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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 If are not ordered 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) 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. Feminist Attitude index = 30 (highest score possible) Feminist Attitude index = 5 (lowest score possible) 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 RATIO STRONGEST INTERVAL ORDINAL NOMINAL WEAKEST