ANOVA - which one to use?

[KatkaK]

Hello,

we are doing an experiment where body consistence (weight, proportion of muscles, fat, water in body etc.) is measured. We have 103 respondents, water and banana (factor meal) were given to EACH of them a then they were measured in 5 different times (time 0, immediately after consuming water or banana, after 30, 60 and 90 minutes) - once after drinking water, once after eating banana. We also have an information about sex of participants.

I would like to find out how long after consuming water/banana is the body consistence in the original level (time 0); at first without sex separation (factors: meal, time), then including sex as the third factor (factors: meal, sex, time).
So, I would test if the means differ for each group (meal*time or meal*sex*time), that is why I can find out (post-hoc analysis) in which time occations are the means of body consistence the same. I would choose ANOVA. I am not sure which ANOVA test to use.
Can ANOVA be used at all? Factor "time" has 5 levels (5 different time occations), these are highly correlated (almost 1), i.e. levels of time factor are correlated. Can I use ANOVA if levels of one factor are correlated? If not, which test is appropriate?

I would be grateful for any response.
Thank you!

 

[Karabiner]

Seemingly you could do a repeated-measures or "mixed" ANOVA, with 2 repeated-measures factors (time with 5 levels and meal with 2 levels) and a between-subjects factor (sex).

HTH

K.

 

[KatkaK]

Originally I thought the same, but now I am not sure. Maybe I dont understand the crucial idea of repeated-measures/mixed ANOVA well.

As I understand repeated-measures ANOVA (and mixed ANOVA similarly), several repetitions for each combination of factors levels and EACH subject have to be in the data. For example, for "time 0" and "banana" I should have more than one observation for each subject, however I have only one observation per person.
I mean the problem is that I have the data with repeated-measures, but in other sense. As I need the time factor for my analysis, there are no repetitions inside levels of factor on one subject. I would consider my data appropriate for repeated-measures/mixed ANOVA analysis if I dont need the time factor - I would have five measurements for "banana" and subject and five measurements for "water" and subject. As I need time factor I have in all 5 * 2 levels (time * meal) only one observation per subject, with no repated measures.

This is the reason why I left repeated-measures and mixed ANOVA and tried to do "simple" two-way ANOVA. As I tried to compute the correlation matrix of weight for all five time points I got very high (almost 1) correlation among time levels. Yes, this makes sense - the weight of subject in "time 0" would have to be highly correlated with its weights in other times. If I didnt have any information about the subject's ID (if I mixed the data) and then if I count correlations on unordered data, I could make "low" or "almost no" correlation. ANOVA does not depend on the order of observation in the groups, it works with means only. It gives the same results also for post/hoc analysis. It is not so suprising for me now.
The question is - if I take account the idea above, I think I could use two-way ANOVA and the question "dependence" of levels of time factor (from my original post) could not be a problem.

Am I right?

 

[Karabiner]

You wrote

water and banana (factor meal) were given to EACH of them a then they were measured in 5 different times (time 0, immediately after consuming water or banana, after 30, 60 and 90 minutes) - once after drinking water, once after eating banana.

If each participant received banana and was measured 5 times, and each participant also received water and was measured 5 times, then you have a 2*5 repeated-measures design (with a total of 10 measurements for each participant).

With kind regards

K.