Transcript Level of measurement - Cooley, Wilson Hall, Sociology Lab

The Vocabulary of
Science
1. Concepts
2. Operationalization
3. Direction of the relationship
4. Level of measurement
Concepts
 Concept is an abstraction/representation of
an object or a behavioral phenomenon
 Each discipline develops its unique set of
concepts
 Political science: “power”, “social status”,
“relative deprivation”
 Psychology: “depression”, “perception”,
“learning”
 Sociology: “social status”, “role”
Why do we need concepts?
 Concepts provide a common language, which
enables scientists to communicate with one
another within an area
 “Power” can mean different thing to different
people
 Science cannot progress with ambiguous and
imprecise language
 Vocabulary of science
Vocabulary of science
 Conceptual Definitions (definitions that describe
concepts by using other concepts)
 Power has been conceptually defined as the
ability of an actor (group/the state) to get another
actor to do something that the latter would not
otherwise do
 Concepts ability, actor, group, state can be
defined by other concepts, and so on.
Vocabulary of science
 At a certain point in this process, scientists encounter
concepts that cannot be defined by other concepts
 These are called primitive terms
 For example, a group is two or more individuals
 Use of primitive terms is less efficient than use of
more complex concepts; it is easier to say the word
“group” than constantly repeat the primitive terms that
compose the definition of “group”.
Concepts – Variables
 A variable is any entity that can take on different
values.
 Anything that can vary can be considered a variable
 For instance, age can be considered a variable
because age can take different values for different
people or for the same person at different times
 Similarly, country can be considered a variable
because a person's country can be assigned a value
Variables
 Variables aren't always 'quantitative' or
numerical
 The variable 'gender' consists of two text
values: 'male' and 'female'.
 We can, if it is useful, assign quantitative
values instead of (or in place of) the text
values, but we don't have to assign numbers
in order for something to be a variable
Attribute
 An attribute is a specific value on a variable
 The variable sex or gender has two
attributes:
 1 = male
 2 = female
Attribute
 The variable agreement might be defined as
having five attributes:
 1 = strongly disagree
 2 = disagree
 3 = neutral
 4 = agree
 5 = strongly agree
Variable should be exhaustive
 Each variable should be exhaustive, it should
include all possible answerable responses/attributes
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Variable “Religion"
1. "Protestant",
2. "Jewish“
3. "Muslim"
 The list does not exhaust all possibilities.
 The way to deal with this is to explicitly list the most
common attributes and then use a general category
like "Other" to account for all remaining ones.
Attributes should be mutually
exclusive
 No respondent should be able to have two attributes
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simultaneously
Variable "Employment Status“
1) "employed“
2)"unemployed"
But these attributes are not necessarily mutually
exclusive -- a person who is looking for a second job
while employed would be able to check both
attributes!
we can ask the respondent to "check all that that
apply" and then list a series of categories
Mutually Exclusive Attributes
With whom do you currently live? (Choose all that
apply)
 Alone
 Roommate(s)
 Housemate(s
 Spouse
 Partner
 Parent(s)
 Other relative(s)
 Other________________
Types of Variables
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Independent Variable (Causal variable,
variable you change
Dependent variable (Effect, variables you
are trying to predict)
Independent Variable
Dependent Variable
Types of variables
Independent
Variable
Gender
Female
Male
Attributes
Dependent
Variable
Occupation
Income
< $5,000
> $ 5,000
Attributes
Hypotheses
 After we indentify the variables of interest, we
posit a relationship between them—
HYPOTHESIS
 Hypotheses can be either true or false
 We create them in order to test whether the
posited relationship between the variables
are true or false
Example
 H1: Gender affects occupation
 H2: Differences in age are related to
difference in income
Relationship between Variables
 Positive
 An increase/decrease in the independent
variable yields an increase/decrease in the
dependent variable
Independent variable/ dependent variable
Independent variable/ dependent variable
Example of positive relationship
 H1: People with higher education are more
likely to earn more money
 Dependent variable:
 Independent variable:
Relationship between Variables
 Negative
 An increase/decrease in the independent
variable yields a decrease/increase in the
dependent variable
Independent variable/ dependent variable
Independent variable/ dependent variable
Example of negative relationship
 H1: Increased exercise causes decreased
weight
 H2: The higher your social class the less
likely you are arrested for committing a crime
 Dependent variable:
 Independent variable:
Undetermined
 H1: Males are more likely to earn more money
than females are
 Independent variable / dependent variable
Male
Low Income
Female
High income
Practice
 Let say you want to test the relationship
between exercise and weight
 Formulate the hypothesis which posits a
positive relationship between these two
variables
Operational Definition
 After we select variables and formulate the
hypothesis, we must create operational
definition for each of our variables
 Operational definition – transforming a
variable into something we can observe
 Listing attributes
Operationalizing
 Gender
 Female
 Male
Operationalizing
 Occupation
 Professional
 Manager or owner of business
 Skilled laborer
 Unskilled laborer
 Not employed
 Other
Operationalizing
 Income
 $5,000 or less
 $5, 001-15,000
 $15,001-25,000
 $25,001-35,000
 $35,001-50,000
 $50,001 or more
Practice in Operationalizing
 Marital status
 Never married
 Married
 Divorced
 Separated
 Widowed
 Other
Operationalization
 “Love”
Sternberg (1988) The Psychology of Love
 Emotional Intimacy dimension focuses on friendship,
trust and feelings of emotional closeness that result
from being able to share one's innermost thoughts
and feelings with a partner
 The passion dimension focuses on those intense
feelings of arousal that arise from physical attraction
and sexual attraction
 The commitment dimension of love is often viewed as
the decision to stay with one's partner for life.
Commitments may range from simple verbal
agreements (agreements not to become emotionally
and/or sexually involved with other people) to
publically formalized legal contracts (marriage)
“Love”
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Desiring to promote the welfare of the loved one;
Experiencing happiness with the loved one;
Having high regard for the loved on;
Being able to count on the loved one in times of need;
Mutual understanding with the loved one;
Sharing one's self and one's possessions with the loved
one;
Receiving emotional support from the loved one;
Giving emotional support to the loved one;
Having intimate communication with the loved one;
Response categories: “Always” “Often” “Occasionally” “Rarely” “Never”
Why is Level of Measurement Important?
 First, knowing the level of measurement
helps you decide how to interpret the data
from that variable
 Second, knowing the level of measurement
helps you decide what statistical analysis is
appropriate on the values that were assigned
 If a measure is nominal, then you know that
you would never average the data values or
do a t-test on the data.
Four levels of measurement
 Nominal
 Ordinal
 Interval
 Ratio
Nominal Measurement
 At the nominal level of measurement, numbers or
other symbols are assigned to a set of categories for
the purpose of naming, labeling, or classifying the
observations
 Gender is an example of a nominal level variable.
 Using the numbers 1 and 2, for instance, we can
classify our observations into the categories
"females" and "males,"
 When numbers are used to represent the different
categories, we do not imply anything about the
magnitude or quantitative difference between the
categories.
Nominal Variables
Ordinal variables
 In ordinal measurement the attributes can be rank-
ordered.
 For example, on a survey you might code
Educational Attainment as
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0= less than H.S.;
1= H.S. degree;
2= college degree;
3= post college
 In this measure, higher numbers mean more
education
 But is distance from 0 to 1 same as 2 to 3? Of course
not. The interval between values is not interpretable
in an ordinal measure
Ordinal variable
Overall, how satisfied or dissatisfied are you
with the quality of education that you are
getting at WSU?
 1=Very satisfied
 2=Somewhat satisfied
 3=Neither
 4=Somewhat dissatisfied
 5=Very dissatisfied
Interval variables
 In interval measurement the distance
between attributes does have meaning
 For example, when we measure temperature
(in Fahrenheit), the distance from 30-40 is
same as distance from 70-80
Interval variable
 The interval between values is interpretable
 We can compute an average of an interval
variable
 There is no absolute zero
 But note that in interval measurement ratios
don't make any sense - 80 degrees is not
twice as hot as 40 degrees (although the
attribute value is twice as large)
Ratio-level variables
 In ratio measurement there is always an absolute
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zero that is meaningful
This means that you can construct a meaningful
fraction (or ratio) with a ratio variable
Weight is a ratio variable
In applied social research most "count" variables are
ratio, for example, the number of clients in past six
months.
Why? Because you can have zero clients and
because it is meaningful to say that "...we had twice
as many clients in the past six months as we did in
the previous six months."
Hierarchy of levels
 There is a hierarchy implied in the level of
measurement idea.
 At lower levels of measurement, assumptions tend to
be less restrictive and data analyses tend to be less
sensitive
 At each level up the hierarchy, the current level
includes all of the qualities of the one below it and
adds something new
 In general, it is desirable to have a higher level of
measurement (e.g., interval or ratio) rather than a
lower one (nominal or ordinal).
Exercise
 Political Affiliation is measured as
 0 = Republican
 1 = Democrat
 2 = Independent
 3 = Reform Party
 4 = Green Party
 5 = Socialist
 6 = Other
 This measure is a(n) _____ scale