Hi,

1) If you are comparing three groups, then either ANOVA or MANOVA may make sense. What determines your choice of ANOVA or MANOVA is whether you have more than one dependent variable.

2) A MANOVA is for multiple dependent variables by definition, so a single dependent variable would imply use of ANOVA.

3) There are a variety of post-hoc multiple comparison procedures, each of which has features that are desirable in certain circumstances. Scheffe has the property of holding the Type I error rate fixed for any possible comparison of means (pairwise, linear combination, etc.). It is criticized for this reason too since it controls Type I error for comparisons that the analyst may not ever do or be interested in, so there is a loss of power compared to another post-hoc procedure for a limited number of contrasts between means. In your case, you could make three (maximum) pairwise comparisons. If you are not planning to do more complex comparisons than that, Scheffe may be too much Type I error control for your purposes.

A final important consideration for MANOVA is whether the multiple dependent variables can be considered related to one another. Functionally, MANOVA creates a linear composite of all the dependent variables and compares the groups on that linear composite. If there is no conceptual relationship among the variables, then the composite created by MANOVA has no meaning and therefore the group comparisons would not be meaningful. In that case, multiple ANOVAs, one for each dependent variable, make more sense. The post-hoc tests following those ANOVAs would tell you which groups differ on which dependent variables.

Hope this helps,

Scot

Hi,

1) If you are comparing three groups, then either ANOVA or MANOVA may make sense. What determines your choice of ANOVA or MANOVA is whether you have more than one dependent variable.

2) A MANOVA is for multiple dependent variables by definition, so a single dependent variable would imply use of ANOVA.

3) There are a variety of post-hoc multiple comparison procedures, each of which has features that are desirable in certain circumstances. Scheffe has the property of holding the Type I error rate fixed for any possible comparison of means (pairwise, linear combination, etc.). It is criticized for this reason too since it controls Type I error for comparisons that the analyst may not ever do or be interested in, so there is a loss of power compared to another post-hoc procedure for a limited number of contrasts between means. In your case, you could make three (maximum) pairwise comparisons. If you are not planning to do more complex comparisons than that, Scheffe may be too much Type I error control for your purposes.

A final important consideration for MANOVA is whether the multiple dependent variables can be considered related to one another. Functionally, MANOVA creates a linear composite of all the dependent variables and compares the groups on that linear composite. If there is no conceptual relationship among the variables, then the composite created by MANOVA has no meaning and therefore the group comparisons would not be meaningful. In that case, multiple ANOVAs, one for each dependent variable, make more sense. The post-hoc tests following those ANOVAs would tell you which groups differ on which dependent variables.

Hope this helps,

Scot

Thank you Mr. McNary so much for kind explanations. I think I'd have to use MANOVA.

But if I have more than 5 dependent variables, would there be a "specific preference" as the post-poc?

I considered Scheffe because from the book I learned Scheffe is useful for different Ns. Independent variables are composed from different samples. What would you recommend in this case?

With 3 groups of variables where at least one of them is a quantitative variable, you can apply the following tests (of course each test has its own assumptions that should be met):

2-factorial ANOVA.EXAMPLE:

We measure people’s weight and happiness{yes, no} and classify them according to gender{male, female}. Study the effect of gender and happiness (and their interactions) on people’s weight.

Dependent variable (DV): people’s weight [kg]

Independent variable (IV): gender{male, female}. Independent (unpaired).

Independent variable (IV): happiness{yes, no}. Independent (unpaired).

Mixed ANOVA (within-between ANOVA or split-pot ANOVA).EXAMPLE:

We measure people’s weight 2 different moments in time and classify them according to gender{male, female}. Study the effect of gender and time (and their interactions) on people’s weight.

Dependent variable (DV): people’s weight [kg]

Independent variable (IV): gender{male, female}. Independent (unpaired).

Independent variable (IV): time{M1, M2}. Related (paired).

MANOVA.EXAMPLE:

We measure people’s weight and height and we classify them according to gender. Study the effect of gender on people’s weight and height.

Dependent variable (DV): people’s weight [kg].

Dependent variable (DV): people’s height[cm].

Independent variable (IV): gender{male, female}. Independent (unpaired).

ANCOVA.EXAMPLE:

We measure people’s weight and height and we classify them according to gender. Study the effect of gender on people’s weight after controlling for people’s height.

Dependent variable (DV): people’s weight [kg].

Covariate variable (DV): people’s height[cm].

Independent variable (IV): gender{male, female}. Independent (unpaired).

REPEATED MEASURES ANOVA. EXAMPLE:

We measure people’s weight in 3 different moments in time. Study the effect of time on people’s weight.

Dependent variable (DV): people’s weight [kg]

Independent variable (IV): time{moment 1, moment 2, moment 3}. Related (paired).

ONE-WAY ANOVA. EXAMPLE:

We measure people’s weight and classify them according to age group{young, middle age, old}. Study the effect of age on people’s weight.

Dependent variable (DV): people’s weight [kg]

Independent variable (IV): age group{young, middle age, old}. Independent (unpaired).

Regarding post-hoc tests:

I usually use the Bonferroni for Repeated measures-like tests and Tukey for one-way ANOVA-like tests.