal, interval & ratio scales of measurement
Nominal variables (qualitative): observations consist of separate
categories that are labeled (cannot order them).
“Dummy” (dichotomous) variables;
Examples: Religious affiliation; Party affiliation; Social Class;
Dummy: Gender
Ordinal variables:
- observations consist of separate categories that are arranged in rank
order (can be ordered, but we don’t know if the distance between the steps
is equal for all steps).
Ex: Likert scales
When no. of categories = large (7/more)  treat rank-order scales as
continuous
Interval variables: observations consist of ordered categories,
where distances between categories, called intervals, reflect
differences in magnitude.
Ex: Celsius
Ratio variables: interval scale with the additional feature of an
absolute zero point.
Ex: Income (in Zloty, Dollars, …), Education (in years)
STATA example
An indicator consists of a single observable measure, such as a
single questionnaire item.
Ex: What year have you been born in?
Composite measures: Scales & Indexes
- use several indicators combined, to create a new variable
Ex: attitudes toward immigrants; self-esteem scale; Notingham
scale
Relationships btw. Variables
Changes in one variable are accompanied by systematic
changes in the other(s).
For nominal variables: measures of association that tell us:
- If the relationship exists (i.e. is it statistically significant)
- How strongly are the two variables associated
For ordinal & interval variables: is the relationship linear or not?
Linear Relationship (correlation):
Y = a +b*X
Positive correlation: the 2 variables consistently change in the
same direction
Ex: higher values on education ‘go together with’ (correspond to)
higher values on income; lower values on education go together
with lower values on income.
Negative correlation: changes in one variable are in opposite
direction to changes in the other variable.
Ex: higher values on age go together with lower values on hearing
accuracy
Measures of correlation for interval variables (assuming linear
relationship) tell us:
(a) How strongly the 2 variables are related (value of coefficient):
r = 1; -1  perfect correlation
r = 0  no relationship
(b) If the relationship is positive/negative (sign of coefficent)
Test of statistical significance to assess whether the relationship
btw. the 2 variables exists in the population
Statistical Significance:
- a result is significant if it is NOT likely that it occurred by
chance.
When we find a relationship whose probability of happening by
chance is equal to, or less (p  0.05) than 5 in 100 random
samples we conclude that our result is statistically significant
Null hypothesis: there is no relationship in the larger population
from which we drew our sample (i.e. r = 0)
Approaches to measurement:
-
Verbal reports (self-report);
Surveys;
Observation (firsthand, or through various devices);
Archival records (statistical documents, diaries, mass
communications, etc).
In social research, one is interested in representing and/or
explaining differences (variations) btw. the units of
observation (cases).
Three sources of variation:
Observed variation = true differences + systematic
measurement error + random measurement error