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Quantitative and Design Methods in Business ResearchTable of contents
Factor analysis ...............................................................................................................................................2
Lecture 1 Introduction.........................................................................................................................................2
Design & behavioral research ............................................................................................................................4
Lecture 2 Principal Component Analysis and Exploratory Factor Analysis ......................................................5
Discussion Factor Analysis.................................................................................................................................8
Regression Analysis .......................................................................................................................................8
Guest lecture .......................................................................................................................................................8
Lecture regression analysis ...............................................................................................................................10
Discussion Regression Analysis ........................................................................................................................13
ANOVA ........................................................................................................................................................13
Lecture ANOVA (Analysis of CoVariance) ........................................................................................................13
Structural Equation Modeling .....................................................................................................................16
Lecture SEM .....................................................................................................................................................16
1
,Factor analysis
Lecture 1 Introduction
Multivariate data analysis comprises all statistical methods that simultaneously analyze
multiple measurements on each individual or object under investigation. Motivation for using
this are measurement, explanation and prediction, and hypothesis testing.
Basic concepts are measurement scales (nonmetric and metric),
measurement and measurement error, statistical inference and
types of techniques.
Measurement scales:
• Nonmetric measures qualitative characteristics of variables
o Nominal: size of number is not related to the
amount of the characteristic being measured
§ Gender, colour
o Ordinal: larger numbers indicate more (or less) of
the characteristics measured, but not how much
more (or less)
§ Type of residence, category of vehicle
• Metric measures quantitative characteristics or variables
o Interval: contains ordinal properties, and in addition, there are equal
differences between scale points
§ Temperature in Celcius, IQ scale
o Ratio: contains interval scale properties, and
in addition, there is a natural zero point
§ Body height, monthly income
Measurement error distorts observed relationships and makes
multivariate techniques less powerful. All variables have some error.
Researchers have summated scales, for which several variables are
summed or averaged together to form a composite representation of a
concept. The higher the measurement error, the smaller the beta.
In addressing measurement error, researchers evaluate two important
characteristics of measurement:
• Reliability: the observed variable’s degree of precision
(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 1 error, or alfa, is the probability of rejecting
the null hypothesis when it is true. Null hypothesis
is usually that there is no effect. Severe in
management studies because you could lose money
if you invest while there is no effect.
• Type 2 error, or beta, is the probability of failing to reject the null hypothesis when it
is false. You miss an effect, less severe in management studies because you do not lose
money.
2
, • Power, or 1-beta, is the probability of rejecting the null hypothesis when it is false.
Power is the probability that a test of significance will detect a deviation from the null
hypothesis, should such a deviation exist.
• Effect size: the actual magnitude of the effect of interest. The difference between
means or the correlations between variables.
• Alpha (a): is the level of significance. As a is set at smaller levels, power decreases.
Typically a=0.05
• 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 versus statistical significance.
Effect size, alpha and sample size are all related.
Statistical power analysis:
• Researchers should design the study to achieve a power level of 0.80 at the desired
significance level.
• More stringent significance levels (0.01 versus 0.05) require larger samples to achieve
the desired power level
• Power can be increased by choosing a less stringent alpha level.
• 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 knows as independent
variables.
o Multiple regression, ANOVA, Structural Equation Modeling (SEM)
• Interdependence techniques: they involve the simultaneous analysis of all variables in
the set, without distinction between dependent and independent variables.
o Exploratory factor analysis, Principal component 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: a single metric dependent variable is predicted by several metric
independent variables.
Analysis of Variance (ANOVA): a metric dependent variable is predicted by a set of
nonmetric (categorical) independent variables.
Structural Equation Modeling (SEM) estimates multiple, interrelated dependence
relationships based on components: structural model and measurement model.
Guidelines for multivariate analysis: establish practical significance (is it important?) as well
as statistical significance, sample size affects all results, know your data, strive for model
parsimony (do not make it too complicated), look at your errors and validate your results.
A structured approach to multivariate model building:
1. Define the research problem, objectives, and multivariate techniques to be used.
2. Develop the analysis plan
3. Evaluate the assumptions underlying the multivariate techniques
4. Estimate the multivariate model and assess overall model fit
5. Interpret the coefficients
6. Validate the multivariate model
3
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