Nominal scales ecture 2 Nominal data is the simplest form of data in which data falls into unordered Types of Data to represent non-numeric categories Nominal data can have two or more categories Where there are only two categories variable(or indicator) is generally referred to as dichotomous or binary Types of data Nominal scales (levels of measurement) The most common example of this type of variable is SEX. There are two categories Data(variables)can be classified into four male and female, and there is no logical main types: nominal, ordinal, interval and order in the categories. That s, one ratio gory is not higher bigger, or bet Understanding the type of data you are than the other. It is standard practice for using is important because some males to be given the value 1 and females statistical measures are only meaningful the value 2, although there is no statistical for some types of data or mathematical reason for this
1 1 Lecture 2 Types of Data 2 Types of data (levels of measurement) • Data (variables) can be classified into four main types: nominal, ordinal, interval and ratio. • Understanding the type of data you are using is important because some statistical measures are only meaningful for some types of data. 2 3 Nominal scales • Nominal data is the simplest form of data in which data falls into unordered categories. Essentially, numbers are used to represent non-numeric categories. Nominal data can have two or more categories. • Where there are only two categories the variable (or indicator) is generally referred to as dichotomous or binary. 4 Nominal scales • The most common example of this type of variable is SEX. There are two categories, male and female, and there is no logical order in the categories. That is, one category is not higher, bigger, or better than the other. It is standard practice for males to be given the value 1 and females the value 2, although there is no statistical or mathematical reason for this
41塔吉克族 Nominal scales 23高山 5堆吾尔 45鄂显克度 Nominal variables can have Relis 2T纳西陕 more than two categories. -Buddhist An example is religion. We 2柯尔柯孜赛 2=Catholic 10朝鲜 60塔塔尔族 could label religions any way we wanted. for example in 3=Protestant order of size or 4=Muslim 33羌族 alphabetically Some more examples 6=None 1?萨克 的外国人加入中国籍 Direction Occupation vice Government leaders Examples from the 1997 Survey West 104. What is your mantal status? 1). Never manage Industrial workers 2). First time mamed North Professionals and technicians Shanxi 405. Are you amenity usng any conceive method Commercial employees Neimenggu ) Not using any method 3). Female sterlization Service workers Unknown Liaoning 7). Condom 9).oders(please speafy)
3 5 Nominal scales • Nominal variables can have more than two categories. An example is religion. We could label religions any way we wanted, for example, in order of size or alphabetically. • Some more examples: Religion 1=Buddhist 2=Catholic 3=Protestant 4=Muslim 5=Other 6=None 6 …… Unknown Liaoning Service workers Jilin Farmers Heilongjiang Commercial employees Neimenggu North Professionals and technicians Shanxi South Industrial workers Hebei West Clerical workers Tianjin East Government leaders Beijing Direction Occupation Province 4 7 8 Examples from the 1997 Survey
Nominal scales Ordinal scales The category ordering helps us learn them, The term "ordinal refers to order or ordering but means nothing in terms of the variable This suggests a quantifiable ranking from mos itself. We could list " West" before "East"or to least or some other logical sequence or dering of a variable's categories. When the Shanghai"before "Beijing"and lose no quantification is by rank order, it suggests a information sequence but not yet an exact amount of a variable Feminists could place Women" before To say that in terms of population size China Men, assigning 1 to Women "and 2 to ranks first: India, second and the former Men U.S.S.R., third gives us an ordering. But we do not know how much larger China is than India We still do not know the exact population sizes Ordinal scales Ordinal scales Ordinal data are similar to nominal data in Level of education can be an ordinal that they are labels for non-numeric data variable. We could classify education as The only difference is that they have a ly logical order. However, the magnitude of the numeric label is still not important. 2=Secondary 3=Tertiary The category 3 is higher than the tegories 1 and 2 but the difference between 1 and 2 or 2 and 3 are not equal
5 9 Nominal scales • The category ordering helps us learn them, but means nothing in terms of the variable itself. We could list "West" before “East" or “Shanghai" before “Beijing" and lose no information. • Feminists could place “Women” before “Men”, assigning 1 to “Women” and 2 to “Men”. 10 Ordinal scales • Ordinal data are similar to nominal data in that they are labels for non-numeric data. The only difference is that they have a logical order. However, the magnitude of the numeric label is still not important. 6 11 Ordinal scales • The term “ordinal” refers to order or ordering. This suggests a quantifiable ranking from most to least or some other logical sequence or ordering of a variable's categories. When the quantification is by rank order, it suggests a sequence but not yet an exact amount of a variable. • To say that in terms of population size China ranks first; India, second; and the former U.S.S.R., third gives us an ordering. But we do not know how much larger China is than India. We still do not know the exact population sizes. 12 Ordinal scales • Level of education can be an ordinal variable. We could classify education as 1=Less than secondary 2=Secondary 3=Tertiary • The category 3 is higher than the categories 1 and 2 but the differences between 1 and 2 or 2 and 3 are not equal
Individuals can be placed into ranked ategories ordered highest to lowest (or In the 1997 Survey lowest to highest) E Health cond tons of live births? Height Economic status 1). Healty 2). Bascally healty 4). Congenitally asable 317. What do you think of the imact of induced abort 5). Diabled after birth on your physical and mental health? 1). No impact. Medium 2).Some impact 5).Noidea Very short Poor Sex-selection should be banned Ordinal scales Strongly agree? Both nominal and ordinal data are referred to as categorical variables. Neither type of data can be used in mathematica calculations or transformations Disagree? trongly disagree? 8
7 13 • Individuals can be placed into ranked categories ordered highest to lowest (or lowest to highest) Very short Short Medium Tall Very tall Height Poor Modest income Lower-middle income Upper-middle income Wealthy Economic status 14 Sex-selection should be banned Do you: Strongly disagree? Disagree? Unsure? Agree? Strongly agree? 8 15 In the 1997 Survey 16 Ordinal scales • Both nominal and ordinal data are referred to as categorical variables. Neither type of data can be used in mathematical calculations or transformations
Interval scales EXamples from the 1997 Survey 302Have you ever had any live birth? If yes, howman For interval data both ordering and Have you ever had any foetus death or still birth? If yes, how many? magnitude are important. The number Have you ever experenced induced abortion? If yes, how many times? given to interval data represents actual Are you currently pregnant? measurable quantities. In addition, interval 201. At what age did you have your first Examples are age, children ever born, the menstruation? number of road fatalities in a given period 313. Number of month into pregnancy at last or the number of doctors in an area nduced abortion 315. Number of days of rest after you had induced nterval scales Years of schooling For example the number of times a woman has given birth provides a variable 103. What is vour educational level with a range starting from 0 where the 1). literate or semi-literate difference between 1 and 2 is the same as the difference between 4 and 5. that is Junior middle school one child. a larger number indicates that a 4. Senior middle scho woman has had more children ) Secondary techm cal 6). College and above
9 17 Interval scales • For interval data both ordering and magnitude are important. The number given to interval data represents actual measurable quantities. In addition, interval data can only take on specified values. Examples are age, children ever born, the number of road fatalities in a given period or the number of doctors in an area. 18 Interval scales • For example the number of times a woman has given birth provides a variable with a range starting from 0 where the difference between 1 and 2 is the same as the difference between 4 and 5, that is, one child. A larger number indicates that a woman has had more children. 10 19 Examples from the 1997 Survey 201. At what age did you have your first menstruation? 313. Number of month into pregnancy at last induced abortion 315. Number of days of rest after you had induced abortion 20 Years of schooling 16 12 12 9 6 0
Ratio scales The temperature example Educational level as measured in years of In the commonly used Fahrenheit and schooling would appear to be measured at Celsius scales, zero is arbitrarily selected the interval level, but it is really an even and it is possible to have below-zero higher level of measurement known as the temperatures In the Kelvin scale, however, ratio level zeo·K(-273·c) is called absolute zero In theory, it cannot get any colder than absolute zero so there are no below-zero Ratio scales Ratio scales Interval and ratio levels are nearly identical In the social sciences, many variables The difference between the two is the above the ordinal level of measurement nature of the meaning of zero. In interval are actually ratio level. We encounter few data, zero is an arbitrary point, whereas in examples where zero is arbitrarily ratio data. zero is an absolute zero assigned meaning a complete lack of the variable More examples of ratio data are monetary baht, lira being measured units such as dollars measurement of size such as weight, height. or a
11 21 Ratio scales • Educational level as measured in years of schooling would appear to be measured at the interval level, but it is really an even higher level of measurement known as the ratio level. 22 Ratio scales • Interval and ratio levels are nearly identical. The difference between the two is the nature of the meaning of zero. In interval data, zero is an arbitrary point, whereas in ratio data, zero is an absolute zero, meaning a complete lack of the variable being measured. 12 23 The temperature example • In the commonly used Fahrenheit and Celsius scales, zero is arbitrarily selected and it is possible to have below-zero temperatures. In the Kelvin scale, however, zero 。K (-273。C) is called absolute zero. In theory, it cannot get any colder than absolute zero, so there are no below-zero readings on the Kelvin scale. 24 Ratio scales • In the social sciences, many variables above the ordinal level of measurement are actually ratio level. We encounter few examples where zero is arbitrarily assigned. • More examples of ratio data are monetary units such as dollars, cents, baht, lira, measurement of size such as weight, height, or age
Discrete and continuous variables Note: Interval data can be recoded into The four types of measurement sca categorical data which have two or more above can be grouped into two bro categories. Be careful that you do not categories, discrete and continuous recode interval data into categories which Discrete variables are those that are make them lose their meaning or become measured on a nominal or ordinal scale less useful in the analysis They classify persons, objects or events according to the quality of their attributes Discrete variables are often called categorical variables Discrete and continuous If you have a mixture of different types of variables data, you may have to record interval data into categorical data in order to use certain Continuous variables are those that are atistical procedures which require data to measured on an interval or ratio scale be categorical. However, there are some They classify persons, objects or events procedures that will work with a mixture of according to the magnitude or quantity of numeric and categorical data. You have to their attributer decide what procedures are appropriate for your analysis, based on the topic of your study, the type of data you are analysing and whether the meaning of the data will be affected by recoding
13 25 Discrete and continuous variables • The four types of measurement scales above can be grouped into two broader categories, discrete and continuous. • Discrete variables are those that are measured on a nominal or ordinal scale. They classify persons, objects or events according to the quality of their attributes. Discrete variables are often called categorical variables. 26 Discrete and continuous variables • Continuous variables are those that are measured on an interval or ratio scale. They classify persons, objects or events according to the magnitude or quantity of their attributes. 14 27 • Note: Interval data can be recoded into categorical data which have two or more categories. Be careful that you do not recode interval data into categories which make them lose their meaning or become less useful in the analysis. 28 • If you have a mixture of different types of data, you may have to record interval data into categorical data in order to use certain statistical procedures which require data to be categorical. However, there are some procedures that will work with a mixture of numeric and categorical data. You have to decide what procedures are appropriate for your analysis, based on the topic of your study, the type of data you are analysing and whether the meaning of the data will be affected by recoding
You can also combine categories in ordinal or categorical variables into two categories to form dichotomous variables Certain statistical procedures require the dependent variable to be dichotomous recoded into dichotomous variables known as dummy variables for statistica procedures that require independent variables to be all interval data
15 29 • You can also combine categories in ordinal or categorical variables into two categories to form dichotomous variables. Certain statistical procedures require the dependent variable to be dichotomous. Categorical variables also have to be recoded into dichotomous variables known as dummy variables for statistical procedures that require independent variables to be all interval data
