Statistics: A Tool For Social Research

1
Statistics A Tool ForSocial Research

• Seventh Edition
• Joseph F. Healey

2
Chapter 1

• Introduction

3
Chapter Outline

• Why Study Statistics?
• The Role of Statistics in Scientific Inquiry
• The Goals of This Text
• Descriptive and Inferential Statistics
• Discrete and Continuous Variables
• Level of Measurement

4
In This Presentation

• The role of statistics in the research process
• Statistical applications
• Types of variables

5
The Role Of Statistics

• Statistics are mathematical tools used to
  organize, summarize, and manipulate data.

6
Data

• Scores on variables.
• Information expressed as numbers (quantitatively).

7
Variables

• Traits that can change values from case to case.
• Examples
• Age
• Gender
• Race
• Social class

8
Case

• The entity from which data is gathered.
• Examples
• People
• Groups
• States and nations

9
The Role Of StatisticsExample

• Describe the age of students in this class.
• Identify the following
• Variable
• Data
• Cases
• Appropriate statistics

10
The Role Of Statistics Example

• Variable is age.
• Data is the actual ages (or scores on the
  variable age) 18, 22, 23, etc.
• Cases are the students.

11
The Role Of Statistics Example

• Appropriate statistics include
• average - average age of students in this class
  is 21.7 years.
• percentage - 15 of students are older than 25

12
Statistical Applications

• Two main statistical applications
• Descriptive statistics
• Inferential statistics

13
Descriptive Statistics

• Summarize variables one at a time.
• Summarize the relationship between two or more
  variables.

14
Descriptive Statistics

• Univariate descriptive statistics include
• Percentages, averages, and various charts and
  graphs.
• Example On the average, students are 20.3 years
  of age.

15
Descriptive Statistics

• Bivariate descriptive statistics describe the
  strength and direction of the relationship
  between two variables.
• Example Older students have higher GPAs.

16
Descriptive Statistics

• Multivariate descriptive statistics describe the
  relationships between three or more variables.
• Example Grades increase with age for females but
  not for males.

17
Inferential Statistics

• Generalize from a sample to a population.
• Population includes all cases in which the
  research is interested.
• Samples include carefully chosen subsets of the
  population.

18
Inferential Statistics

• Voter surveys are a common application of
  inferential statistics.
• Several thousand carefully selected voters are
  interviewed about their voting intentions.
• This information is used to estimate the
  intentions of all voters (millions of people).
• Example The Republican candidate will receive
  about 42 of the vote.

19
Types Of Variables

• Variables may be
• Independent or dependent
• Discrete or continuous
• Nominal, ordinal, or interval-ratio

20
Types Of Variables

• In causal relationships
• CAUSE ? EFFECT
• independent variable ? dependent variable

21
Types Of Variables

• Discrete variables are measured in units that
  cannot be subdivided.
• Example Number of children
• Continuous variables are measured in a unit that
  can be subdivided infinitely.
• Example Age

22
Level Of Measurement

• The mathematical quality of the scores of a
  variable.
• Nominal - Scores are labels only, they are not
  numbers.
• Ordinal - Scores have some numerical quality and
  can be ranked.
• Interval-ratio - Scores are numbers.

23
Nominal Level Variables

• Scores are different from each other but cannot
  be treated as numbers.
• Examples
• Gender
• 1 Female, 2 Male
• Race
• 1 White, 2 Black, 3 Hispanic
• Religion
• 1 Protestant, 2 Catholic

24
Ordinal Level Variables

• Scores can be ranked from high to low or from
  more to less.
• Survey items that measure opinions and attitudes
  are typically ordinal.

25
Ordinal Level Variables Example

• Do you agree or disagree that University Health
  Services should offer free contraceptives?
• A student that agreed would be more in favor than
  a student who disagreed.
• If you can distinguish between the scores of the
  variable using terms such as more, less, higher,
  or lower the variable is ordinal.

26
Interval-ratio Variables

• Scores are actual numbers and have a true zero
  point and equal intervals between scores.
• Examples
• Age (in years)
• Income (in dollars)
• Number of children
• A true zero point (0 no children)
• Equal intervals each child adds one unit

27
Level of Measurement

• Different statistics require different
  mathematical operations (ranking, addition,
  square root, etc.)
• The level of measurement of a variable tells us
  which statistics are permissible and appropriate.