IntroductionIntroductionChapter 1Chapter 1

SHARON LAWNER WEINBERG SARAH KNAPP ABRAMOWITZ

StatisticStatisticss

SPSSSPSSAn Integrative Approach

SECOND EDITION

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OverviewOverview

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

Variables and ConstantsVariables and Constants

Variables – Vary from person to person or object to object

Constants – Remain constant from person to person or object to object

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

Levels of MeasurementLevels of Measurement

•Nominal

•Ordinal

•Scale• Ratio

• Interval

NominalNominal

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.)

OrdinalOrdinal

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)

ScaleScaleAn 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)

Other ExamplesOther ExamplesFind 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

Scale: Ratio

Scale: Ratio

Scale: Ratio

Discrete and Continuous VariablesDiscrete 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.

ExamplesExamplesClassify 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

Discrete

Discrete

Discrete

Discrete

Discrete

Discrete

The NELS Data SetThe 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.

SPSS – The NELS Data SetSPSS – The NELS Data Set• Recommended setting: Display Variable Names in

Alphabetical order – Use Edit/Options

• Data View versus Variable View

• The Output Window

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

Scale: Interval

Scale: Interval

Nominal

Ordinal

Ordinal

Nominal or Ordinal