# Assumptions for mix design anova with covariates

#### talgef

##### New Member
Hello

I Would like to nake a mix design (I HAVE TWO GROUPS -SICK AND HEALTHY), AND I made a cognitive measure of long / short exposure stimulus.
I want to add two covariates (depression and cognitive level). What assumptions should I met? I found assumptions for mix anova, and ancova- but not for "mix ancova".
In addition, the sick group has a significant higher measure of depression. Does it mean I cannot use this test?

Thank you

#### mmercker

##### New Member
Hi, at what point do you have repeated measurements of the same participants making the mixed design necessary? Did you perform long and short exposure stimulus at the same participants?

If the covariate differs between the treatment groups (e.g. evaluated by a significant T-Test) this is indeed a problem in ANCOVA, I would therefore not include depression as a covariate.

However, if you have a mixed design, it is more recommended to use a Multilevel Mixed Model rather than an ANCOVA, which requires less assumptions (e.g., no sphericity is required) and is more flexible.

#### talgef

##### New Member

Yes, I do have a mixed design, will interduce it shortly so it will be clear: dependent variable : A measure of mind wandering (MW), and I checked it when participant watch a long/ short stimulation (this is also the in between variable). The in between variable is two separate groups: healthy/ people with Parkinson. I also want to add two covariates because there is a significant pearson correlation between those and the MW measure: depression measure (there is a significant difference in the depression between the two groups) and a cognitive ability measure.

When I did Ancova with repeated measures - there was a significant interaction between time and group, and the two covariates were significant. However it seems I lack some of assumptions like linearity, and the significant level of depression between two groups.

Multi level mix midel- this what you mean? https://en.wikipedia.org/wiki/Multilevel_model

Can you use covariates with this?

Thank you very much

#### mmercker

##### New Member
Yes, this is what I mean. Here, you formulate your model directly as a regression model which has many advantages compared to ANCOVA, which are amongst others: they deal better with unbalanced design and missing values, you need less assumptions (no sphericity, no homogeneity of regression slopes), you have more flexibility regarding repeated-measures components, and so on. And yes, you can use an arbitrary amount of categorical predictors and continuous covariates. Which software do you use? I could provide you a corresponding code in R if you give me a sketch of your data structure

#### talgef

##### New Member
Thanks!

I use SPSS.

I could provide you a corresponding code in R if you give me a sketch of your data structure

I didn't understand well- what exactly do you want that I give you?
do you mean description of the experiment?
There is a conrtol group- 30 healthy/ 30 sick people.
We had 8 trails that people watch a simple stimulus (there are 4 short presentation and 4 long presentations). so we have a short measure of mind wandering score and long one for every patient - (this is the inbetween variable, and also dependent variable). In addition I have 2 covariates I would like to add: depression score, and cognition score.
all of the variables are ratio scale.

Is this what you mean?

#### mmercker

##### New Member
Hi, never mind, I'll give the variables some names:

data$MW = outcome (continuous and normally distributet, I guess) data$ID = participant ID
data$H = healthy/thick categorical variable data$D = depression score
data$C = cognition score data$LS = long/short measure

The following is the R-code:

#packages:
install.packages("nlme"); library(nlme)

#model:
model <-lme(data=data, MW ~ H + LS + H:LS + D + C, random=~(D|ID) + (C|ID))

#results:
summary(model)

Here, I think you are mostly interested in the significance of the interaction term H:LS, since this term tells you if short/versus long measure differs between control and thick people.

Finally, you should also check model assumptiions: 1.) Residuals of the model should be normally distributed for each predictor level (look at QQ-plots and histograms o residuals, or perform a Shapiro-Wilk Test), and 2.) Variances should be equal for each predictor level and along each coivariate (you can check this with scatterplot or Levenes test)

#### talgef

##### New Member
thanks!

But I don't understand- is it for excell? or SPSS? Or a program I should download? I don't have any backround in programing, so please explain this.

Thanks again

#### talgef

##### New Member
I just tried to install it, however, I cannot open now the icon on my desktop. Can it be because there is no connection to my real location (Im in Israel, but there is no Israel link connection, I picked a place in Europe instead)

#### talgef

##### New Member
I have another question regards the model u offered (with R). In this case do I need assumption of linearity? I ask this since in one of my covariates there is a statistical significant difference between the two groups.

#### mmercker

##### New Member
Yes, what you usually do after setting up the model is to look at residual plots (you get them in R via res(model)). Ideally, you plot every covariate versus the residuals. And if you see any residual patterns, you can e.g. solve this by adding nonlinear or polynomial terms regarding the corresponding covariate. E.g.polynomials of Nth order in the covariate X are created via poly(X,N)

#### talgef

##### New Member
I will use at the end ancova with repeated measures. Can u please tell me what are the assumption for this test?