multivariate statistics Vs anova

[aaa34169]

Hi I open a new discussion, as required it might be basic but help another users.

I hesitate between 3 statistical process !

I have only on dependant variable for multiple conditions. Initially i choose to carry out an spm-anova for examining the mean equality betwwen all independant variables mean_1=mean2=mean3=mean4=mean 5=mean 6 the spm anova showed significant regions. Then i stated 3 posthoc tests only : mean_1=mean2 mean_3=mean4 mean_5=mean6 I set aside other comparisons because they are not relevant according my research question I found no significant difference.

So, i wonder if a multivariate anova would be more adapted. This multivariate would consider two vectors collecting (mean1,mean3,mean5) and (mean2,mean4,mean6) separatly. But, for me, there is no reason to think that mean1 covariates with mean3 and mean 5 ! these componants could be assumed as indepedants. in this case : is multiple ttest comparison better suited?

What do you think about that ?

regards

Fabien Fabien

[0todd0000]

Hi Fabien,

It is possible that other pairs are driving the ANOVA results. ANOVA looks for differences between all pairs, irrespective of your post hoc analyses.

Regarding MANOVA: It is not possible to choose whether your data are univariate or multivariate; the data themselves define whether they are univariate or multivariate.

If you measure a 3D force vector, for example, that variable is multivariate. If you measure a planar angle (like knee flexion), that variable is univariate.

Can you please explain the difference between your six dependent variable?

Todd

[aaa34169]

thank for your answer, Todd.

I understand the explanation for anova. I just wonder if manova would be more suit because i set aside the posthoc comparisons.

I agree that a 3d force vector lead to a multivariate analysis because componants can covariate.

But in the emg application of your article, you assume that emg of the rectus femoris covariates with emg of the vastus lateralis and eight others... Then,you built a vector of 10 emg componants for two groups. I think, i tend to fit this case. Indeed, i have one dependant variable VD:( emg maximal amplitude) , 6 indepedant variables ( 6 gait conditions ) and two groups( PC versus TD). I want highlight a difference between groups. so i state the vector comparison : VD( group 1, condition1) = VD( group 2, condition1) VD( group 1, condition2) = VD( group 2, condition2) ... ... VD( group 1, condition6) = VD( group 2, condition6)

But, nothing indicates me that VD covariates between condition. I might consider no covariation and carry out multiple t-test no ?

regards

Fabien

2014-10-24 1:59 GMT+02:00 Todd Pataky notifications@github.com:

Hi Fabien,

It is possible that other pairs are driving the ANOVA results. ANOVA looks for differences between all pairs, irrespective of your post hoc analyses.

Regarding MANOVA: It is not possible to choose whether your data are univariate or multivariate; the data themselves define whether they are univariate or multivariate.

If you measure a 3D force vector, for example, that variable is multivariate. If you measure a planar angle (like knee flexion), that variable is univariate.

Can you please explain the difference between your six dependent variable?

Todd

— Reply to this email directly or view it on GitHub https://github.com/0todd0000/spm1d/issues/5#issuecomment-60327437.

Fabien Leboeuf

• Ingénieur de recherche au CHU de Nantes

- Docteur en mécanique-Biomécanique de l'Université de Poitiers

Pôle Médecine Physique et Réadaptation Hôpital St Jacques 85 rue saint Jacques 44 093 Nantes cedex1 --------------- Tél : 02 40 84 60 88

Port: 06 07 79 02 44 *

[0todd0000]

Hi Fabien,

From your description it sounds like the VD variable is univariate (a scalar) at each point in time and not multivariate (a vector) at each point in time. If that's true then univariate procedures like ANOVA are appropriate. You're absolutely right: if your VD variable is univariate then there is no covariance. Covariance can only exist when the variable is multivariate.

In our paper we regarded the EMG data as multivariate because there were ten different EMG values at each point in time, thus forming a ten-component vector time series. In that case multivariate procedures like MANOVA or a Hotelling's T2 test are appropriate.

In your experiment it sounds like there are two independent variables: CONDITION and GROUP. Thus your design sounds like two-way ANOVA:

Dependent variable: VD Independent variable 1: CONDITION (six different levels) Independent variable 2: GROUP (two different levels)

In this case multiple t tests are OK for post hoc analysis, but those are only justified if the main ANOVA reaches significance. Also, there might be a non-negligible CONDITION x GROUP interaction. If that's true then interpreting post hoc results can be somewhat complicated.

Just in case you haven't seen this already, here's a link to an example two-way ANOVA: http://www.spm1d.org/doc/Examples_stats_basic.html#two-way-anova

Todd

[aaa34169]

OK, for your new explanations. Now it 's clear my VD is univariate !

My question had stemmed from your emg example. I have never saw an article collecting in one vector all emg signals. I think you're right. the rectus femoris signal can covariates with others. I really interest in adding this multivariate analysis to my library implemented for clinical gait analysis. I will wait your next release

Now, you re right. a two-way anova is probably better suitable. i am implementing it

regards

Fabien

2014-10-24 14:56 GMT+02:00 Todd Pataky notifications@github.com:

Hi Fabien,

From your description it sounds like the VD variable is univariate (a scalar) at each point in time and not multivariate (a vector) at each point in time. If that's true then univariate procedures like ANOVA are appropriate. You're absolutely right: if your VD variable is univariate then there is no covariance. Covariance can only exist when the variable is multivariate.

In our paper we regarded the EMG data as multivariate because there were ten different EMG values at each point in time, thus forming a ten-component vector time series. In that case multivariate procedures like MANOVA or a Hotelling's T2 test are appropriate.

In your experiment it sounds like there are two independent variables: CONDITION and GROUP. Thus your design sounds like two-way ANOVA:

Dependent variable: VD Independent variable #1 https://github.com/0todd0000/spm1d/issues/1: CONDITION (six different levels) Independent variable #2 https://github.com/0todd0000/spm1d/issues/2: GROUP (two different levels)

In this case multiple t tests are OK for post hoc analysis, but those are only justified if the main ANOVA reaches significance. Also, there might be a non-negligible CONDITION x GROUP interaction. If that's true then interpreting post hoc results can be somewhat complicated.

Just in case you haven't seen this already, here's a link to an example two-way ANOVA: http://www.spm1d.org/doc/Examples_stats_basic.html#two-way-anova

Todd

— Reply to this email directly or view it on GitHub https://github.com/0todd0000/spm1d/issues/5#issuecomment-60382869.

Fabien Leboeuf

• Ingénieur de recherche au CHU de Nantes

- Docteur en mécanique-Biomécanique de l'Université de Poitiers

Pôle Médecine Physique et Réadaptation Hôpital St Jacques 85 rue saint Jacques 44 093 Nantes cedex1 --------------- Tél : 02 40 84 60 88

Port: 06 07 79 02 44 *

[0todd0000]

OK, great. I'll close this issue now, please open a new one if you encounter any two-way ANOVA difficulties. Todd