VARIABLES

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VARIABLES

• Topic 3

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Variables and the Unit of Analysis

• Variables are characteristics of the things
  that we are studying.
• These things are commonly called cases or
  units.
• A case study focuses on a single thing.
• The kind of thing that is being studied is
  called the unit of analysis.
• Individuals constitute the unit of analysis for
  much empirical social science research (and
  almost all survey research in political science).
  
• A particular research project focuses on a
  particular set or population of cases
  (individuals or other units),
• often by studying a sample of cases drawn from
  the population.

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American National Election Studies

• ANES focuses on individuals as the units of
  analysis in the American voting age population
  (VAP).
• ANES variables pertain to these individuals
• ANES variables include
• gender, race, education, and other demographic
  variables
• party identification, voting intention, President
  approval, ideology, abortion opinion, political
  trust, and other attitudinal variables
• whether registered/voted, candidate vote for,
  whether contributed campaign , and other
  behavioral variables
• These are all variable properties of individuals,
• not households, elections, nations, etc.

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Other Populations of Individuals

• Population All Members of Congress
• additional variables pertaining to this
  specialized population of individuals include
• number of terms served, campaign expenditure in
  last election, last re-election margin, party
  affiliation, committee assignments, roll-call
  vote on specified bill, ADA (etc.) rating,
  NOMINATE score, etc.
• Annual Survey of Social Security and Medicare
  Beneficiaries
• British etc. Election Studies

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Other Units of Analysis in Political Research

• Presidential elections variables include
• winning party, winners vote popular vote , Dem.
  candidates popular vote , winners electoral
  vote margin, turnout , whether the incumbent was
  running for re-election, total campaign
  expenditures, etc.
• States in a given Presidential election
  variables include
• number of electoral votes, winning
  party/candidate, winners vote Rep.
  candidates vote , turnout , etc.
• States in all historical Presidential elections
  variables include
• all of above for each election year
• Nations variables include
• population, GNP, per capita income, literacy
  rate, military spending as of GNP, size of
  army, type of party system, etc.
• States, counties, other jurisdictions, precincts,
  legislatures, political parties, etc.

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Households

• Households are often the unit of analysis in
  economic and sociological research
• Variables include
• size ( of persons)
• type (single-parent, no children, unrelated,
  etc.)
• type of housing unit
• household income
• etc.
• Current Population Survey (CPS)
• Panel Study of Income Dynamics (PSID)
• Rotating panel surveys of households

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Variables vs. Values

• Variables that pertain to a given unit of
  analysis take on different values from case to
  case cross-sectional analysis.
• Gender individuals male, female
• Education individuals primary school only,
  years completed, etc.
• Income individuals or households dollar amount
  (or dollar range), quintile, etc.
• Type of dwelling households detached,
  townhouse, apartment, etc.
• Literacy rate nations numerical
• Turnout elections numerical
• Variables can also vary over time in the same
  case longitudinal analysis,
• e.g., state democratic candidate vote over time.

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Variables are the building blocks of empirical
political science research

• Researchers have to figure out how to measure the
  variables they are interested in by designing
• appropriate survey questions
• or other kinds of measures
• Researchers next need to actually collect the
  data, e.g., by carrying out
• the survey they have designed
• or other data collecting operations.
• With the data at hand, researchers then ask such
  questions as the following
• What is the average or typical value of a
  variable in a set of cases?
• For example, what is typical level of interest
  among voters, or the average rate of turnout in
  recent elections?

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Questions (cont.)

• How are the values of a variable distributed in a
  set of data, i.e., do most of the same cases have
  about the same value (low dispersion) or do
  different cases have very different values (high
  dispersion). For example
• Do all voters have about the same level of
  interest or are some very interested while others
  not interested at all?
• Do all elections have about the same level of
  turnout, or do some have very high turnout while
  others have very low turnout?
• Distribution of income or wealth.
• How are two variables related or associated in a
  set of data? For example
• Is the level of interest among voters related to
  their level of education?
• Does the level of turnout in elections depend on
  how close elections are expected to be?
• Does one variable have a (direct) causal impact
  on another variable? For example
• Does higher education cause people to become more
  interested in politics?
• Does the prospect of a close election cause more
  voters to turn out and vote?
• Does one variable have an (indirect) causal
  impact on another variable? For example
• Does the prospect of a close election cause
  greater activity by campaign organizations that
  in turn causes more voters to turn out and vote?

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Variables and Their Values

• To repeat, variables vary they take on
  different values from case to case or from time
  to time
• Thus, associated with every variable is a list or
  range of possible values. For example
• PARTY IDENTIFICATION (pertaining to individuals)
  in the U.S has values REPUBLICAN, DEMOCRAT,
  INDEPENDENT (or perhaps refinements like STRONG
  REPUBLICAN, WEAK DEMOCRAT, etc., and/or other
  values like MINOR PARTY).
• VOTED IN 2008 ELECTION? is another variable
  pertaining to individuals, with just two possible
  values, YES and NO.
• HEIGHT is a physical variable pertaining to
  individuals with values that are real numbers
  (expressed in units such as inches, centimeters,
  or feet).
• SIZE ( of persons) is a variable pertaining to
  households with values that are whole numbers gt 1
  (values are counts)
• LEVEL OF TURNOUT is a variable pertaining to
  elections (or to different jurisdictions in a
  given election), with values ranging potentially
  from 0 to 100.

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Naming Variables

• As a reminder that any variable must have a range
  of two or more possible values, it is useful to
  give variables names like
• LEVEL OF EDUCATION
• WHETHER OR NOT VOTED IN 2000 ELECTION
• SIZE OF POPULATION
• TYPE OF POLITICAL REGIME
• LEVEL OF VOTING TURNOUT
• DIRECTION OF IDEOLOGY
• ETC.
• In quantitative research, variable names are
  often written in capital letters (as above).

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Observations/Observed Values

• The actual value of a variable in a particular
  case is called an observation (or observed
  value). For example,
• we "observe by asking the appropriate
  question(s) in a survey that Joe Smith (the
  case) has the PARTY IDENTIFICATION (the variable)
  WEAK DEMOCRAT (the observed value), and likewise
• we observe by consulting the appropriate
  records that the 2008 Presidential election (the
  case) has a LEVEL OF TURNOUT (the variable) of
  61 (the observed value).

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Identifying Variables (PS3A)

• Each of the following statements makes an
  empirical assertion (which may or may not be
  true) each refers (at least implicitly) to two
  variables (and asserts that there is some kind of
  relationship between them). For each statement
• (a) indicate to what unit of analysis
  (individuals, nations, elections, etc.) and, as
  appropriate, what particular population the
  variables pertain
• (b) identify the two variables, with appropriate
  names (probably TYPE OF _____, LEVEL OF _____,
  DEGREE OF _____, AMOUNT OF _____, WHETHER OR NOT
  _____) and
• (c) indicate a range of possible values for each
  variable (often, but certainly not always, LOW
  and HIGH will do).
• (Note both variables in each sentence pertain
  to the same units.)
• 1. Junior members of Congress are less
  pragmatic than their senior colleagues.
• 2. Education tends to undermine religious
  faith.
• 3. Capital punishment deters murder.
• 8. When times are bad, incumbent candidates
  are punished in elections. gt
• 11. If you want to get ahead, stay in school.

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CLASS LIST (Data Spreadsheet)

• Case ID
  Variable 1 Var2 Var3 Var4
• 
  Grad.
• Name SSN Class Major GPA Cand?
• Jones, R. 215-14-6609 Senior POLI 3.12 No
• Kim, S. 144-56-9231 Sophomore PYSC 2.78 No
• Smith. H. 502-45-2323 Junior POLI 2.75 No
• Williams, R. 212-16-7834 Senior HIST 3.28 Yes
• Etc.
• What distinctions between different types of
  variables can we make?

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Types of Variables

• Our concern here is with drawing distinctions
  among variables with respect to their logical
  properties, not their substantive nature (e.g.,
  demographic, attitudinal, etc.)
• Every variable has at least two possible values
  (otherwise it could not vary).
• A variable is dichotomous (also called a dummy
  variable) if it has exactly two possible values
  (typically yes and no), e.g.,
• GRADUATION CANDIDATE? Students (Yes/No)
• WHETHER VOTED IN 2000 ELECTION Inds. (Yes/No)
• GENDER Inds. (M/F)
• However, most variables have three or more
  possible values.
• Some variables have an infinite number of
  possible values.

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Qualitative Variables

• A variable is qualitative if its values are given
  by words
• MAJOR Students POLI, HIST, BIOL, etc.
• TYPE OF REGIME nations Free, Partly Free,
  Unfree
• ABORTION OPINION Inds. Never permit, etc.
• In a data spreadsheet e.g., SPSS, these verbal
  values are typically recorded in terms of
  numerical codes, because this
• saves space, and
• facilitates machine processing.
• Moreover, survey data from closed-form questions
  is often pre-coded (e.g., the Student Survey).

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• In a spreadsheet
• Rows are cases
• Columns are variables
• Cell are values (varying from case to case)
• Values (except V01 YEAR OF SURVEY) in the Student
  Survey and SETUPS are numerically coded.

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Quantitative Variables

• A variable is quantitative if its (true, not
  coded) values are given by numbers
• GPA Students 3.12, 2.78, etc.
• LITERACY RATE Nations 98, 55, etc.
• HEIGHT Inds. 72", 62", etc.
• SIZE Households 1 person, 2 persons, etc.
• LEVEL OF TURNOUT Elections or jurisdictions
  51, etc.
• The magnitude of these numbers may depend on the
  units of measurement used (e.g., is HEIGHT given
  in inches, feet, centimeters, etc.?).
• In spreadsheet, such values are typically
  recorded in terms of their actual numerical
  values.
• The SETUPS data contains data pertaining to
  variables that, while truly quantitative in
  nature, are recoded in broad categories, e.g.,
• AGE (V60) 18-24, 25-34, etc. or
• INCOME (V65A) 0-16th percentile, 17-33rd
  percentile, etc.

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Truly Quantitative Data Need Not be Coded
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Variables and the Unit of Analysis

• Substantively related variables may be of
  different types depending on the unit of analysis
  to which they pertain.
• TURNOUT pertaining to individuals is a
  dichotomous variable with values yes voted
  and no did not vote.
• LEVEL OF TURNOUT pertaining to elections (or
  jurisdictions, precincts, etc.) is a quantitative
  variable with possible values ranging from 0 to
  100.

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Types of Variables / Levels of Measurement

• It is useful to refine both qualitative and
  quantitative variables further by distinguishing
  among four
• different types of variables, or (equivalently)
• different levels of measurement of pertaining to
  variables.
• Note these distinctions are relevant only as
  they pertain to non-dichotomous variables.
• Please take note of this with respect to PS 3B,
  Question 2.

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Nominal Variables

• A nominal variable (or a variable measured at the
  nominal level) has values that are unordered
  categories.
• Accordingly, nominal variable are qualitative in
  nature.
• Given two cases and a nominal variable, we can
  observe
• that they have the same value or they have
  different values, but (if they have different
  values)
• we cannot say that one has the higher/bigger
  value and the other the lower/smaller, etc.

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Nominal Variables (cont.)

• A nominal variable typically has a name like
• NAME OF ____
• TYPE OF ____
• NATURE OF ____
• KIND OF ____
• Examples
• (NAME OF) MAJOR Political Science, Economics,
  History, etc.
• (TYPE OF) RELIGIOUS AFFILIATION Protestant,
  Catholic, Jewish, etc.
• PREFERENCE FOR REPUBLICAN NOMINATION Giuliani,
  McCain, Romney, etc.
• In a data spreadsheet, numerical codes must be
  assigned to values of nominal variables in an
  essentially arbitrary manner,
• so it is certainly illegitimate to do arithmetic
  on the numerical code values.
• Typically the numerical codes are consecutive
  whole numbers.

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Ordinal Variables

• An ordinal variable (or a variable measured at
  the ordinal level) has values that fall into some
  kind of natural ordering,
• often (but not always) running from (in some
  sense) LOW to HIGH.
• Therefore, cases can be ranked or ordered with
  respect to their values on an ordinal variable.
• An ordinal variable is also qualitative in
  nature.
• Given two cases and a ordinal variable, we can
  observe
• that they have the same value or they have
  different values, and also (if they have
  different values)
• that one has the higher/bigger value and the
  other lower/smaller, etc., but
• we cannot say how much higher/bigger or
  lower/smaller.
• Given three cases with different values on an
  ordinal variable,
• we can identify the case with the observed value
  between the other two
• but we cannot say which of the other value it is
  closer to.

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Ordinal Variables (cont.)

• An ordinal variable typically has a name like
• DIRECTION OF ___
• EXTENT OF ____
• LEVEL OF ____
• DEGREE of ____
• Examples
• TYPE OF REGIME/DEGREE OF FREEDOM nations Free,
  Partly Free, Unfree
• (LEVEL OF) INTEREST IN THE ELECTION CAMPAIGN
  individuals from low to high
• (DIRECTION OF) IDEOLOGY individuals from most
  liberal to most conservative
• (DEGREE OF) PRESIDENTIAL APPROVAL individuals
  from strongly approve to strongly disapprove
• DIRECTION OF ABORTION OPINION individuals
  Never permit, . . . , Always permit
• (LEVEL OF) CLASS STANDING students freshman,
  sophomore, junior, senior
• When data is recorded in coded form, numerical
  codes should be assigned to values in a manner
  consistent with the natural ordering of the
  values.

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Ordinal Variables (cont.)

• If the natural ordering is from LOW to HIGH, the
  codes should likewise run from lower to higher
  numbers.
• If the natural ordering is not from LOW to HIGH,
  e.g., DIRECTION OF IDEOLOGY,
• the two extreme values (or poles), e.g., MOST
  LIBERAL and MOST CONSERVATIVE, should be assigned
  the minimum and maximum code values, but
• which gets which is arbitrary ,
• and intermediate values, e.g., MODERATE, should
  be assigned intermediate codes).
• In any event, values are typically assigned
  numerical codes that are consecutive integers,
• but this is not a logical necessity (because only
  their order matters).
• It remains illegitimate to do arithmetic on the
  numerical code values
• unless we are willing to attribute interval
  status to the code values.

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Ordinal Variables (cont.)

• Note that DIRECTION OF IDEOLOGY could be renamed
  DEGREE OF LIBERALISM,
• which does range from LOW (i.e., least liberal
  or most conservative) to HIGH (most liberal
  or least conservative).
• We could also reverse the polarity of the
  renamed variable and call it DEGREE OF
  CONSERVATISM,
• ranging from LOW (i.e., least conservative or
  most liberal) to HIGH (most conservative or
  least liberal).

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Ordinal Variables (cont.)

• Opinion variables with closed-form values running
  from (STRONGLY) AGREE (or APPROVE) to (STRONGLY)
  DISAGREE (or DISAPPROVE) are ordinal in nature.
• The value INDEPENDENT is usually deemed to fall
  between DEMOCRAT and REPUBLICAN, so PARTY
  IDENTIFICATION is usually deemed to be ordinal in
  nature.
• But this works only if we treat cases with minor
  party or DK values as missing data (since these
  values dont fall in the natural ordering).
• An SPSS spreadsheet normally displays a numerical
  code (rather than a blank) for missing data
  (unobserved values), which must be understood
  as not part of the natural ordering.
• In the SETUPS and Student Survey data, missing
  data coded as (9).
• SPSS must be told the missing data code(s) for
  each variable, so that it can set cases so coded
  aside when it processes data.

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Interval Scale Variables

• An interval variable (or variable measured at the
  interval level) has values that are real numbers
  that can appropriately be added together,
  subtracted one from another, and averaged.
• SPSS refers to scale variables
• An interval variable is quantitative in nature.
• Given two cases and an interval variable, we can
  say they have the same value or they have
  different values, and also (if they have
  different values)
• that one has the higher value and the other
  lower, etc., and also
• how much higher or lower one value is than the
  other, because
• we can subtract one value from another,
• i.e., we can determine the magnitude of the
  interval separating them and thus say how far
  apart the cases are with respect to the
  variable.
• Given three case with different values on an
  interval variable, we can identify the case with
  the observed value between the other two and we
  can also determine which of the to other cases it
  is closer to.
• But we cannot say how many times greater one
  value is than another.

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Interval Variables (cont.)

• An interval variable typically has a name like
• LEVEL OF ____
• DEGREE OF ____ 
• NUMBER OF ____
• AMOUNT OF ____
• In a spreadsheet, actual numerical values (rather
  than numerical codes) are normally entered into a
  data array (e.g., Presidential election data).
• But sometimes (numerically coded) class intervals
  are used instead (e.g., SETUPS V60 AGE), as
  will be discussed later. See gt
• Variables like PARTY IDENTIFICATION,IDEOLOGY, and
  ISSUE OPINIONS are often treated as interval
  variables (e.g., my Student Survey/ANES
  longitudinal charts that showed changing average
  levels of Party ID, Ideology, etc., over time).

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A Truly Interval Variable May Be Recoded into An
Ordinal One
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Ordinal vs. Interval Variables

• Example Baseball Standings
• Rank Standing of a team (first place, second
  place, etc.) is ordinal information
• Winning Percent (or Games Behind Leader) is
  interval information
• For the league playoffs
• the determination of division winners is based on
  ordinal information only but
• the determination of the wild card entry is
  based on interval information (best winning
  percent not otherwise in playoffs)
• A team that fails to make the playoffs may have a
  higher winning percent that a team that does make
  the playoffs

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Ratio Variables

• A ratio variable (or a variable measured at the
  ratio level) is an interval variable (that has
  values that are real numbers that can
  appropriately be added together, subtracted one
  from another, and averaged) but in addition
• one can appropriately divide one value by another
  (i.e., compute their ratio), and
• say, for example, that one case has twice the
  observed value of another.
• This requires that the ratio variable have a
  non-arbitrary zero value,
• which usually represents in some sense the
  complete absence of the characteristic or
  property to which the variable refers.
• Even if negative values are possible, the zero
  value is non-arbitrary, e.g.,
• level of profit (of a business) may have a
  negative value, or
• rate of economic growth (over years) may have a
  negative value.

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Ratio Variables (cont.)

• Examples of interval variables that are not
  ratio
• LEVEL OF SAT (or IQ) SCORE there is no 0 score
• DEGREE OF TEMPERATURE (Fahrenheit or Celsius)
  while each has a 0 value,
• 0F and 0C represent different temperatures, so
• 0 has no fundamental significance in either
  temperature scale
• vs. Kelvin Temperature scale with absolute 0K.
• IDEOLOGY, PARTY IDENTIFICATION and OPINION
  variables
• may perhaps be treated as interval rather than
  merely ordinal,
• but they certainly are not ratio.

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Ratio Variables (cont.)

• Examples of ratio variables include
• NUMBER OF CHILDREN or AGE (uncoded) individuals
• SIZE/NUMBER OF MEMBERS households or
  legislatures
• SIZE OF POPULATION nations
• LEVEL OF INCOME individuals or households
• PER CAPITA INCOME nations
• LEVEL OF PROFITS firms
• SIZE OF BUDGET SURPLUS governments or fiscal
  years
• NUMBER OF VOTES FOR DEM CAND elections, states
• PERCENT OF VOTES FOR DEM CAND elections, states
• Even though LEVEL OF PROFITS or SIZE OF BUDGET
  SURPLUS can have negative values, their zero
  points are not arbitrary.
• However, ratio comparisons can only be made
  between observed values with the same positive
  or negative sign.

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Freeway Exits and Levels of Measurement

• The identification of freeway exits has changed
  over the years, progressing from lower to higher
  levels of measurement.
• Nominal exits were once only given names (e.g.,
  name of crossroad or town),
• So you could tell only whether the upcoming exit
  is your exit or not.
• Ordinal Exits then were ordered (e.g., from east
  to west) and consecutively numbered, so you could
  tell
• whether you have passed your exit or not, and
• how many exits there are between your exit and
  where you are now.
• (Otherwise exit numbers are uninformative gt)
• Interval/Ratio Exits are now usually numbered in
  terms of their distance in miles from the state
  line,
• so can tell how far you have to go to get to your
  exit
• (and also that your exit is X times as far from
  the state line as where you are now).

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Ordinal Information May Not Be Informative
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But Ordinal Is Better Than Nominal
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Discrete vs. Continuous Variables

• Quantitative interval and ratio variables may
  be either discrete or continuous.
• Qualitative variables are pretty much
  necessarily discrete.
• A discrete variable has a finite (and typically
  small) number of possible values that usually (if
  the variable is quantitative) correspond to whole
  numbers (or integers) only.
• NUMBER OF CHILDREN households
• NUMBER OF MEMBERS councils or legislatures
• NUMBER OF ELECTORAL VOTES WON BY DEM CANDIDATE
  Presidential elections vs.
• PERCENT OF POPULAR VOTE WON BY DEM CANDIDATE
  Presidential elections

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Continuous Variables

• A continuous variable can have any real number
  (at least within some range) as a value (i.e.,
  including fractional values between the
  integers).
• So a continuous variable has (at least in
  principle) an infinite number of possible values,
  
• so that given two cases with distinct values of
  the continuous variable, it is in principle
  always possible that there is another case with
  an intermediate value of the variable.
• Discrete vs. Continuous temperature controls
  on a kitchen range.
• Digital vs. old fashioned thermometer

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Continuous Variables (cont.)

• Examples
• LEVEL OF DAILY HIGH TEMPERATURE places
  (cross-sectional), days (longitudinal)
• HEIGHT, WEIGHT, and AGE individuals
• Because we typically round off the value of such
  variables to the nearest degree, inch, pound,
  year, etc., such variables may look discrete.
• IDEOLOGY might be thought of as a truly
  continuous variable.
• Some interval variables are in principle discrete
  but are virtually continuous because they have
  so many possible (numerical) values, e.g.,
• RATE OF TURNOUT elections
• PERCENT OF VOTE FOR DEMOCRATIC CANDIDATE
  elections