Amber,

I would like to see examples of analyses in which "a single ANOVA is used and multiple DVs are entered as a factor"; but I interpret that description as saying that the data on the various DVs are arranged as a single DV for the ANOVA, and the identity of the particular DV is given by a factor (i.e., a set of indicator variables).

If one writes out the model corresponding to such an ANOVA, it involves a very strong assumption: the other factors have the same contributions to each of the DVs, and the means of the DVs differ only by a constant.

If the ANOVA model actually contains interactions for the DVs with all the other factors, the result will be similar to using a separate ANOVA for each DV, but assuming that all the DVs have the same "error variance" (for which the error mean square in the combined ANOVA will give a pooled estimate).  This might make some sense if the various DVs are closely related (e.g., have essentially the same scale) and could reasonably have the same error variance.  Otherwise, it would seem difficult to justify.

Combining the DVs in a single ANOVA hides the problem of multiplicity but does resolve it.

It is difficult to give a correct answer to an open question. If I knew about so e experiment, I could maybe discuss the models that could be used for reasonably good results. The researcher decides which variables are response variables and which variables are classification factors. Each approach addresses different hypotheses.

Typically, the variables of interest are the response variables that we want to study.

Hello, I think that it is ok to use the SPSS for this purpose, for more information about this subject you have to read much more about SPSS, you are the only one who knows your experiment.

It all depends on what error-rate you want to control. Actually, ANOVAs are not required to control these error rates, - this job is done by the post hoc tests. There are many ways to control error-rates, and there are different kinds of rates (e.g. the family-wise error-rate or the false-discovery rate). One may decide to define a family of hypotheses being all null hypotheses belonging to one DV. Or to a subset of the DV's, or all DV, or even all tests performed in the entire publication, or... Nothing is right or wrong, these decisions can only be more or less reasonable - depending on the case and the context.

MANOVA is helpful to identify IVs with explanatory power when the different DVs are correlated. But the answer then refers to the set of DVs, so nothing can be said about the relation of the IV to any particular of the DVs.

Amber, the notions of direction of causality and endogeneity are brought up by the problem you pose. To be entierly apt, regression techniques  require that the independent variables influence the dependent variables and not the other way around. It sounds like you have seen papers where dependent variables have been cast as independent variables (factors) and so problems with endogeneity pretty surely result. So, if you are going to do 1 at a time ANOVA's and not control for endogeneity then it is best to not include the other dependent variables as factors. So, 1 at a time ANOVA's almost always involve loss of information. Nevertheless, there is not a lot of openess in my organization to MANOVA like approaches because they tend to seem obscure to clients.

Amber,

I would like to see examples of analyses in which "a single ANOVA is used and multiple DVs are entered as a factor"; but I interpret that description as saying that the data on the various DVs are arranged as a single DV for the ANOVA, and the identity of the particular DV is given by a factor (i.e., a set of indicator variables).

If one writes out the model corresponding to such an ANOVA, it involves a very strong assumption: the other factors have the same contributions to each of the DVs, and the means of the DVs differ only by a constant.

If the ANOVA model actually contains interactions for the DVs with all the other factors, the result will be similar to using a separate ANOVA for each DV, but assuming that all the DVs have the same "error variance" (for which the error mean square in the combined ANOVA will give a pooled estimate).  This might make some sense if the various DVs are closely related (e.g., have essentially the same scale) and could reasonably have the same error variance.  Otherwise, it would seem difficult to justify.

Combining the DVs in a single ANOVA hides the problem of multiplicity but does resolve it.

How about first transforming all DV's into normal quantiles with common mean and standard deviation, David?

"This might make some sense if the various DVs are closely related (e.g., have essentially the same scale) and could reasonably have the same error variance. Otherwise, it would seem difficult to justify."

Raid,

Some aspects of this discussion would be clearer if we had a concrete example.

My reading of Amber's question was that the ANOVAs involved other factors and that some people then added a factor that identified the DVs.  In that situation it would not make sense to first transform all the DVs into normal quantiles, because that step would not take into account (or adjust for) the contributions of the other factors in the ANOVA.

I did not assume that the DVs, if closely related, had distributions that were well approximated by normal distributions, and I would not want to make that assumption.  Real data are never normal.

A normal quantile transformation implies that the underlying distribution of the DV's are non-normal.

As for the posted question, I will make up an example to see if this is what Amber is asking about or not.

Example: We study several variables on physical fitness as they are related to exercise level used by some random sample of participants in a study.

Approach 1: MANOVA

Response variables: 1. weight  2. blood pressure  3. BMI. 4. resting pulse rate

Factor: level of exercising

(in SAS):

proc glm;

class exercise;

model weight bmi pressure rate=exercise;

manova H=exercise;

run;

We would be testing the null hypothesis that the mean vector levels for the four response variables are equal for the levels of exercising. We make use of the information on the covariances in the multivariate test.

Approach 2: We categorize the variables weight, blood pressure, and resting pulse rate (based on percentiles maybe) and we keep BMI as the response variable.

proc glm;

class exercise, weight_c, pressure_c, rate_c;

model bmi= exercise weight_c pressure_c rate_c;

We would be testing the null hypothesis that the mean BMI levels are the same for each of the factor levels for weight, resting pulse rate, blood pressure, and exercise. The emphasis is on BMI.

Is this is what you asked us about, Amber?

A different approach to the ANOVA could be a regression analysis where we predict BMI from the rest of the (continuous) variables, plus an indicator variable for exercise levels.

Raid's example relates to my question and answers it. Thanks for your responses.

Just to add to the answers already provided, this paper has been very useful in answering my question (see link below). The authors discuss scenarios where it might be appropriate to use multiple ANOVAs or t-tests over MANOVA when dealing with several dependent variables.

http://psycnet.apa.org/psycinfo/1989-21163-001