Chapter 1:
Introduction to Statistics
PowerPoint Lecture Slides
Essentials of Statistics for the Behavioral
Sciences
Tenth Edition
by Frederick J Gravetter, Larry B. Wallnau, and Lori-Ann B. Forzano
Learning Outcomes
1.
2.
3.
4.
5.
Know key statistical terms
Know key measurement terms
Know key research terms
Know the place of statistics in science
Understand summation notation
Math Skills Assessment
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Statistics requires basic math skills
Inadequate basic math skills puts you at risk in
this course
Appendix A, Math Skills Assessment, helps you
determine if you need a skills review
Appendix A, Math Skills Review, provides a quick
refresher course on those areas.
The final Math Skills Assessment identifies your
basic math skills competence
1-1 Statistics and Behavioral
Sciences
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Statistics means “statistical procedures”
Uses of statistics
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Organize and summarize information
Determine exactly what general conclusions are
justified based on the specific results that were
obtained
Goals of statistical procedures
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Accurate and meaningful interpretation
Standardized evaluation procedures
Populations and Samples
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Population
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The set of all the individuals of interest in a
particular study
Vary in size; often quite large
Sample
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A set of individuals selected from a population
Usually intended to represent the population in a
research study
Figure 1.1 The Relationship between a
Population and a Sample
Variables and Data
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Variable
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Data (plural)
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Measurements or observations of a variable
Data set
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Characteristic or condition that changes or has
different values for different individuals
A collection of measurements or observations
A datum (singular)
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A single measurement or observation
Commonly called a score or raw score
Parameters and Statistics
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Parameter
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A value, usually a
numerical value,
that describes a
population
Derived from
measurements of
the individuals in
the population
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Statistic
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A value, usually a
numerical value,
that describes a
sample
Derived from
measurements of
the individuals in
the sample
Descriptive & Inferential
Statistical Methods (1 of 2)
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Descriptive statistics
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Inferential statistics
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Summarize data
Organize data
Simplify data
Familiar examples
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Tables
Graphs
Averages
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Study samples to make
generalizations about
the populations from
which they were
selected
Interpret experimental
data
Common terminology
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“Sampling error”
(“margin of error”)
“Statistically significant”
Descriptive & Inferential
Statistical Methods (2 of 2)
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Sample is never identical to the population
Sampling error
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The discrepancy, or amount of error, that
exists between a sample statistic and the
corresponding population parameter
Example: Margin of error in polls
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“This poll was taken from a sample of registered
voters and has a margin of error of plus or minus 4
percentage points.”
Figure 1.3
The Role of Statistics in Research
FIGURE 1.3
The role of statistics in research.
Learning Check 1 (1 of 2)
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A researcher is interested in the effect of amount of
sleep on high school students’ exam scores. A
group of 75 high school boys agree to participate in
the study. The boys are _____.
A. A statistic
B. A variable
C. A parameter
D. A sample
Learning Check 1– Answer (1 of 2)
•
A researcher is interested in the effect of amount of
sleep on high school students’ exam scores. A
group of 75 high school boys agree to participate in
the study. The boys are _____.
A. A statistic
B. A variable
C. A parameter
D. A sample
Learning Check 1 (2 of 2)
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Decide if each of the following statements
is True or False.
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T/F
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Most research studies data from samples
T/F
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When sample differs from the population there is a
systematic difference between groups
Learning Check 1– Answer (2 of 2)
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True
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Samples used because it is not feasible or possible
to measure all individuals in the population
False
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Sampling error due to random influence may
produce unsystematic group difference
1-2 Observations, Measurement, and
Variables
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Science is empirical—it is based on observation
The scores that make up the data from a research
study are obtained by observing and measuring
variables
The process of measurement consists of applying
carefully defined measurement procedures for
each variable
Constructs & Operational Definitions
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Constructs
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Internal attributes or
characteristics that
cannot be directly
observed
Useful for
describing and
explaining behavior
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Operational definition
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Identifies the set of
operations for
measuring an
external (observable)
behavior
Uses the resulting
measurements as
both a definition and
a measurement of a
hypothetical
construct
Discrete and Continuous
Variables
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Discrete variable
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Has separate, indivisible categories
No values can exist between two neighboring
categories
Continuous variable
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Has an infinite number of possible values between
any two observed values
Is divisible into an infinite number of fractional parts
Figure 1.4
Example: Continuous Measurement
Real Limits of Continuous
Variables
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Real limits are the boundaries of intervals for
scores that are represented on a continuous
number line
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The real limit separating two adjacent scores is
located exactly halfway between the two scores
Each score has two real limits
• The upper real limit marks the top of the interval
• The lower real limit marks the bottom of the interval
Scales of Measurement (1 of 2)
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Measurement assigns individuals or events to
categories
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The categories can be names such as
introvert/extrovert or employed/unemployed
They can be numerical values such as 68 inches or
175 pounds
The categories used to measure a variable make
up a scale of measurement
Relationships between the categories determine
different types of scales
Scales of Measurement (2 of 2)
Scale
Characteristics
Nominal • Label and categorize
Examples
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No quantitative distinctions
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Ordinal
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Categorizes observations
Categories organized by size or
magnitude
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Rank in class
Clothing sizes (S, M, L, XL)
Olympic medals
Interval
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Temperature
IQ
Golf scores (above/below par)
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Ordered categories
Interval between categories
of equal size
Arbitrary or absent zero point
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Ordered categories
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Equal interval between categories •
Absolute zero point
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Ratio
Gender
Diagnosis
Experimental or Control
Number of correct answers
Time to complete task
Gain in height and/or weight since last
year
Learning Check 2 (1 of 2)
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A study assesses the optimal size (number of other
members) for study groups. The variable size of
group is _____.
A. Discrete and interval
B. Continuous and ordinal
C. Discrete and ratio
D. Continuous and interval
Learning Check 2 – Answer (1 of 2)
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A study assesses the optimal size (number of other
members) for study groups. The variable size of
group is _____.
A. Discrete and interval
B. Continuous and ordinal
C. Discrete and ratio
D. Continuous and interval
Learning Check 2 (2 of 2)
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Decide if each of the following statements
is True or False.
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T/F
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Variables that cannot be measured directly cannot
be studied scientifically
T/F
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Research measurements are made using specific
procedures that define constructs
Learning Check 2 – Answer (2 of 2)
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False
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Constructs (interval states) can only be observed
indirectly, but can be operationally measured
True
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Operational definitions assure consistent
measurement and provide construct definitions
1-3 Three Data Structures, Research
Methods, and Statistics
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Data structure 1: descriptive research (individual
variables)
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One (or more) variables measured per individual
Statistics describe the observed variable
May use category and/or numerical variables
Not concerned with relationships between variables
Relationships between Variables
(1 of 3)
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Relationships between variables
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Two (or more) variables are observed and
measured in order to determine a relationship
The resulting measurements can be classified into
two distinct data structures that are used to
determine what type of relationship exists
Relationships between Variables
(2 of 3)
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Data structure 2: the correlational method
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One group of participants
Measurement of two variables for each participant
The goal is to describe type and magnitude of the
relationship
Patterns in the data reveal relationships
Nonexperimental method of study
Figure 1.5 Data Structure 2: One Group with Two
Variables Measured for Each Individual. The
Correlational Method
Limitations of the Correlational
Method
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Can demonstrate the existence of a relationship
between two variables
Does not provide an explanation for the
relationship
Most importantly, does not demonstrate a
cause-and-effect relationship between the two
variables
Relationships between Variables
(3 of 3)
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Data structure 3: experimental and
nonexperimental methods
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Comparing two (or more) groups of scores
One variable defines the groups
Scores are measured on the second variable
Both experimental and nonexperimental studies
use this structure
Figure 1.6 Data Structure 3: Comparing Two (or
More) Groups of Scores. Experimental and
Nonexperimental Methods
The Experimental Method
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The goal of an experimental method
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Manipulation
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To demonstrate a cause-and-effect relationship
between two variables
The level of one variable is determined by the
experimenter
Control rules out influence of other variables
(so-called extraneous variables)
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Participant variables
Environmental variables
Terminology in the Experimental
Method
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Independent variable: the variable that is
manipulated by the researcher
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Independent because no other variable in the study
influences its value; is manipulated prior to
observing the dependent variable
Dependent variable: the one that is observed to
assess the effect of treatment
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Dependent because its value is thought to depend
on the value of the independent variable
Control Conditions in an
Experiment
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Methods of control
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Control condition
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Random assignment of subjects
Matching of subjects
Holding the level of some potentially influential variables
constant
Individuals do not receive the experimental treatment
They either receive no treatment or they receive a neutral,
placebo treatment
Purpose: to provide a baseline for comparison with the
experimental condition
Experimental condition
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Individuals do receive the experimental treatment
Nonexperimental Methods: Nonequivalent
Groups and Pre-Post Studies
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Nonequivalent groups
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Pretest/posttest
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Researcher compares groups of scores
Researcher cannot control who goes into which
group
Individuals measured at two points in time
Researcher cannot control the influence of the
passage of time
Independent variable is quasi-independent
Figure 1.7 Two Examples of
Nonexperimental Studies (1 of 2)
Figure 1.7 Two Examples of
Nonexperimental Studies (2 of 2)
Learning Check 3 (1 of 2)
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Researchers observed that students’ exam scores
were higher the more sleep they had the night
before. This study is _____.
A. Descriptive
B. Experimental comparison of groups
C. Non-experimental group comparison
D. Correlational
Learning Check 3 – Answer (1 of 2)
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Researchers observed that students’ exam scores
were higher the more sleep they had the night
before. This study is _____.
A. Descriptive
B. Experimental comparison of groups
C. Non-experimental group comparison
D. Correlational
Learning Check 3 (2 of 2)
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Decide if each of the following statements
is True or False.
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T/F
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All research methods have an independent variable
T/F
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All research methods can show cause-and-effect
relationships
Learning Check 3 – Answer (2 of 2)
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False
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Correlational methods do not need an independent
variable
False
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Only experiments control the influence of
participants and environmental variables
1-4 Statistical Notation
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Statistics uses operations and notations you have
already learned
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Appendix A has a Mathematical Review
Statistics also uses some specific notation
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Scores are referred to as X (and Y)
N is the number of scores in a population
n is the number of scores in a sample
Summation Notation
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Many statistical procedures involve summing
(adding up) a set of scores
The summation sign Σ stands for summation
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The Σ is always followed by a symbol or equation
that defines what is to be summed
Summation is done after operations in
parentheses, squaring, and multiplication or
division
Summation is done before other addition or
subtraction
Learning Check 4 (1 of 2)
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∑X2 + 47 instructs you to _____.
A. Square each score and add 47 to it, then sum
those numbers
B. Square each score add up the squared scores,
then add 47 to that sum
C. Add 47 to each score, square the result, and
sum those numbers
D. Add up the scores, square that sum, and add
47 to it
Learning Check 4 – Answer (1 of 2)
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∑X2 + 47 instructs you to _____.
A. Square each score and add 47 to it, then sum
those numbers
B. Square each score add up the squared
scores, then add 47 to that sum
C. Add 47 to each score, square the result, and
sum those numbers
D. Add up the scores, square that sum, and add
47 to it
Learning Check 4 (2 of 2)
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Decide if each of the following equations
is True or False
T/F ∑X2 = (∑X)2
T/F (∑X) • (∑X) = (∑X)2
Learning Check 4 – Answer (2 of 2)
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False
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When the operations are performed in a different
order, the results will be different
True
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This is the definition of (∑X)2
Clear Your Doubts, Ask Questions