1. Introduction Chapter 1 SHARON LAWNER WEINBERG SARAH KNAPP ABRAMOWITZ StatisticsSPSS An Integrative Approach SECOND EDITION Using

2. Overview Descriptive and Inferential Statistics Variables and Constants Levels of Measurement Discrete and Continuous Variables The NELS data set SPSS

3. Variables and Constants Variables – Vary from person to person or object to object Constants – Remain constant from person to person or object to object

4. Example A study is conducted to determine if there are gender differences in fine motor skills among five year olds from middle class families. What are the variables in the study? What are the constants in the study? Note: Whether a trait is a constant or a variable is determined by the nature of the particular study. Gender, Fine motor skills Age, Socio-economic status

5. Levels of Measurement Nominal Ordinal Scale Ratio Interval

6. Nominal Objects observed to be similar on some characteristic (e.g., college student) are assigned to the same class or category, while objects observed to be dissimilar on that characteristic are assigned to different classes or categories. (Example: Car types: Toyota, Honda, Volvo, BMW, Audi, etc.)

7. Ordinal The ordinal level of measurement is not only based on observing objects as similar or dissimilar, but also on ordering those observations in terms of an underlying characteristic. (Example: Height in size place ranking)

8. Scale An ordinal level of measurement can be developed into a higher level of measurement if it is possible to assess how near to each other the persons or objects are in the underlying characteristic being observed, that is, if numbers can be assigned in such a way that equal numerical differences along the scale correspond to equal increments in the underlying characteristic. If this is done so that the score 0 corresponds to having none of the property being measured, the level of measurement is ratio. (Example: Distance from home to school) Otherwise, it is interval. (Example: Temperature Scale)

9. Other Examples Find the levels of measurement of the following variables measured on college students: Residence: 1 = College dormitory, 2 = Off campus apartment, 3 = Parents’ home, 4 = Other Whether or not the student’s parents live in the same state as the student’s college Class rank Year graduated high school Number of earned credits to date Height Family Income Number of siblings Nominal or Ordinal Nominal Scale: Interval Ordinal Scale: Ratio

10. Discrete and Continuous Variables A variable is discrete if the values it takes on are integers or can be thought of in some unit of measurement in which they are integers. A variable is continuous if in any unit of measurement, whenever it can take on the values a and b, it can also theoretically take on all the values between a and b.

11. Examples Classify each of the following variables as discrete or continuous: Residence: 1 = College dormitory, 2 = Off campus apartment, 3 = Parents’ home, 4 = Other Whether or not the student’s parents live in the same state as the student’s college Class rank Year graduated high school Number of earned credits to date Height Family Income Number of siblings Continuous Discrete

12. The NELS Data Set The NELS data set was collected by the U.S. Department of Education’s National Center of Education Statistics (NCES). It is a nationally representative longitudinal data set to measure achievement outcomes in four core subject areas (English, history, mathematics, and science), in addition to personal, familial, social, institutional, and cultural factors that might relate to these outcomes.

13. SPSS – The NELS Data Set Recommended setting: Display Variable Names in Alphabetical order – Use Edit/Options Data View versus Variable View The Output Window

14. What is the level of measurement for the following variables from the NELS data set? Twelfth grade math achievement (ACHMAT12). Whether or not the student took advanced math in eighth grade (ADVMAT08). Urbanicity (URBAN). REGION. The number of hours spent on HW in school in twelfth grade (HWKIN12) – Look carefully at the coding! Similar variables are HWKOUT12, LATE12, CUTS12, ABSENT12, EXTRACURR12. Socio-economic status (SES). Rating of teacher interest (TCHRINT). Scale: Interval Nominal Ordinal Nominal or Ordinal