Basic Social Statistics-Lecture01-Sociology, Study notes of Social Statistics and Data Analysis

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Professor: David Knoke

Teaching Assistants: Kyungmin Baek

Yu-Ju Chien

Jasmine Harris

Department of Sociology

SPRING 2011

SOC 3811

BASIC SOCIAL STATISTICS

Chapter 1

The Social Research Process

1.1 Ideas into Research Projects

1.2 Concepts in Propositions

1.3 Variables into Hypotheses

1.4 Observations into Records

1.5 Data into Numbers

1.6 Statistical Analysis

1.7 The General Linear Model

TYPES OF VARIABLES

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 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

Identify These Variables’ Types

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)

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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.

Statistical Significance

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).

The General Linear Model

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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