Sociology 2205A/B Chapter Notes - Chapter 1-4: Univariate, Unimodality, Skewness
9 May 2018
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Stats 2205A Midterm Saturday, October 21, 2017
1pm-3pm SSC 3024
Part 1 of Textbook
- 63 M/C
- 18 T/F
Chapter 1
Summary
- In social research, the purpose of statistics is to organize, manipulate and analyze data so
researchers can test their theories and answer their questions. Statistics are a basic tool by
which social scientists attempt to enhance their understanding of the social world.
- Two classes of statistics:
o Descriptive – used to summarize the distribution of a single variable and the
relationships between two or more variables.
o Inferential statistics – provide us with techniques by which we can generalize to
populations from random samples.
- Two basic guidelines for selecting statistical techniques – discrete or continuous, measured at
any of three levels:
o Nominal – compare category sizes
o Ordinal – categories & cases can be ranked
o Interval-Ratio – all mathematical operations are permitted
o Variables at nominal/ordinal levels are almost always discrete
Terms
- Continuous Variable: A variable with a unit of measurement that can be subdivided infinitely.
- Data: Any information collected as part of a research project and expressed as numbers.
- Data Reduction: Summarizing many scores with a few statistics. A major goal of descriptive
statistics.
- Dependent Variable: A variable that is identified as an effect, result, or outcome variable. The
dependent variable is thought to be caused by the independent variable.
- Descriptive Statistics: The branch of statistics concerned with (1) summarizing the distribution
of a single variable or (2) measuring the relationship between 2 or more variables.
- Discrete Variable: A variable with a basic unit of measurement that cannot be subdivided.
- Hypothesis: A statement about the relationship between variables that is derived from a
theory. Hypotheses are more specific than theories, and all terms and concepts are fully
defined.
- Independent Variable: A variable that is identified as a causal variable. The independent
variable is thought to cause the dependent variable.
- Inferential Statistics: The branch of statistics concerned with making generalizations from
samples to populations.
- Level of Measurement: The mathematical characteristic of a variable and the major criterion for
selecting statistical techniques. Variables can be measured at any of three levels, each
permitting certain mathematical operations and statistical techniques.
- Measures of Association: Statistics that summarize the strength and direction of the
relationship between variables.
- Population: The total collection of all cases in which the researcher is interested.
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Stats 2205A Midterm Saturday, October 21, 2017
1pm-3pm SSC 3024
- Research: Any process of gathering information systematically and carefully to answer
questions or test theories. Statistics are useful for research projects in which the information is
represented in numerical form or as data.
- Sample: A carefully chosen subset of a population. In inferential statistics, information is
gathered from a sample and then generalized to a population.
- Statistics: A set of mathematical techniques for organizing and analyzing data.
- Theory: A generalized explanation of the relationship between two or more variables.
- Variable: An trait that can change values from case to case.
Concepts
- The Wheel of Science
o Walter Wallace
o How the knowledge base of any scientific enterprise grows and develops.
o Scientific theory & research continuously shape each other
o Theory
▪ Explains relationships between phenomena
▪ People wonder things about society and attempt to understand things by coming
up with explanations
▪ Informal theorizing – everyday explanations of social phenomena
▪ Ex. Materialistic theory
• Health is affected by social class
• Individual choices (exercise, getting a flu shot) are constrained by social
class
• Independent Variable: Social Class
• Dependent Variable: Health
o Hypothesis
▪ Derived from theory, but more specific
▪ Definitions develop, hypothesis takes shape, decide how to gather data
▪ Plans lead to observations
▪ Clear idea of direction of research
o Observations
▪ Organize and analyze information
Theory
Hypothesis
Observations
Empirical
Generalizations
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Stats 2205A Midterm Saturday, October 21, 2017
1pm-3pm SSC 3024
▪ Statistics will provide ideas on what to do with the data
o Empirical Generalization
▪ Look for trends in the data
▪ Address theory
▪ Theory could be changed after addressing observations
• Design a new research project
- Descriptive & Inferential Statistics
o Descriptive Statistics are relevant in certain situations:
▪ When the researcher needs to summarize or describe the distribution of a single
variable (univariate descriptive statistics).
• Goal is data reduction
▪ When the researcher wants to describe the relationship between two or more
variables (bivariate or multivariate descriptive statistics).
• Measures of association
• Ability to investigate causation & prediction
o Inferential Statistics are relevant when the goal is to generalize findings from a sample
to a population.
▪ Uses information from a sample to make inferences about the population
o The divide between inferential and descriptive statistics:
▪ Descriptive
• Univariate
o Frequencies and graphs
o Measures of central tendency and dispersion
o Z-scores, normal curve
• Bivariate
o Bivariate tables
o Measures of association
o Regression and correlation
• Multivariate
o Multiple regression, partial correlation
▪ Inferential
• Estimation
• Hypothesis testing
o One-sample test
o Two-sample test
o Analysis of variance
o Chi square test
o ***ONLY FOCUS ON DESCRIPTIVE UNIVARIATE
- Levels of Measurement: mathematical nature of the variables under consideration, helps to
decide selection of statistics
o Nominal
▪ Classify observations into scores or categories
▪ Ex. Gender, area code, province of residence, religious affiliation, etc.
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Document Summary
In social research, the purpose of statistics is to organize, manipulate and analyze data so researchers can test their theories and answer their questions. Statistics are a basic tool by which social scientists attempt to enhance their understanding of the social world. Two classes of statistics: descriptive used to summarize the distribution of a single variable and the relationships between two or more variables. Inferential statistics provide us with techniques by which we can generalize to populations from random samples. Two basic guidelines for selecting statistical techniques discrete or continuous, measured at any of three levels: nominal compare category sizes, ordinal categories & cases can be ranked. Interval-ratio all mathematical operations are permitted: variables at nominal/ordinal levels are almost always discrete. Continuous variable: a variable with a unit of measurement that can be subdivided infinitely. Data: any information collected as part of a research project and expressed as numbers. Data reduction: summarizing many scores with a few statistics.
