help with ANCOVA results

#1
I need to do an ANCOVA for an ecology paper, but as the title says, I need help to report the results. I ran the ANCOVA in Excel using the xlstat plugin, but my teacher wants us to report the main effect, the covariate, the interaction term and the ANCOVA table. Sorry if this seems like a simple question, but as you can see I am not stats saavy, as I haven't done any in a long time. I can't seem to find this information in the results of the test, or I just don't know what I am looking for. Do I need to run further analysis? The teacher won't help us and I was not able to find the information anywhere.

Basically, I am trying to see if both log volume (continuous variable) and decomposition stage (categorical variable) influence arthropod abundance. If I'm right, I should use ANCOVA as to "merge" the regression model (log volume) and the ANOVA model (decomposion stage). The teacher approved, but I am just not sure how to properly interpret everything other than R square and p values. I tried reading online, but everything I found was not clear to me (and we do't have a textbook, it's an ecology class and not a stats class, although it is part of it)
Thank you very much for your help

P.S. I attached the excel file to the post if it might help, the ANCOVA is on the Decomp graph sheet
 
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#2
after talking with a friend of mine, I understood the following (if I'm not mistaken):
-ANCOVA evaluates whether population means of a dependent variable (DV) are equal across levels of a categorical independent variable (IV) often called a treatment, while statistically controlling for the effects of other continuous variables that are not of primary interest, known as covariates (CV) or nuisance variables.
-the covariate would be log volume in that case (interaction, not confounding)
-the main effect would be the effect of decomposition stage (categorical variable) on the abundance of arthropods
-and the interaction term would be the effect of both independent variables on the dependent variable (not so sure?)

What I am still not sure is that I feel like I should have numerical values to quantify these effects, but I don't understand where to find them.
 
#3
I didn't realize how unfriendly xlstat might be. My lack of French doesn't help either.
Here are the results with and without the interaction using the data in A15:C43, if they are any help. See if you can find any of the numbers in your printout.
There is no significant interaction. If there was an interaction, then the slopes of the graphs you have drawn would be noticeably different but they are all much the same.
So, for the second run, the interaction term was removed.
You can tell from the high p value that Stage has no significant effect. Volume might be a candidate high volume/low abundance but has yet to get to significance.
You might try an ordinary regression relating abundance to volume and ignore the Stage.
 
#4
Thank you so much, that really helps. I'm sorry I know my spreadsheet is really messy, cause I was trying to figure things out. I,ll do as you say and run a regression, but I would still need to report the fact that there was no significant interaction with the stage.

Was I right with what I said in the previous post regarding covariate, main effect and interaction term? I udnerstand that the interaction term is Vlm*Stg, but whats the value I should use? Its sums of squares?

As for the covariate, I should just describe what it is, there is no numerical value? And I think for the main effect there should be a value, is it the Sums of Squares of Volume?

I know what I'm asking is alot and I am so grateful for your help!
 
#5
Also, just to be sure, on the tables you provided, it says Analysis of Variance, which is an ANOVA, but I want to do an ANCOVA. Looking at the table and the fact that there is both Volume and Stage, as well as the interaction term, I guess that it is an ANCOVA.

Agin, I'm sorry if this sounds stupid, I just want to make sure I'm doing the right thing.
 
#6
I start to understand! Vlm*Stg is the interaction term, would the covariate then be volume and the main effect stage? Do you quantify them with any value (let's say interaction term = 3.50) or you just describe them an significant or not?

Thank you so much it really helped
 

Dragan

Super Moderator
#7
... it says Analysis of Variance, which is an ANOVA, but I want to do an ANCOVA.
It is still an Analysis of Variance. In fact, ANCOVA is combination of regression and ANOVA and the end result is that ANCOVA is really nothing more than doing an ANOVA on the adjusted means.
 
#9
What would you say the sample size is? 30 sites were sampled. Each one has their log volume measured and were categorized as one of the decomposition stage (1 to 4). Is the sample size 4 or 30? I'd say 4 because there is 4 groups, and each samples in the 4 groups have their own log volumes, but in the end n = 4 (I don't know hot to phrase it properly haha)
 
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noetsi

Fortran must die
#10
A good rule of thumb is not to do regression/ANOVA in excel...although I am sure in the class you have little choice.

As dason noted ANCOVA is identical to regression (or ANOVA) when you mix dummy predictor variables with interval ones. ANOVA/ANCOVA and regression are the same method developed by different people using different wording.
 
#11
Ancova was originally developed to allow for an extra variable that might influence the result of the anova. Then people realized that regression and anova were mathematically the same so these days you can use a General Linear Model which allows any number of numeric and categorical predictors. The output above was done using a GLM.
 
#12
Thanks guys that's useful! The thing is the teacher literally mentionned that our experimental design was an ANCOVA and that I must do an ANCOVA with the data I have. I know he is good with stats so I guess there is a reason for him to ask for an ANCOVA and not a GLM? Is it more simple to use?

In any case, thanks you've been really helpful
 
#13
Terminology can differ from field to field. A covariate is simply any numerical predictor. If it is significant (p<0.05), it is quantified as a slope or rate. A factor is a categorical predictor. If it is significant then at least two of the groups are different, and you can then test between them (post hoc tests with p values). You can quote the average levels.
An interaction is difficult to quantify. Just say sig/not sig p = ... Sometimes tutors like you to quote the F value as well. F(3, 20) = 0.179 in this case.
 

noetsi

Fortran must die
#14
ANOVA really is GLM or a form of it anyway. But for a class just look at examples of desired results in your text or handouts and reproduce that with your data.