Quantitative Design & methodology
Lecture 1 - Introduction
Basic concepts of multivariate data analysis
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 analysis
Multivariate Data Analysis comprises all statistical methods that simultaneously
analyze multiple measurements on each individual or object under investigation.
Motivation:
- Measurement
- Explanation & Prediction
- Hypothesis testing
Basic concepts
- Measurement scales
o Nonmetric
o Metric
- Measurement and measurement error
- Statistical inference
- Types of techniques
Types of Data and Measurement Scales
,Measurement Scales
– Nonmetric
o Nominal – size of number is not related to the amount of the
characteristic being measured
o Ordinal – larger numbers indicate more (or less) of the characteristic
measured, but not how much more (or less).
– Metric
o Interval – contains ordinal properties, and in addition, there are equal
differences between scale points.
o Ratio – contains interval scale properties, and in addition, there is a
natural zero point.
The level of measurement is critical in determining the appropriate multivariate
technique to use!
Measurement error
– All variables have some error.
– Measurement error = distorts observed relationships and makes multivariate
techniques less powerful.
– Researchers use summated scales, for which several variables are summed or
averaged together to form a composite representation of a concept.
In addressing measurement error, researchers evaluate two important characteristics
of measurement:
– Reliability: the observed variable’s degree ofprecision (reproducibility of results)
and thus the lack of random measurement error.
– Validity: the degree to which a measure accurately represents what it is
supposed to
Statistical Significance and Power
– Type I error, or α, is the probability of rejecting the null hypothesis when it is true.
– Type II error, or β, is the probability of failing to reject the null hypothesis when it
is false.
– Power, or 1-β, is the probability of rejecting the null hypothesis when it is false.
, – Effect size: the actual magnitude of the effect of interest (e.g., the difference
between means or the correlation between variables).
– Alpha (α): as α is set at smaller levels, power decreases. Typically, α = .05.
– Sample size: as sample size increases, power increases. With very large sample
sizes, even very small effects can be statistically significant, raising the issue of
practical significance vs. statistical significance.
Statistical Power Analysis
– Researchers should design the study to achieve a power level of .80 at the
desired significance level.
– More stringent significance levels (e.g., .01 instead of .05) require larger samples
to achieve the desired power level.
– Conversely, power can be increased by choosing a less stringent alpha level
(e.g., .10 instead of .05).
– Smaller effect sizes always require larger sample sizes to achieve the desired
power.
– Any increase in power is most likely achieved by increased sample size.
Types of multivariate techniques
Dependence techniques:
A variable or set of variables is identified as the dependent variable to be predicted or
explained by other variables known as independent variables.
Examples:
– Multiple regression*
– Logistic Regression
– Analysis of Variance (ANOVA) and Covariance (ANCOVA)*
– Conjoint Analysis
– Canonical Correlation
Structural Equation Modeling (SEM)* *Covered in this course
, Interdependence techniques:
They involve the simultaneous analysis of all variables in the set, without distinction
between dependent variables and independent variables.
Examples:
– Exploratory factor analysis*
– Principal component analysis*
– Cluster analysis
– Multidimensional scaling (perceptual mapping)
– Correspondence analysis *Covered in this course
Selecting a multivariate technique
What type of relationship is being examined – dependence or interdependence?
– Dependence relationship: How many variables are being predicted?
• What is the measurement scale of the dependent variable?
• What is the measurement scale of the predictor variable?
– Interdependence relationship: Are you examining relationships between
variables, respondents, or objects?
Factor analysis
Factor analysis analyzes the structure of
the interrelationships among a large
number of variables to determine a set of
common underlying dimensions (factors).
Multiple regression analysis
A single metric dependent variable is predicted by
several metric independent
variables.
Lecture 1 - Introduction
Basic concepts of multivariate data analysis
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 analysis
Multivariate Data Analysis comprises all statistical methods that simultaneously
analyze multiple measurements on each individual or object under investigation.
Motivation:
- Measurement
- Explanation & Prediction
- Hypothesis testing
Basic concepts
- Measurement scales
o Nonmetric
o Metric
- Measurement and measurement error
- Statistical inference
- Types of techniques
Types of Data and Measurement Scales
,Measurement Scales
– Nonmetric
o Nominal – size of number is not related to the amount of the
characteristic being measured
o Ordinal – larger numbers indicate more (or less) of the characteristic
measured, but not how much more (or less).
– Metric
o Interval – contains ordinal properties, and in addition, there are equal
differences between scale points.
o Ratio – contains interval scale properties, and in addition, there is a
natural zero point.
The level of measurement is critical in determining the appropriate multivariate
technique to use!
Measurement error
– All variables have some error.
– Measurement error = distorts observed relationships and makes multivariate
techniques less powerful.
– Researchers use summated scales, for which several variables are summed or
averaged together to form a composite representation of a concept.
In addressing measurement error, researchers evaluate two important characteristics
of measurement:
– Reliability: the observed variable’s degree ofprecision (reproducibility of results)
and thus the lack of random measurement error.
– Validity: the degree to which a measure accurately represents what it is
supposed to
Statistical Significance and Power
– Type I error, or α, is the probability of rejecting the null hypothesis when it is true.
– Type II error, or β, is the probability of failing to reject the null hypothesis when it
is false.
– Power, or 1-β, is the probability of rejecting the null hypothesis when it is false.
, – Effect size: the actual magnitude of the effect of interest (e.g., the difference
between means or the correlation between variables).
– Alpha (α): as α is set at smaller levels, power decreases. Typically, α = .05.
– Sample size: as sample size increases, power increases. With very large sample
sizes, even very small effects can be statistically significant, raising the issue of
practical significance vs. statistical significance.
Statistical Power Analysis
– Researchers should design the study to achieve a power level of .80 at the
desired significance level.
– More stringent significance levels (e.g., .01 instead of .05) require larger samples
to achieve the desired power level.
– Conversely, power can be increased by choosing a less stringent alpha level
(e.g., .10 instead of .05).
– Smaller effect sizes always require larger sample sizes to achieve the desired
power.
– Any increase in power is most likely achieved by increased sample size.
Types of multivariate techniques
Dependence techniques:
A variable or set of variables is identified as the dependent variable to be predicted or
explained by other variables known as independent variables.
Examples:
– Multiple regression*
– Logistic Regression
– Analysis of Variance (ANOVA) and Covariance (ANCOVA)*
– Conjoint Analysis
– Canonical Correlation
Structural Equation Modeling (SEM)* *Covered in this course
, Interdependence techniques:
They involve the simultaneous analysis of all variables in the set, without distinction
between dependent variables and independent variables.
Examples:
– Exploratory factor analysis*
– Principal component analysis*
– Cluster analysis
– Multidimensional scaling (perceptual mapping)
– Correspondence analysis *Covered in this course
Selecting a multivariate technique
What type of relationship is being examined – dependence or interdependence?
– Dependence relationship: How many variables are being predicted?
• What is the measurement scale of the dependent variable?
• What is the measurement scale of the predictor variable?
– Interdependence relationship: Are you examining relationships between
variables, respondents, or objects?
Factor analysis
Factor analysis analyzes the structure of
the interrelationships among a large
number of variables to determine a set of
common underlying dimensions (factors).
Multiple regression analysis
A single metric dependent variable is predicted by
several metric independent
variables.
