# What type of ANOVA/model to use for hypothesis test?

#### PhD

##### New Member
I am trying to work out the most appropriate way to analyse some data from
an experiment and would be really grateful for any ideas. The experiment involved getting people to perform an action using four different types of object, each obstacle type at two different sizes (same two sizes for all obstacles).

I want to test the hypothesis that [kinematic parameter measured during the action] is not affected by object type or size.

I have four object types, each at two sizes = 8 objects.
Each subject performed five trials with each object.

I was thinking I could use a two-factor ANOVA with object type and size as factors but the same subjects performed trials with all 8 objects. Does this mean that I should be using a different model as the groups will not be independent? A repeated measures ANOVA?

I also don't know how to deal with the fact that I have five trials from each subject for each object type-size combination - can I just group all the object type-size
trials from all subjects or should I be acknowledging that some are repeats from the same subject?

Thanks very much in advance.

#### noetsi

##### No cake for spunky
I took a single course with ANOVA so take my comments with a grain of salt. As far as I know one subject doing each level of size at each level of object is the normal way to measure a two factor ANOVA (there are special designs where this is not the case which are more complex). Normally you do repeated measure ANOVA if some interaction over time is occuring. What may be a problem in your case is order effect. That is if the order in which they used an object of a certain size varied (or vice versa) and this mattered. You deal with that by the way you measure your data (your design) not repeated measure ANOVA to the best of my knowledge. Regardless of that issue you need to test for an interaction effect of size with object to see if that is an issue (you normally hope its not as it complicates the analysis - sometimes signficantly).

#### GretaGarbo

##### Human
Did you randomize the experiment and in particular the order of the eight objects to each person?

(And did you use formally random numbers?)

#### PhD

##### New Member
Thanks for your comments.

GretaGarbo - Each subject performed 40 trials (8 objects x 5 trials with each object) and the order of these trials was randomised (using formally pseudorandom numbers).

#### GretaGarbo

##### Human
@PhD!

It is randomized, then I guess there is nothing to prevent you from running a three-way-anova with subjects, size and object type as factors.

I want to test the hypothesis that [… Y ...] is not affected by object type or size.
“is not affected...”. So maybe you want to try a bioequvalence test. (Roughly to confirm that they are alike.) Search the web for it.

Don't forget to check the residuals and so on and remember that the normal distribution is not the only parametric distribution. You can use many more distributions within the generalized linear models.

#### PhD

##### New Member
When I say 'is not affected' I mean that my null hypothesis is that there is no effect - sorry for not being clear. I am expecting to find differences.

#### noetsi

##### No cake for spunky
Be sure to test for interaction effects between your main effects like size and object. If you have signficant interaction effects this changes analysis signficantly.