Statistics

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StatisticsChapter 2

• Levels of Measurement

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Classifying Variables by Levels of Measurement

• Levels of measurementthe way researchers collect
  data
• Survey instrument mail, phone, face-to-face, or
  internet
• As the instrument is developed, decisions need to
  be made about how to collect data and what data
  to collect

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ExampleAge 1

• Age can be provided by selection from a
  particular range in a category, or (as in General
  Social Survey (GSS)) by providing date of birth

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Categorical vs Numerical variables 2

• Categorical variables variables for which data
  are gathered in response categories that have
  been set up or predetermined by the researcher.
• Numerical (or scale) variables Variables for
  which data are gathered as numbers with no
  attempt by the researcher to precategorize the
  answers

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Categorical variables 3

• Demographic variables
• SexMale, female
• Race Black, white and other
• Marital status married, widowed, divorced,
  separated, never married

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Categorical variables

• Attitude variablesData almost always gathered in
  categories
• (ex/book) How important is it for teens to be
  given a strong message from society that they
  should abstain from sex until they are at least
  out of high school
• Very important
• Somewhat important
• Not too important
• Not at all important

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Categorical variables

• Discussion about morals
• If a man and a woman are in their early teens,
  say 14 to 16 years old is sex before marriage
• Always wrong
• Almost always wrong
• Wrong only sometimes
• Not wrong at all

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Categorical variables

• Behaviors
• Have you ever had sex with someone other than
  your husband or wife while you were married?
• Yes
• No
• Never married

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Numerical variables

• How many brothers and sisters do you have? Please
  count those born alive but no longer living, as
  well as those alive now. Also include
  stepbrothers, stepsisters, and children adopted
  by your parents
• How many children have you ever had? Please count
  any that were born alive at any time (including
  any you had from a previous marriage)

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Types of numerical variables

• Ratio variables numerical variables having 3
  characteristics
• Zero is meaningful, representing the absence of
  the characteristic being measured (ex/ if 0 is
  the answer to How many brothers and sisters do
  you have, can assume you have no brothers or
  sisters)
• The distance between each unit on the scale are
  the same or constant (ex/ age)
• The distance between each of the units must be
  proportional

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Types of numerical variables

• Interval variables numerical variables having 3
  characteristics
• Zero is either not used or does not indicate the
  absence of the characteristic (Ex/ IQno true
  zero Temperature (F,C)--zero does not mean the
  absence of temperature (K)zero is absence of
  heat)
• Pp. 41-42 Avoiding common pitfalls

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Types of categorical variables

• Nominal variables categorical variables which
  are measured in such a way that the categories
  indicate differences among respondents (ex/ race,
  sex)
• Ordinal variables categorical variables having
  some inherent rank, hierarchy or order these
  could represent feelings (stronger or weaker),
  attitudes (more favorable or less favorable),
  frequency of an action or activity, how long
  something has been happening, how much of
  something someone has (such as money)

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Types of categorical variables

• Commonly used answer scales for ordinal variables
• Very important, somewhat important, not too
  important, not at all important
• Always wrong, almost always wrong, wrong only
  sometimes, not wrong at all
• Total household income
• Common pitfallsp44
• Skills practice 2, pp 45-46

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Discrete and continuous variables

• Discrete Can be counted(ex/ number of brothers
  and sistersunits of 1)
• Continuous The variables that have a
  characteristic being measured which is infinitely
  reducible (ex/ ageyears, hours, minutes,
  seconds, fractions of seconds)
• P. 48-49 Figure 2.2
• Common pitfallsp49

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Homework

• Read pp. 35-50
• Do p. 51-53// General Exercises 1,3
• Hand in Thursday p 53//General Exercise 2, P.
  53//SPSS 1