Statistics—Chapter 2 Levels of Measurement

Classifying Variables by Levels of Measurement Levels of measurement—the 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

Example—Age 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

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

Categorical variables 3 Demographic variables Sex—Male, female Race– Black, white and other Marital status– married, widowed, divorced, separated, never married

Categorical variables Attitude variables—Data 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

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

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

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)

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

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/ IQ—no true zero; Temperature (F,C)--zero does not mean the absence of temperature ; (K)—zero is absence of heat) Pp Avoiding common pitfalls

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)

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 pitfalls—p44 Skills practice 2, pp 45-46

Discrete and continuous variables Discrete : Can be counted(ex/ number of brothers and sisters—units of 1) Continuous : The variables that have a characteristic being measured which is infinitely reducible (ex/ age—years, hours, minutes, seconds, fractions of seconds) P Figure 2.2 Common pitfalls—p49;

Homework Read pp Do p // General Exercises 1,3 Hand in Thursday: p 53//General Exercise 2, P. 53//SPSS 1