Student Learning Outcomes

At the completion of this unit of instruction students will be able to:

1. Explain and illustrate the difference between univariate and multivariate statistical techniques (related principally to the number and type of variables being investigated).
2. Provide an example of, and explain the purpose of a discriminant analysis.
3. Provide an example of, and explain the purpose of a multivariate analysis of variance.

Techniques that allow only one dependent variable are univariate techniques (t-tests, Pearson r, Simple ANOVA, Factorial ANOVA, Multiple Regression)

But often IVs influence more than one DV and require investigation using multivariate methods of analysis.

The are multivariate techniques for experimental data (discriminant analysis, ANOVA, ANCOVA) and multivariate techniques for correlational data (canonical correlation, factor analysis, path analysis)

In all cases the techniques help us to evaluate the two critical questions: significance and meaningfulness. First let's consider experimental data.

Discriminant Analysis

Used with one IV and two or more DVs

Is a combination of multiple regression (several IVs and one DV) and simple ANOVA

Now the DVs are being combined (remember, regression techniques include the combination of variables) to predict group affiliation (remember, differentiating between groups was the main task in ANOVA)

So considering the example in the text, several physical tests were used to separate (predict) affiliation to one of three groups (according to playing position)

Q: Why might this be of interest?

A: Physical tests could be used to determine a person's potential for certain positions

What discriminant analysis permitted was the determination of those key variables that best predicted playing position.

Q: What did we learn?

A: That bench press was the best, followed by 40-yard dash, and vertical jump. After that the remaining variables made little difference.

We could use these three scores to separate players into groups but note that only 35% of the variance is accounted for

Q: Implications

A: Don't rely on this test!

Multivariate Analysis of Variance (MANOVA)

Q: How many variables?

A: More than one IV and more than one DV

Involves the combination of DVs to maximally separate out IVs in an experimental setting

The text example includes the following variables:

IV #1 Age levels (two groups)

IV #2 Level of expertise (two groups)

DV #1 Basketball knowledge test

DV #2 Basketball shooting test

DV #3 Basketball dribbling test

Repeated Measures with Multiple Dependent Variables

Used in a study that has more than one DV that is measured on more than one occasion.

For example you might be testing two different teaching methods and examining their effect on five measures of learning. You might be interested in observing changes in learning that occur over the course of the instruction, and decide to measure the learning variables each week. Statistics are available to analyze this case but see a statistician!

Canonical Correlation

Used with more than one IV and more than one DV

Variables are entered into a statistical computation that looks at best relationships between the variables.

Useful in exploratory analysis which might later lead to using the best IVs later in an experimental setting.

Factor Analysis

Useful when the variables we choose have a shared relationship (i.e. are correlated). Factor analysis is way of reducing constructs. For example, in text you have the example of person developing a questionnaire and listing many questions according to each topic. What they wanted to know was whether the questions were highly correlated with the topic they were listed under, and had low correlation with other topics.

Example:

Thurstone was interested in intelligence factors and their measurement and factor analyzed 60 tests. The study revealed the same set of so-called primary factors that had been found in previous studies.

Structural Modeling (Path Analysis and LISREL)

Is a form of applied multiple regression that uses path diagrams to guide problem conceptualization or to test complex hypotheses.

LISREL (Linear structural relations) is a similar modeling approach that attempts to test theoretical relationships

Example in your test examined attitude, background, subjective data, and intention to discover the relationship between these and exercise behavior. Was found that prediction of exercise behavior by attitude or subjective data was significantly mediated by intention.

Clearly these techniques are a way to study v. complex problems and leaves me with the question are we tending to find out less and less about more and more??

(Revised 2/3/99)