Chapter 4: Conceptualization and Measurement

Levels of Measurement

• Level of Measurement=Mathematical precision with which values of a variable can be expressed.

• Nominal level of measurement:• Qualitative• No mathematical interpretation

Levels of Measurement

Quantitative levels of measurement: Ordinal Interval Ratio

Progressively more precise mathematically

Nominal Measures (Labels)

Identifies variables whose values have no mathematical interpretation

Categories are not ordered

If only two categories:Referred to as a dichotomous or “Dummy” variable

Examples of Nominal Measures

Ordinal Measures

Categorical--Some categories are higher than others.

For example: Income tax brackets Social class Levels of education

Cannot measure the distance between categories, only which is higher or lower Cannot say that someone is twice as educated as

someone else Can be used as a dependent variable

Example: Ordinal Measures

When attributes can be rank-ordered… Distances between attributes do not have any meaning For example : code Educational Attainment as

0=less than H.S. 1=some H.S. 2=H.S. degree 3=some college 4=college degree 5=post college

Is the distance from 0 to 1 the same as 3 to 4?

Example: Ordinal Measures

Interval Measures

Called scalar or index variables Provide scale or index to measure between

levels Can measure which is higher or lower and how

much Measured between points on a scale with even

units Example: Temperature in Fahrenheit or

Celsius

Example: Interval Measures

When distance between attributes has meaning, for example, temperature (in Fahrenheit) –

Distance from 30-40 degrees = Distance from 70-80 degrees

Variety of statistical analysis For example, central tendency can be measured

by mode, median, or mean Standard deviation can be calculated

Cannot calculate ratios

Index of feminist attitudes

Feminist Attitude index = 30 (highest score possible)

Feminist Attitude index = 5 (lowest score possible)

Do you agree or disagree with the following statements?(SD =1, D=2, N=3, A=4, SA=5)1. A woman should have the same job opportunities as a man.2. Men should respect women more than they currently do. 3. America should pass the Equal Rights Amendment. 4. Women should be considered as seriously as men as candidates for

the Presidency of the United States. 5. Doctors need to take women's health concerns more seriously. 6. Women have been treated unfairly on the basis of their gender

throughout most of human history.

Two women were asked a series of questions. Their answers were compiled, and an index of their feminist attitudes calculated, but the index had no absolute zero. Still, their scores could be compared.

Ratio Level Measurement Similar to interval level

Can measure distance between two points But can do so in absolute terms

Ratio measures have a true zero (unlike interval measures) Example, can say that someone is twice

as rich as someone else based on the value of their assets.

To have no money is based on a starting point of zero

Ratio Level Measurement Has an absolute zero that is meaningful

Can construct a meaningful ratio (fraction), for example, number of clients in past six months

It is meaningful to say that “...we had twice as many clients in this period as we did in the previous six months.

Ratio Level Measurement

Ratio scales are the ultimate when it comes to measurement scales

They tell us about the order They tell us the exact value between units

AND they also have an absolute zero–which allows for a wide range of both descriptive and inferential statistics

Types of Comparisons That Can Be Made With Different Levels of Measurement

Measurement Hierarchy

NOMINAL

ORDINAL

INTERVAL

RATIO

WEAKEST

STRONGEST