Part I – MULTIVARIATE ANALYSIS
C1 Introduction to MA
© Angel A. Juan & Carles Serrat - UPC 2007/2008
1.1.1: Why Multivariate Statistics?
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Variables are roughly dichotomized into two major types: independent variables
or IVs are the differing conditions to which you expose your subjects, or
characteristics the subjects themselves bring into the research situation. IVs are
usually considered either predictor or causal variables because they predict or
cause the dependent variables or DVs –the response or outcome variables

Multivariate statistics are increasingly popular techniques used for analyzing
complicated data sets. They provide analysis when there are many IVs and/or
many DVs, all correlated with one another to varying degrees

Multivariate statistics are an extension of univariate and bivariate statistics.
Multivariate statistics are the general case

In an experiment, the researcher has control over the levels of at least one IV to
which a subject is exposed. In nonexperimental (correlational or survey)
research, the levels of the IV(s) are not manipulated by the researcher. Attribution
of causality to results is crucially affected by the experimental-nonexperimental
distinction

The trick in multivariate statistics is not in computation; that is easily done by
computer. The trick is to select reliable and valid measurements, choose the
appropriate program, use it correctly, and know how to interpret the output
1.1.2: Some Definitions (1/2)

Continuous (interval or quantitative) variables are measured on a scale that
changes values smoothly rather than in steps. They take on any value within the
range of the scale, and the size of the number reflects the amount of the variable
(ex.: time, annual income, age, temperature, distance, grade point average, …)

Discrete (nominal, categorical or qualitative) variables take on a finite and usually
small number of values and there is no smooth transition from one value or
category to the next (ex.: time as displayed by a digital clock, continents,
categories of religious affiliation, type of community, …)

Discrete variables composed of qualitatively different categories are sometimes
analyzed after being changed into a number of dichotomous or two-level
variables, called dummy variables

Samples are measured in order to make generalizations about populations.
Ideally, samples are selected, usually by some random process, so that they
represent the population of interest. In real life, however, populations are
frequently best identified in terms of samples, rather than viceversa; the
population is the group from which you were able to randomly sample
1.1.2: Some Definitions (2/2)

Descriptive statistics describe samples of subjects in terms of variables or
combinations of variables. Inferential statistics test hypothesis about differences
in population on the basis of measurements made on samples of subjects

Ortogonality is perfect nonassociation between variables. If two variables are
orthogonal, knowing the value of one variable gives no clue as to the value of the
other; the correlation between them is zero

Multivariate analyses combine variables to do useful work such as predict scores
or predict group membership. In most cases the combination that is formed is a
linear combination

A general rule is to get the best solution with the fewest variables. If there are too
many variables relative to sample size, the solution provides a wonderful fit to the
sample that may not generalize to the population, a condition known as
overfitting

A few reliable variables give a more meaningful solution (model) than a large
number of unreliable variables

The difference between the predicted and obtained values is known as the
residual and is a measure of error of prediction
References for Multivariate Analysis

Anderson, D.; Sweeney, D.; Williams, T. (2004): Statistics
for Business and Economics. South-Western College Pub.

Frees, E. (1995): Data Analysis Using Regression Models:
The Business Perspective. Prentice Hall.

McKenzie, J.; Goldman, R. (1998): The Student Edition of
MINITAB for Windows. Addison Wesley Longman.

Mendenhall, W.; Sincich, T. (2003): A Second Course in
Statistics: Regression Analysis. Prentice Hall.

Montgomery, D.; Runger, G.; Hubele, N. (2006):
Engineering Statistics. John Wiley & Sons.

StatSoft (2007): Electronic Statistics Textbook. Available
at http://www.statsoft.com/textbook/stathome.html

Tabachnick, B.; Fidell, L. (2006): Using Multivariate
Statistics. Allyn & Bacon.