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Variables - characteristics of a population or sample where the observations (individuals or things) differ from one another Examples: 1. In a population of students, one may differ in gender, age, intelligence and opinion toward a political issue from another.

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In Example 1, the variables are gender, age (in years), Intelligence Quotient (IQ), and opinion toward a political issue. 2. In a sample of patients, one may differ in blood type, blood sugar level, Body Mass Index (BMI), risk of contracting a disease

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Classifications of variable: Quantitative or Qualitative variables 1. Quantitative variable (Numerical) - values are expressed in numbers - Expressed differences in values among observations along a continuum of amounts that run from high to low - can be further classified either a continuous or discrete variable

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a. Continuous Variable - may take any value within a defined range; possible values of a continuous variable are intervals on the number line Examples: 1. The variable Car’s Fuel Efficiency can have the measurements 27.0, 27.13, 27.12, or 29.8, in miles per gallon (mpg)

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2. The variable Length of Time in a Reading Test can have the measurements 35.2, 23.1, 25.0, 20.4, 15.6 (minutes) 3. The variable Weight of Sacks of Rice labeled with a net weight of 50 kilos can have the measurements 50.0 49.8, 49.5, 50.1, 49.6, 48.9 (kilos)

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b. Discrete Variable - can take specific values only - possible values are isolated points on the number line Examples: 1. The variable Size of a Family may consists of 1, 2, 3, or more children. 2. The variable Number of Telephone Calls to a Drug Hotline in 24-hour period may have values such as 3, 4, 3, 0, 6, 2, 0, 0, 1, 2 calls per hour.

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3.The variable Number of Classes a Student is Registered in a semester can have values such as 4, 5, 6, 7, 8 classes. 2. Qualitative variable - levels are expressed in categories - expressed as nonnumeric differences in the categories or responses among observations in a population or sample

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Examples of Qualitative Variables: 1. The Gender of a student in a sample of 50 applicants for a scholarship. Its levels are either “Male” or “Female”. Numeric values such as 1 for Male and 2 for Female are substituted for coding and identification purposes 2. Opinion on Abortion Policy is a qualitative variable. Its levels maybe “Strongly Disagree”, “Disagree”, “Undecided”, “Agree” and “Strongly Agree”

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3. Taste-Test on a new brand fruit juice is a variable. Its levels maybe “Excellent”, Good”, “Fair” or “Poor” Kinds of Variables 1.Independent variable 2.Dependent variable

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1. Independent Variable (Predictor Variable) - manipulated or changed by the experimenter to make the outcome (dependent variable) varies or differs expected or hypothesized to bring about a change in the dependent variable 2. Dependent Variable (Response Variable) - observed variable whose values are results of the effects of the different levels of the independent variable (outcome variable)

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Examples: 1.There is a relationship between two variables, Height (Independent Variable) and Weight (Dependent Variable) 2. There is an effect of high and low levels of teacher enthusiasm (independent variable) upon student attention (dependent variable)

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3. Exercise is thought to have an effect on anxiety. The independent variable is Exercise and the dependent variable is Anxiety.

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Section 2.1 ~ Data Types and Levels of Measurement

Section 2.1 ~ Data Types and Levels of Measurement

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