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Any characteristic or attribute of persons, objects, or events that can take on different numerical values. Social Research, Types of Variables, Discrete Variables, Dichotomous variable, Continuous variable, Descriptive vs. Inferential Stats, random sampling, General linear model, General Social Surveys, Basic Social Statistics, Lecture Slides, Sociology, David Knoke, Minnesota State University (MN), United States of America (USA)
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Variable: Any characteristic or attribute of persons, objects, or events that can take on different numerical values
To test a research hypothesis, choose a test statistic that is appropriate for a specific type of variable
A Typology of Variables Nonorderable Variables Orderable Variables Discrete Discrete Polychotomous (many categories) Polychotomous (many categories) Dichotomous (2 categories) Dichotomous (2 categories) Continuous
No nonorderable continuous variables!
Discrete variable: classifies persons, objects, or events according to the kind or quality of their attributes
Discrete variables may have many categories (polychotomous) or only two (dichotomous)
Nonorderable discrete: the sequence of categories cannot be meaningfully ordered Eye color: black, blue, brown, green, grey, purple, … Nationality: Indonesian, Iraki, Iranian, Japanese, Kenyan, … Music: blues, classical, country, hip hop, jazz, rap, rock, …
Orderable discrete: the sequence of categories can be meaningfully ordered (numbers show low-high sequence) Life-stage: infant, toddler, child, adolescent, young adult, ... Social class: lower, working, middle, upper Company size: small, medium, large, very large Attitude: strongly disagree, disagree, agree, strongly agree
Continuous variable: a variable that, in theory, can take on all possible numerical values in a given interval Ideally, precise intervals (distances) should be measured, as in the natural sciences. In practice, social variables usually allow only a limited number of values on a underlying continuous scale.
How many total categories for each continuous variable? Education: 0, 1, 2, 3, …. 20 years of schooling Age: 1, 2, 3, 4, 5, 6, …. 125 years old Annual Income: <$500; $501-999; $1,000-1,999; $2,000-2,999, … Pres. Obama’s job rating: Poor, good, fair, excellent Attitude: Strongly disagree, Disagree, Agree, Strongly agree
Reasonable people may disagree on whether the last two examples are discrete orderable or continuous variables. How about you?
We should feel comfortable in treating a variable as continuous only if a statistical test we apply is robust: it’s insensitive to small departures from assumptions on which it depends; e.g., continuous measurement
Classify the following. Keep in mind that a variable’s type may be ambiguous, reflecting imprecision of social measurements:
Class Role: (Instructor, TA, Student)
Desserts Eaten: (None, One, Two, ….)
Social Class: (Lower, Working, Middle, Upper)
Textbook Price: (dollars and cents)
Religion: (Christian, Nonchristian)
Marital Status: (Single, Married, Widowed)
Residential Area: (ZIP code)
Population growth: (Down, Unchanged, Up)
Workplace Accidents: (Number of injuries)
Industrialization: (Pre-industrial, Industrial)
Inferential statistics apply the mathematical theory of probability to make decisions about the likely properties of populations based on the sample evidence
The Gallup Poll stated that the “margin of error is ±3%” (plus or minus three percent) around the respondents’ responses to the item. What does this phrase mean?
The t-test, an inferential statistic that you will learn, allows us to infer (make conclusions or generalize) about the probable value of the population parameter.
The American public had a 95% “confidence interval,” from 45% to 51%, in approving Pres. Obama’s job.
A statistical significance test allows us to make a statement about the probability that a population with a hypothesized parameter value could have produced the observed value of a sample statistic.
When random sampling assures us of a sample that highly represents the population, then we can make inferences about likely population parameters with a high level of confidence (but not with complete certainty).
General linear model: assumes the relationships among independent and dependent measures basically vary according to straight line patterns
The regression line in the figure on next slide shows that, as respondents’ years of formal education increase, expected occupational prestige scores increase in a linear pattern.
We’ll learn how to program the computer to calculate and graph the “best-fitting line” through a scatterplot showing the relationship between two variables.
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