chapter 4: conceptualization and measurement
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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
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