DARYAN VDW Ó
PSYCHOLOGY 253
CHAPTER ONE: INTRODUCTION TO STATISTICS
STATISTICS, SCIENCE AND OBSERVATIONS
Statistics serves two general purposes:
1. Statistics are used to organize and summarize the information so that the
researcher can see what happened in the research study and can
communicate the results to others
2. Statistics help the researcher to answer the question that initiated the
research by determining exactly what general conclusions are justified based
on the specific results that were obtained
Statistics à a set of mathematical procedures for organizing, summarizing, and
interpreting information
Population à is the set of all individuals of interest in a particular study
Sample à is a set of individuals selected from a population, usually intended to
represent the population in research study
The relationship between a population and a sample:
The Population
The results from the sample are The sample is selected
generalized too the population from the population
The Sample
Variable à is a characteristic or condition that changes or has different values for
different individuals
Data (plural) à are measurements or observations
A Data Set à is a collection of measurements or observations
A Datum (singular) à is a single measurement or observation and is commonly called
a Score or Raw score
A Parameter à a value (usually a numerical value) that describes a population,
usually derived from measurements of the individuals in the population.
A Statistic à a vale (usually a numerical value) that describes a sample, usually
derived from measurements of the individual in the sample
Sampling Error à is a naturally occurring discrepancy, or error, that exists between a
sample statistic and the corresponding population parameter
Statistical Methods
Descriptive Statistics à are statistical procedures used to organize, and simplify data
Inferential statistics à consist of techniques that allow us to study samples and then
generalize about the populations from which they were selected
1
, DARYAN VDW Ó
VARIABLES AND MEASUREMENT
Constructs à are internal attributes or characteristics that cannot be directly
observed but are useful for describing and explaining behaviour
Operational Definition à Identifies a measurement procedure (a set of operations)
for measuring an external behaviour and uses the resulting measurements as a
definition and measurement of hypothetical construct
• It describes a set of operations for measuring a construct
• It defines the construct in terms of the resulting measurements
Discrete Variable à consists of separate, indivisible categories. No values can exist
between two neighboring categories
• They are commonly restricted to whole, countable numbers
• May also consists of observations that differ qualitatively
Continuous variable à there are an infinite number of possible values that fall
between any two observed values.
• Is divisible into an infinite number of fractional parts
• When measuring continuous variables two factors apply:
§ It should be very rare to obtain identical measurements for two
different individuals
§ Researchers must first identify a series of measurement categories on
the scale of measurement. However each measurement category is
actually an interval that must have defined boundaries (these boundaries
are called real limits)
Real Limits à are boundaries of intervals for scores that are represented on a
continuous number line.
• The real limit separating two adjacent scores is located exactly halfway between
the scores.
• Each score has two real limits: The Upper real limit is at the top of the interval
and the Lower real limit is at the bottom
SCALES OF MEASUREMENT
• Measurement assigns individuals or events to categories
• The categories can be names, such as male/female or employed/unemployed
or they can be numerical values, such as 68 inches or 175 pounds
• The complete set of categories makes up a scale of measurement
• Relationships between the categories determine different types of scales
Scale Characteristics Examples
Nominal • Consists of a set of categories that have • Gender
different names • Diagnosis
• Label and categorize • Experimental or Control
• No quantitative distinctions
Ordinal • Consist of a set of categories that are • Rank in class
organized in an ordered sequence • Clothing sizes (S,M,L,XL)
• Categorizes observations • Olympic medals
• Categories organized by size or magnitude
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Interval • Ordered categories • Temperature
• Interval between categories • IQ
of equal size • Golf scores (above/below
• Arbitrary or absent zero point par)
Ratio • Ordered categories • Number of correct answers
• Equal interval between categories • Time to complete task
• Absolute zero point • Gain in height since last
year
THREE DATA STRUCTURES, RESEARCH METHODS AND STATISTICS
Data Structure I: Descriptive research (individual variables)
• One (or more) separate variables measured per individual
• “Statistics” describe the observed variable
• May use category and/or numerical variables
Example: three separate variables measured for each individual in a group of students
Individual Number of hours Number of hours Number of hour
exercise in a day sleeping in a day studying in a day
A 2 6 4
B 1 7 3
C 3 4 5
D 4 8 2
Descriptive research/Descriptive research strategy à measuring one or more
separate variables for each individual with the intent of simply describing the individual
variables
Relationships between variables
• Two (or more) variables observed and measured
• The resulting measurements can be classified into two distinct data structures
that also help to classify different research methods and different statistical
techniques
• One of two possible data structures used to determine what type of relationship
exists
Data Structure II: The correlational method
• One group of participants
• Measurement of two variables for each participant
• The researchers then look for consistent patterns in the data to provide
evidence for a relationship between variables
• Goal is to describe type and magnitude of the relationship
• Consistent patterns in the data are easier to see in a graph
• Non-experimental method of study
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, DARYAN VDW Ó
Example: Figure 1.5 Data structures for studies evaluating the relationship between
variables
Correlational Method à two different variables are observed to determine whether
there is a relationship between them
Statistics for Correlational Method
• When the data from a correlational study consist of numerical scores, the
relationship between two variables is measured and described using a statistic
called Correlation
• The measurement process classifies individuals into categories that do not
correspond to numerical values
• This type of data is typically summarized in a table
• The relationship between variables for non-numerical data is shown using a
statistical technique known as Chi-square test (pg. 19 in textbook)
Correlational Method Limitations
• Can demonstrate the existence of a relationship
• Does not provide an explanation for the relationship
• Most importantly, does not demonstrate a cause-and-effect relationship
between the two variables
Data Structure III: Comparing two (or more) groups of scores
• One variable defines the groups
• The relationship between variables is examined by using one of the variables to
define the groups, and then measuring the second variable to obtain scores for
each group
• Both experimental and non-experimental studies use this structure
Statistics for Comparing Two (or more) Groups of Scores
• When the measurement procedure produces numerical scores the statistical
evaluation typically involves computing the average score for each group and
then comparing the averages
4
PSYCHOLOGY 253
CHAPTER ONE: INTRODUCTION TO STATISTICS
STATISTICS, SCIENCE AND OBSERVATIONS
Statistics serves two general purposes:
1. Statistics are used to organize and summarize the information so that the
researcher can see what happened in the research study and can
communicate the results to others
2. Statistics help the researcher to answer the question that initiated the
research by determining exactly what general conclusions are justified based
on the specific results that were obtained
Statistics à a set of mathematical procedures for organizing, summarizing, and
interpreting information
Population à is the set of all individuals of interest in a particular study
Sample à is a set of individuals selected from a population, usually intended to
represent the population in research study
The relationship between a population and a sample:
The Population
The results from the sample are The sample is selected
generalized too the population from the population
The Sample
Variable à is a characteristic or condition that changes or has different values for
different individuals
Data (plural) à are measurements or observations
A Data Set à is a collection of measurements or observations
A Datum (singular) à is a single measurement or observation and is commonly called
a Score or Raw score
A Parameter à a value (usually a numerical value) that describes a population,
usually derived from measurements of the individuals in the population.
A Statistic à a vale (usually a numerical value) that describes a sample, usually
derived from measurements of the individual in the sample
Sampling Error à is a naturally occurring discrepancy, or error, that exists between a
sample statistic and the corresponding population parameter
Statistical Methods
Descriptive Statistics à are statistical procedures used to organize, and simplify data
Inferential statistics à consist of techniques that allow us to study samples and then
generalize about the populations from which they were selected
1
, DARYAN VDW Ó
VARIABLES AND MEASUREMENT
Constructs à are internal attributes or characteristics that cannot be directly
observed but are useful for describing and explaining behaviour
Operational Definition à Identifies a measurement procedure (a set of operations)
for measuring an external behaviour and uses the resulting measurements as a
definition and measurement of hypothetical construct
• It describes a set of operations for measuring a construct
• It defines the construct in terms of the resulting measurements
Discrete Variable à consists of separate, indivisible categories. No values can exist
between two neighboring categories
• They are commonly restricted to whole, countable numbers
• May also consists of observations that differ qualitatively
Continuous variable à there are an infinite number of possible values that fall
between any two observed values.
• Is divisible into an infinite number of fractional parts
• When measuring continuous variables two factors apply:
§ It should be very rare to obtain identical measurements for two
different individuals
§ Researchers must first identify a series of measurement categories on
the scale of measurement. However each measurement category is
actually an interval that must have defined boundaries (these boundaries
are called real limits)
Real Limits à are boundaries of intervals for scores that are represented on a
continuous number line.
• The real limit separating two adjacent scores is located exactly halfway between
the scores.
• Each score has two real limits: The Upper real limit is at the top of the interval
and the Lower real limit is at the bottom
SCALES OF MEASUREMENT
• Measurement assigns individuals or events to categories
• The categories can be names, such as male/female or employed/unemployed
or they can be numerical values, such as 68 inches or 175 pounds
• The complete set of categories makes up a scale of measurement
• Relationships between the categories determine different types of scales
Scale Characteristics Examples
Nominal • Consists of a set of categories that have • Gender
different names • Diagnosis
• Label and categorize • Experimental or Control
• No quantitative distinctions
Ordinal • Consist of a set of categories that are • Rank in class
organized in an ordered sequence • Clothing sizes (S,M,L,XL)
• Categorizes observations • Olympic medals
• Categories organized by size or magnitude
2
, DARYAN VDW Ó
Interval • Ordered categories • Temperature
• Interval between categories • IQ
of equal size • Golf scores (above/below
• Arbitrary or absent zero point par)
Ratio • Ordered categories • Number of correct answers
• Equal interval between categories • Time to complete task
• Absolute zero point • Gain in height since last
year
THREE DATA STRUCTURES, RESEARCH METHODS AND STATISTICS
Data Structure I: Descriptive research (individual variables)
• One (or more) separate variables measured per individual
• “Statistics” describe the observed variable
• May use category and/or numerical variables
Example: three separate variables measured for each individual in a group of students
Individual Number of hours Number of hours Number of hour
exercise in a day sleeping in a day studying in a day
A 2 6 4
B 1 7 3
C 3 4 5
D 4 8 2
Descriptive research/Descriptive research strategy à measuring one or more
separate variables for each individual with the intent of simply describing the individual
variables
Relationships between variables
• Two (or more) variables observed and measured
• The resulting measurements can be classified into two distinct data structures
that also help to classify different research methods and different statistical
techniques
• One of two possible data structures used to determine what type of relationship
exists
Data Structure II: The correlational method
• One group of participants
• Measurement of two variables for each participant
• The researchers then look for consistent patterns in the data to provide
evidence for a relationship between variables
• Goal is to describe type and magnitude of the relationship
• Consistent patterns in the data are easier to see in a graph
• Non-experimental method of study
3
, DARYAN VDW Ó
Example: Figure 1.5 Data structures for studies evaluating the relationship between
variables
Correlational Method à two different variables are observed to determine whether
there is a relationship between them
Statistics for Correlational Method
• When the data from a correlational study consist of numerical scores, the
relationship between two variables is measured and described using a statistic
called Correlation
• The measurement process classifies individuals into categories that do not
correspond to numerical values
• This type of data is typically summarized in a table
• The relationship between variables for non-numerical data is shown using a
statistical technique known as Chi-square test (pg. 19 in textbook)
Correlational Method Limitations
• Can demonstrate the existence of a relationship
• Does not provide an explanation for the relationship
• Most importantly, does not demonstrate a cause-and-effect relationship
between the two variables
Data Structure III: Comparing two (or more) groups of scores
• One variable defines the groups
• The relationship between variables is examined by using one of the variables to
define the groups, and then measuring the second variable to obtain scores for
each group
• Both experimental and non-experimental studies use this structure
Statistics for Comparing Two (or more) Groups of Scores
• When the measurement procedure produces numerical scores the statistical
evaluation typically involves computing the average score for each group and
then comparing the averages
4
