Training -- the Traditional Model,

¶ … training -- the traditional model, the computer model, and the video model -- feeling that people who receive different kinds (levels) of training should show differences in the dependent variable, which is the level of math anxiety. The researcher's null hypothesis is that there will be no differences in mean level of math anxiety for the three groups (assume there is a valid, interval-level measure of math anxiety). However, after thinking about it, the researcher wonders if the methods may also be effective with anxiety related to public speaking. The null hypothesis here is that there will be no differences in the mean level of anxiety related to public speaking for the three groups (assume there is a valid, interval-level measure of fear of public speaking. The researcher decides to do two separate one-way ANOVAs to analyze the research. However, a colleague reports that they have evidence that math anxiety and public speaking anxiety are positively correlated. In fact, there is about a .4 correlation between math anxiety and anxiety due to public speaking.

As an expert in statistics, the researcher comes to you for guidance. What advise do you offer? Defend your answers.

My suggestion would be to conduct a MANOVA. The difference between an ANOVA and a MANOVA is that whereas an ANOVA deals with one dependent variable, a MANOVA deals with two. I would also recommend a 2-way analysis.

The researcher originally wanted to test whether one of the three methods of training, the traditional model, the computer model, and the video model, have any effect on math anxiety. The researcher, in other words, is playing around with three independent variables and seeing whether they have any effect on one dependent variable: Maths anxiety

In this case, the researcher would be correct in choosing to employ / use an ANOVA.

However, now the researcher wants to see whether the same three independent variables have any impact on two dependent variables:

1. maths anxiety, and

2. anxiety in public speaking.

Here, his statistics become more complex since he is analyzing, not one, but two completely different situations. I would therefore recommend him to use a MANOVA for doing so.

I would also advise him to do a 2-way research. He does not need to do two separate one-way ANOVAs; that would make it more complex.

If he does a 2-way MANOVA, he will be able to see results in either direction. Meaning that he will be able to see whether the 3 independent variables have a positive effect on maths anxiety (i.e. whether they help reduce it) or whether they have a negative effect on the situation (I..e if they increase it). The same applies to anxiety in public speaking. A 2-way will tell him whether it increases or decreases the variable.

Even if someone tells him, as happens in this case, that the two anxieties are related, the researcher should not trust him. This is so for various reasons that include the folowing:

1. They are two different areas: one deals with math, the other public speaking.

2. Precious research on th e subject may be mistaken

3. The researcher is dealing with a separate population sample and separate case. Study results may be different in his.

Furthermore, they likely are correlated in some way. When conducting the MANOVA, therefore, the researcher adds differences to each so as to make the contrast stronger.

2.Discuss the logic of the multiple analysis of variance (MANOVA). Why would a researcher use MANOVA instead of running several separate analyses of variance? Mention specific advantages and disadvantages in doing so.

The MANOVA is useful in that it gives us a multivariate F. value when comparing two things, instead of a univariate F. value. For instance, when comparing which of two textbooks are better for students, we are dealing with two separate factors that, although perhaps correlated, are still different. The MANOVA exaggerates these differences and then sees whether there is any contrast between the two.

The MANOVA is used to see whether (going to the previous example) the 3 factors help reduce math anxiety or whether they reduce public speaking anxiety. They may be helpful with one, but not helpful with the other. The ANOVA lumps them, but the MANOVA separates them and this distinction is very important. The MANOVA, therefore, also shows the researcher more differences that an ANOVA overlooks, as well as avoiding the possibility of a Type 1 error (namely saying that there is a significant result when there isn't').

On the other hand, it is more complicated than the ANOVA so the researcher can make mistakes. It also leads the researcher to make more assumptions that may be false. The researcher has to also add more degrees of freedom and this may bring more error into the test. Finally, the MANOVA cannot be used in every instance. The two dependent vairables have to be very different for the MANOVA to te4st them since if they are matched or similar, confusion may occur. In the case of the maths and public speaking anxiety, the research can differentiate these two dependent variables so that they do become two separate factors. However, assessing whether there is a difference between two very similar textbooks may result in confusion. The researcher would then be best off using an ANOVA rather than a MANOVA.

3. A researcher has found a significant F. with their MANOVA. What is the general interpretation of the result? What might the next steps be in the analysis, given the significant F. For the MANOVA?

The general interpretation of the result is that all three factors / independent variables have a significant effect on either reducing or worsening both maths and public speaking anxiety.

The researcher would now want to run additional tests. He should do the following:

a. examine the Tests of between Subject-effects for each of the dependent variables to see the rate of significance in each. It may be, for instance, that one or more of the three conditions has a stronger impact on maths anxiety than on reading . Or that one condition has an effect on maths and no effect on reading. The researcher will be able to see the contrast of the conditions in each phobia.