1. Chapter 4: Conceptualization and Measurement

2. 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
From Text:
{T}here are many ways of collecting information, or different operations for gathering data: asking questions, using previously gathered data, analyzing texts, and so on. Some of this data contains mathematically detailed information; it represents a higher level of measurement.

3. Levels of Measurement Quantitative levels of measurement: Ordinal
Interval
Ratio
Progressively more precise mathematically

4. 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

5. Examples of Nominal Measures

6. 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
From Text:
The first of the three quantitative levels is the ordinal level of measurement. At this level, you specify only the order of the cases, in “greater than” and “less than” distinctions. At the coffee shop, for example, you might choose between a small, medium, or large cup of decaf—that’s ordinal measurement.
The small might be an 8 oz. cup. The medium might have 12 oz., and the large might have 20 oz. The intervals separating the sizes of cups of coffee are not equal, but they can be ordered.

7. 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?

8. Example: Ordinal Measures

9. 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
This level of measurement is represented by the difference between two Fahrenheit temperatures. Note, for example, that 60 degrees is 30 degrees higher than 30 degrees; but 60 is not “twice as hot” as 30. Why not? Because heat does not “begin” at 0 degrees on the Fahrenheit scale.

10. Example: Interval Measures
When distance between attributes has meaning, for example, temperature (in Fahrenheit) –
Distance from degrees = Distance from 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

11. Index of feminist attitudes
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.
Do you agree or disagree with the following statements?
(SD =1, D=2, N=3, A=4, SA=5)
A woman should have the same job opportunities as a man.
Men should respect women more than they currently do.
America should pass the Equal Rights Amendment.
Women should be considered as seriously as men as candidates for the Presidency of the United States.
Doctors need to take women's health concerns more seriously.
Women have been treated unfairly on the basis of their gender throughout most of human history.
If an index was calculated from answers to six questions that measured one’s feminist attitude, and the lowest score for each question was 1, Strongly Disagree, and the highest was 5, Strongly Agree, then the lowest possible score on the index would be 5 and the highest possible score would be 30.
It’s important to recognize that many social scientists consider indices to be only ordinal measures, even though they are often treated as though they were interval level, by conducting correlation or regression analyses with them.
Feminist Attitude index = 30 (highest score possible)
Feminist Attitude index = 5 (lowest score possible)

12. 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

13. 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.

14. 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

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

16. Measurement Hierarchy
RATIO
STRONGEST
INTERVAL
ORDINAL
NOMINAL
WEAKEST