Summary: Multivariate Data Analysis | 9780130329295 | Joseph F Hair
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1 Overview of Multivariate Methods
What is the difference between a univariate, bivariate and multivariate analysis?Univariate analysis is a statistical technique to determine based on
one dependentmeasure whether samples are from populations with equal means. Analysis of single variable distributions.
Bivariate analysis is a statistical technique that analyses
twovariables. Correlation and simple regression.
Multivariate analysis is a statistical technique that analyses more than 2 variables in a
singleor setof relationships. Multiple regression, factoranalyse.
1.1 What is multivariate analysis?
What is multivariate data analysis? And why is its application helpful for research?Multivariate data analysis is the analysis of
multiplevariables in a singlerelationship or setof relationships. It refers to all statistical techniques that simultaneously analyze multiple measurements on individual or object under investigation, so >2 variables.
Its application is helpful for research because these techniques reveal
relationshipsthat otherwise would not have been identified.
1.2 Three trends
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What is meant by causal inference and how does it supplement the randomized controlled experiment?Causal inference; movement beyond statistical inference to the stronger statement of cause and effect in non-experimental situations. This is a paradigm shift.
Randomized controlled experiment supplement; new analytical framework for non-experimental data. This increases rigor of their analysis and helps to overcome doubts raised by many concerning the pitfalls of big Data analytics.
1.4 Basic concepts of multivariate data analysis
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What are the two main different data discussed in Hair et al., and what measurement scales does it contain?Two main different measurement scales discussed:
Nonmetric--> qualitative data. This can be measured either using a nominalor ordinalscale. Nominaal = categorie, en ordinaal is de een hoger dan de ander --> ranking, maar geen afstand. Metric--> quantitative data. This can be measured either using intervalor ratioscale. Both refer to units of measurements, but interval had an arbitraryzero point (e.g. Celsius), and ratio does have an absolutezero point (e.g. Weight). For interval it is not possible to say that something is *x amount away of another value.
What are the two reasons why the measurement scale is important for doing data analysis?The measurement scale is important for doing data analysis because:
1. The researcher must identify the measurement scale of each variable used, so that non metric data is not used incorrectly.
2. The measurement scale determines which multivariate technique are most applicable.
Basic concepts in multivariate data analysis are: variate, measurement error, and measurement scale. What is the variate?The variate is the building block of multivariate analysis. This is a lineair combination of variables with empirically determined weights. This is a single value representing a combination of the entire set of variables that best achieves the objective of specific multivariate analysis.
In factor analysis the variates are formed which best represent the underlying structure or patterns as represented by intercorrelations. In MRA the variate is determined by the maximum correlation between the IV's and DV.
The variate is determined by the weight and observed variable.
What is statistical power, what three concepts represent this and what does it imply?Statistical power is the
probabilityof finding an effectwhen it is present in the data. It is about the probability of correctly rejecting the null hypothesis in favor of the alternative hypothesis.
Concepts that represent it:
- Statistical significance set by the researcher for a type 1 error (
Effectsize (the size of the effect being examined)
Samplesize While checking for statistical power, as a researcher you search for an adequate probabilityof recovering a significant effect that is present in the data.
Why is the sample size critically important for statistical power?Because given the sample size, the significance level of an estimated parameter is impacted. Almost any parameter can be found significant in a large sample size, and a small sample size might overlook things.
What is the difference between a Type 1 and Type 2 error?Type 1 error: probability of incorrectly
rejectingH0, meaning that you say there is a difference or correlation, while in fact, there is not. This is determined by alpha. Vals positief resultaat: je zegt dat er een effect is, maar het effect is er niet.
Type 2 error: probability of incorrectly
acceptingH0 (failing to reject H0), meaning that you state there is no difference while in fact there is. This is termed by beta. The value of 1-type 2 error is called power. Je zegt dat er geen effect is, terwijl er wel een effect is.
What is the difference between variance, correlations and components?The variance is about the differences in the answers of the respondence WITHIN a certain variable.
The correlation is about whether the differences in answers of the respondents correspond with each other, e.g. do they go up and down together. So this is AMONG variables.
The compontents then explain the underlying dimensions.
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