Quantitative and Design Methods in Business
Research
1.Introduction Lecture
After this lecture you should be able to do the following
1. Explain what multivariate analysis is and when its application is
appropriate
2. Define and discuss the specific techniques included in multivariate
analysis
3. Determine which multivariate technique is appropriate for a specific
research problem
4. Discuss the nature of measurement scales and their relationship to
multivariate techniques
5. Describe the conceptual and statistical issues inherent in multivariate
analyses
Multivariate Data Analysis comprises all statistical methods that
simultaneously analyze multiple measurements of each individual or object
under investigation. Multivariate analysis refers to statistical methods
designed to examine relationships among multiple variables at the same
time.
Three key motivations for Multivariate analysis:
Measurement
a. MVA is often used to measure relationships between variables
Explanation & prediction
a. Multivariate methods help uncover patterns that explain
relationships between variables and enable prediction of
outcomes.
Hypothesis testing
a. MVA is used to test hypotheses involving multiple variables
simultaneously
Multivariate Analysis is appropriate where:
1. Complex relationships exist: The data has multiple interrelated
variables, and you want to understand these relationships.
, 2. Dimensionality reduction is needed: High-dimensional datasets
make interpretation challenging, and you need to simplify while
retaining the key information.
3. Prediction models are required: Predicting an outcome using
multiple predictors
4. Categorization or grouping is needed: Identifying natural
groupings or categorizing data based on multiple variables.
Measurement scales in data are fundamental in statistical analysis because
they determine the type of data collected and the appropriate analytical
techniques to apply. There are two types of data, each with their distinct
measuring scales:
1. Nonmetric (qualitative) data: Nonmetric data represent categories
or ranks that describe a characteristic without measuring its
magnitude.
These scales are:
- Nominal scale: Used to label or classify items into
distinct categories. The numbers or labels assigned have
no inherent order or quantitative meaning.
1. Examples: Gender, Eye color, jersey numbers in
sports
2. Properties: No order or rank, Only equality and
distinction can be assessed (e.g., “equal” or “not
equal”.)
- Ordinal scale: Represents data with an inherent order or
ranking, but the intervals between ranks are not
consistent or meaningful.
1. Examples: Rankings in a competition, satisfaction
levels
2. Properties: Indicates order or relative position, does
not quantify “how much” more or less one level is
compared to another.
, 2. Metric (Quantitative) data: Metric data represent measurable
quantities, and the assigned numbers have meaningful mathematical
properties.
These scales are:
- Interval scale: A numerical scale with equal intervals
between values, but without a true zero point. Ratios of
values are not meaningful because zero does not
represent “nothing”.
1. Examples: Temperature, IQ scores
2. Properties: Equal differences between scale points,
no true zero; “zero” is arbitrary.
- Ratio scale: Contains all the properties of an interval
scale, plus a true zero point, allowing meaningful ratios.
1. Example: Weight, height, income, time, distance
2. Properties: Equal intervals between points, a true
zero exists, ratios are meaningful.
Measurement error
All variables are subject to some level of error, which can distort observed
relationships and reduce the effectiveness of multivariate techniques.
Measurement error occurs when the value measured (Xm) deviates from the
true value (Xt) due to the presence of error terms (E): X m=X t + ε
There are two types of error:
1. Random error (ε r): Unpredictable fluctuations that vary in magnitude
and direction, reducing precision but not necessarily introducing bias.
2. Systematic error ( ε s): Consistent inaccuracies that cause a deviation
in a specific direction, introducing bias in the measurements
The expended equation then is: X m=X t + ε r + ε s
To evaluate measurement error, researchers evaluate two critical properties
of measurements:
Reliability:
o Refers to the precision or reproducibility of a measurement.
o A reliable measure produces consistent results when repeated
under the same conditions, indicating minimal random error.
Validity:
, o Refers to the degree to which a measure accurately represents
the concept it is intended to measure.
o A valid measure ensures minimal systematic error, aligning the
measured value closely with the true value.
Reliability is necessary for validity, but reliability does not guarantee validity.
To mitigate the effect of measurement error,
researchers use summated scales. This involves combining multiple
measurements (by summing or averaging them) to form a composite
representation of a concept. The logic is that combining several imperfect
measures can reduce random error, enhancing the reliability of the overall
measure.
Ensuring reliability and validity is essential to:
Strengthen data integrity
Reduce bias in statistical modeling
Enhance the interpretability of results
Statistical significance and power
Statistical significance and power are foundational concepts in hypothesis
testing. They help determine whether the results of a study are meaningful
and provide guidance for designing robust experiments.
Hypothesis testing involves two possible errors:
1. Type I error ():
o Occurs when the null hypothesis ( Η 0) is rejected even though it is
true.
o The probability of a Type I error is denoted by , commonly set at
0.05 (5%), meaning that there is a 5% chance of incorrectly
rejecting Η 0.
2. Type II error ():
o Occurs when the null hypothesis is not rejected, even though it is
false.
o The probability of Type II error is denoted by .
3. Power (1-):
o Refers to the probability of correctly rejecting the null hypothesis
when it is false.
o High power (e.g., 0.80) is desirable, as it means the study is
likely to detect an effect if it exists.
Research
1.Introduction Lecture
After this lecture you should be able to do the following
1. Explain what multivariate analysis is and when its application is
appropriate
2. Define and discuss the specific techniques included in multivariate
analysis
3. Determine which multivariate technique is appropriate for a specific
research problem
4. Discuss the nature of measurement scales and their relationship to
multivariate techniques
5. Describe the conceptual and statistical issues inherent in multivariate
analyses
Multivariate Data Analysis comprises all statistical methods that
simultaneously analyze multiple measurements of each individual or object
under investigation. Multivariate analysis refers to statistical methods
designed to examine relationships among multiple variables at the same
time.
Three key motivations for Multivariate analysis:
Measurement
a. MVA is often used to measure relationships between variables
Explanation & prediction
a. Multivariate methods help uncover patterns that explain
relationships between variables and enable prediction of
outcomes.
Hypothesis testing
a. MVA is used to test hypotheses involving multiple variables
simultaneously
Multivariate Analysis is appropriate where:
1. Complex relationships exist: The data has multiple interrelated
variables, and you want to understand these relationships.
, 2. Dimensionality reduction is needed: High-dimensional datasets
make interpretation challenging, and you need to simplify while
retaining the key information.
3. Prediction models are required: Predicting an outcome using
multiple predictors
4. Categorization or grouping is needed: Identifying natural
groupings or categorizing data based on multiple variables.
Measurement scales in data are fundamental in statistical analysis because
they determine the type of data collected and the appropriate analytical
techniques to apply. There are two types of data, each with their distinct
measuring scales:
1. Nonmetric (qualitative) data: Nonmetric data represent categories
or ranks that describe a characteristic without measuring its
magnitude.
These scales are:
- Nominal scale: Used to label or classify items into
distinct categories. The numbers or labels assigned have
no inherent order or quantitative meaning.
1. Examples: Gender, Eye color, jersey numbers in
sports
2. Properties: No order or rank, Only equality and
distinction can be assessed (e.g., “equal” or “not
equal”.)
- Ordinal scale: Represents data with an inherent order or
ranking, but the intervals between ranks are not
consistent or meaningful.
1. Examples: Rankings in a competition, satisfaction
levels
2. Properties: Indicates order or relative position, does
not quantify “how much” more or less one level is
compared to another.
, 2. Metric (Quantitative) data: Metric data represent measurable
quantities, and the assigned numbers have meaningful mathematical
properties.
These scales are:
- Interval scale: A numerical scale with equal intervals
between values, but without a true zero point. Ratios of
values are not meaningful because zero does not
represent “nothing”.
1. Examples: Temperature, IQ scores
2. Properties: Equal differences between scale points,
no true zero; “zero” is arbitrary.
- Ratio scale: Contains all the properties of an interval
scale, plus a true zero point, allowing meaningful ratios.
1. Example: Weight, height, income, time, distance
2. Properties: Equal intervals between points, a true
zero exists, ratios are meaningful.
Measurement error
All variables are subject to some level of error, which can distort observed
relationships and reduce the effectiveness of multivariate techniques.
Measurement error occurs when the value measured (Xm) deviates from the
true value (Xt) due to the presence of error terms (E): X m=X t + ε
There are two types of error:
1. Random error (ε r): Unpredictable fluctuations that vary in magnitude
and direction, reducing precision but not necessarily introducing bias.
2. Systematic error ( ε s): Consistent inaccuracies that cause a deviation
in a specific direction, introducing bias in the measurements
The expended equation then is: X m=X t + ε r + ε s
To evaluate measurement error, researchers evaluate two critical properties
of measurements:
Reliability:
o Refers to the precision or reproducibility of a measurement.
o A reliable measure produces consistent results when repeated
under the same conditions, indicating minimal random error.
Validity:
, o Refers to the degree to which a measure accurately represents
the concept it is intended to measure.
o A valid measure ensures minimal systematic error, aligning the
measured value closely with the true value.
Reliability is necessary for validity, but reliability does not guarantee validity.
To mitigate the effect of measurement error,
researchers use summated scales. This involves combining multiple
measurements (by summing or averaging them) to form a composite
representation of a concept. The logic is that combining several imperfect
measures can reduce random error, enhancing the reliability of the overall
measure.
Ensuring reliability and validity is essential to:
Strengthen data integrity
Reduce bias in statistical modeling
Enhance the interpretability of results
Statistical significance and power
Statistical significance and power are foundational concepts in hypothesis
testing. They help determine whether the results of a study are meaningful
and provide guidance for designing robust experiments.
Hypothesis testing involves two possible errors:
1. Type I error ():
o Occurs when the null hypothesis ( Η 0) is rejected even though it is
true.
o The probability of a Type I error is denoted by , commonly set at
0.05 (5%), meaning that there is a 5% chance of incorrectly
rejecting Η 0.
2. Type II error ():
o Occurs when the null hypothesis is not rejected, even though it is
false.
o The probability of Type II error is denoted by .
3. Power (1-):
o Refers to the probability of correctly rejecting the null hypothesis
when it is false.
o High power (e.g., 0.80) is desirable, as it means the study is
likely to detect an effect if it exists.
