Chapter 4: Conceptualization and Measurement

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 • Variables of this type are called scalar or index variables • They provide a scale or index that allows us to measure between levels. • We can not only measure which is higher or lower, but how much so. • Distance is 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 is same as distance from 70-80 degrees • A variety of statistical analysis can be done on these data sets • For example, central tendency can be measured by mode, median, or mean • Standard deviation can be calculated • But we cannot calculate ratios

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 forthe 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. Feminist Attitude index = 5 (lowest score possible) Feminist Attitude index = 30 (highest score possible)

Ratio Level Measurement • Similar to interval level • Can measure distancebetween two points • Butcan 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 RATIO STRONGEST INTERVAL ORDINAL NOMINAL WEAKEST

Chapter 4: Conceptualization and Measurement