measuring and describing variables pt 1

variable

an empirical measurement of a characteristic

what does a variable do?

provides raw materials for describing and analyzing the social and political world

describe the features that variables have

• turn to a discussion of levels of measurement, the amount of information conveyed by a variable’s values and codes

• some characteristics, such as a person’s age, can be measured with greater precision than others, like marital status

• the values and numeric codes of some variables contain more information than do the values and codes of other variables

name, 2+ values, numeric codes

what does every variable have?

at least two values

• if only one: it’s a constant, not a variable (never varies)

ex: marital status

• each status has a number attached to it

question to ask yourself

“what is the unit’s _____?

• answer would be a variable, not a value

characteristics of all variables

mutually exclusive and completely exhaustive

three kinds of variables

nominal, ordinal, and interval

nominal-level variables

communicates differences between units of analysis on the characteristic being measured

what makes nominal-level variables different?

numbers don’t mean anything, only used to differentiate, no quantitative value

translation of nominal

“in name only'“

what is true about nominal variables?

least precise than the other two

ordinal level variables

communicates relative differences between units of analysis

• values can be RANKED

• ranking is reflected in numeric codes

• more precise than nominal level variables

example of ordinal variables

ranking someone’s trust

• always = 1, most of the time = 2, half the time = 3, some of the time = 4, never = 5

• could also be reversed or from 6-10 instead of 1-5

what can’t ordinal variables do?

don’t tell us exact amount of things such as miles, geographic mobility, etc, so it’s not interval-level

what are ordinal values mostly used with?

abundant in social science research

mostly used with measurements of attitudes among individuals

• ex: questions gauging disapproval or approval of gov policies or social behaviors

interval-level variables

communicates exact differences between units of analysis

what do interval-level variables do?

the precision of an interval-level measurement enables you to calculate the precise difference between two data points

example of interval-level variables

age

• numerical values have an exact meaning

• 18 years old: 18 as the numerical value

what kind of values do interval-level variables have?

discrete or continuous values

discrete values

count the number of times something has occurred

• ex: # of times a politician has been re-elects or the # of votes cast in the last election

• always whole numbers

continuous values

have an infinite number of unique values and can be precisely estimated with decimal places

• you could calculate your age down to the millisecond and the distance you drive each day down to the millimeter

• can have a infinite number of unique values

what do poli sci researchers use mostly w/ interval-level variables?

aggregate-level units of analysis

name the three reasons why poli sci researchers love interval variables

• allow the researchers to place units of analysis into different categories

• permit units to be ranked on the measurement

• gauge fine differences between units of analysis

which level of measurement is the best?

it depends what you’re researching and how you want to measure it

what else is true about the different levels of variables?

can be used and translated in different ways

ex: temperature

• interval: the numerical degree (discrete or continuous)

• nominal: any values 32 degrees F or below “cold” and value about 32 degrees F “not cold”

• ordinal: any values 32 degrees F or below “freezing”, 33-50 “cold”, 51-75 “warm”, 76-100 “hot”

central tendency

the average

three kinds of central tendencies

mean, median, mode

mode

most common/frequent value of the variable

• contains the largest # of cases or units of analysis

• in nominal-level variables, it’s the only measure that may be used

median

value of a variable that divides the cases right down the middle

• used for describing variables w/ higher levels of measurement (both ordinal or interval)

• central tendency of an ordinal-level variable may be measured by the mode of the median

mean

comes closest to the everyday use of the term average

• a variable’s man is an arithmetic average

• add them up an divide them by how many values there are

what is another way that data and datasets can be described with?

dispersion: variation or spread of cases across its values

• tells us the degree to which observations share the same value or have diverse values

univariate statistics

when we describe one variable at a time