INTRODUCTION
Multivariate analysis is essentially the statistical process of simultaneously analysing multiple independent (or predictor)
variables with multiple dependent (outcome or criterion ) variables using matrix algebra (most multivariate analyses are correlational). While these analyses have been a part of statistics since the
early 1900’s, the development of mainframe and
PURPOSE
Human behavior is very complex.
Behaviors, emotions, cognitions, and attitudes can rarely be described in terms of one or two variables.
Furthermore, these traits cannot be measured directly, as say
PURPOSE
The researcher must construct his/her view of reality (observations about humans), create multiple measures to assess the constructs, and conduct an appropriate statistical analysis of the data, and
correctly interpret the outcomes.
Basically, the researcher asks two questions, “Do I have anything important?” and “If so, what do I have?”
PURPOSE
Importance is usually based upon how much common or shared variance can be extracted from the data.
Variance is a numerical representation of the distribution of a trait (behavior, emotion, cognition, etc.) in the population.
If two variables are associated or correlated with one another, then they share some common underlying trait/factor that causes some equality in how they vary on the scores in the data set.
PURPOSE
In other words, it is leading to similar variations in scores which is measured as variance.
We can extend this concept to include two sets of variables that are correlated.
BASIC ANALYSIS
Multivariate analysis may either be conducted in a classic experimental design or in non-experimental designs.
Whether one is seeking causality or association depends upon the research question, but both are valid in multivariate analysis.
Most of the time, a data matrix will be analyzed—the form usually consists of rows representing each subject and columns
BASIC ANALYSIS
however, the matrix can also be a correlation matrix, a
variance/covariance matrix, or a sum-of-squares/cross-product matrix.
The matrix is then solved simultaneously through matrix (linear) algebra and yields linear composite scores which are linear
combinations of the variables upon which the final solution is based.
Most analyses construct composite scores that maximize the
BASIC ANALYSIS
The importance of each variable is determined by its weight (degree of contribution) to its set of variables and is usually indicated by a numerical coefficient.
FOUR TYPES OF RESEARCH
QUESTIONS.
Degree of relationship between the variables: Bivariate correlation and regression (simple, multiple, and multivariate/canonical) are used to
1) explain the association between variables or
Measure significant differences between group means: MANOVA (multivariate analysis of variance) is used when group differences are measured on two or more dependent variables that are related to one another in the real world (e.g., depression and anxiety).
Like ANOVA, MANOVA controls for Type I errors if two or more
ANOVAs are run, and different kinds of MANOVA analyses can be conducted: one-way MANOVA, factorial MANOVA,
Predicting membership in two or more groups from one or more
Explaining underlying structure: Often researchers infer that variables may be clustered together based on their common
Level of measurement or scale of measure is a classification that describes the nature of information within the numbers
assigned to variables. Psychologist Stanley Smith Stevens
PROPERTIES OF
MEASUREMENT SCALES
Each scale of measurement satisfies one or more of the following properties of measurement.
Identity. Each value on the measurement scale has a unique meaning.
Magnitude. Values on the measurement scale have an ordered relationship to one another.
That is, some values are larger and some are smaller.
Equal intervals. Scale units along the scale are equal to one another. This means, for
example, that the difference between 1 and 2 would be equal to the difference between 19 and 20.
Data can be broadly classified as qualitative data and Quantitative data
Qualitative data measures behavior which is not commutable by arithmetic relations and is represented by words, pictures, or
images
Quantitative data is a numerical record that results from a process of measurement and on which basic mathematical operations can be performed.
For example if we represent gender male and female as values 1 and 2 still we cannot perform any mathematical operations on it
(adding 1 and 2 does not make sense), the data remains qualitative in nature
Non Metric data: Data collected from binary scales, nominal scales and ordinal scales are jointly termed as non metric data, that is, they do not possess a meter with which distance between scale values can be measured
Metric data: thought for some scales there is metric data with which we can define distance between scale values. Metric data can be further classified into discrete data and continuous data.
Discrete data is countable data for example number of students in class
