Transcript Introduction - University of Western Ontario

Statistics: Introduction
Healey Ch. 1
Outline
The role of statistics in the research
process
 Statistical applications
 Types of variables

The Role Of Statistics

Statistics are mathematical tools
used to organize, summarize, and
manipulate data.
Data
Scores on variables.
 Information expressed as numbers
(quantitatively).

Variables
Concepts in numerical form that can
vary in value
 Traits that can change values from
case to case.
 Examples:
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Age
Gender
Race
Social class
Case
The entity from which data is
gathered.
 Examples

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People
Groups
States and nations
The Role Of Statistics:Example
Describe the age of students in this
class.
 Identify the following:

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Variable
Data
Cases
Appropriate statistics
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.

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

Statistical Applications

Two main statistical applications:
 Descriptive statistics
 Inferential statistics
Descriptive Statistics
Summarize variables one at a time.
 Summarize the relationship between
two or more variables.

Descriptive Statistics

Univariate descriptive statistics
include:

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Percentages, averages, and various charts
and graphs.
Example: On the average, students are 20.3
years of age.
Descriptive Statistics

Bivariate descriptive statistics
describe the strength and direction of
the relationship between two
variables.

Example: Older students have higher GPAs.
Descriptive Statistics

Multivariate descriptive statistics
describe the relationships between
three or more variables.

Example: Grades increase with age for
females but not for males.
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.

Inferential Statistics

Voter surveys are a common
application of inferential statistics.
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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 Conservative candidate will
receive about 42% of the vote.
Types Of Variables

Variables may be:
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Independent or dependent
Discrete or continuous
Nominal, ordinal, or interval-ratio
Types Of Variables

In causal relationships:
CAUSE

EFFECT
independent variable  dependent variable
Independent variables (“causal” or “explanatory”)
are those that are manipulated. Designated as X.
Dependent (“outcome” or “response” variables are
only measured or registered. Designated as Y.
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
Relations Between Variables
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Hypothesis: a statement that describes
the relationship between two or more
variables.
Null hypothesis: What is actually tested in
a statistical test
Alternate hypothesis: The research
hypothesis. “Rejection” of the null builds
up evidence for the research hypothesis
Level Of Measurement

The mathematical quality of the
scores of a variable.
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Nominal - Scores are labels only, they are not
numbers.
Ordinal - Scores have some numerical quality
and can be ranked.
Interval-ratio - Scores are numbers.
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 = Other
 Religion
 1 = Protestant, 2 = Catholic, 3 = Other
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.

Ordinal Level Variables: Example
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“Do you agree or disagree that
University Health Services should
offer free contraceptives?”
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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.
Interval-ratio Variables (see note p. 22)
Scores are actual numbers and have
a true zero point (ratio) and equal
intervals between scores.
 Examples:
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Age (in years)
Income (in dollars)
Number of children
 A true zero point (0 = no children)
 Equal intervals: each child adds one unit
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.

In Class Exercise

Chapter 1: 1.4 a-j and 1.5 a-j.