# What ANOVA fits best?

#### Jurij

##### New Member
Dear all,

can anyone please advice me which ANOVA is the most suitable: An athlete has perfromed multiple runs at constant speed with three different shoes. The kinematic data was analysed for different number of cycles per shoe condition. I want to compare mean cycle times between different shoe conditions (later also other parameters). Do I need to use repeated measures one way ANOVA? I am using Matlab for the statistic analyses but the repeated measures ANOVA does not support unbalanced designs. What should I do? Can I simply perform general one way ANOVA or is there a way to balance the model?

Additional question: The runs were measured in three days, in each day there were 3 sessions and in each session there were 3 runs. Each session was performed with one of the three different shoes. All runs were at same speed.
How can I check if the days, sessions, run order and shoe condition have affect on the mean cycle time? Do I need to use multiple way anova? There is also a similar example
for within model repeated anova (http://www.mathworks.com/help/stats/repeatedmeasuresmodel.ranova.html#bt8plsk-19), but as said before, it does not work for unbalanced data.
Is it necessary to check the normality and sphericity of the data? Or can I just assume them?
I am confused and would appreciate any help. Thank you.

Jurij H.

#### mmercker

##### Member
Hi, I think you can neither artificially balance the design nor use a simple one-way ANOVA. You should analyze the data with a Mixed Effect Model (also called Hierarchical Model or Multilevel Model), where the athlete-ID is a random (intercept) coefficient, the cycle time is the (continuous) outcome and the shoe-type is the (categorical) predictor. Here you don't have to worry about a balanced design.

Regarding your second question: You can also analyze this in the context of Mixed Effect Models, here your Athelete-IDs are appropriately nested within the other variables. And you can compare different models with different nested structures via the AIC-value.

#### Jurij

##### New Member
Hi, thank you for your fast reply. Did you mean linear mixed effect ANOVA model? There is an example in Matlab (http://www.mathworks.com/help/stats/linearmixedmodel.anova.html) which considers fixed effects. Its the first time I hear about this method. Could you please advise me how to continue. How should I define the effect formula (for the Matlab example it is: lme = fitlme(ds,'Yield ~ Fertilizer * Tomato + (1|Soil) + (1|Soil:Tomato)',...
'DummyVarCoding','effects'))?
Regards,
Jurij

#### mmercker

##### Member
Hi, I am not used to Matlab, are you probably able to use R as well?

#### Jurij

##### New Member
Unfortunately I do not have R.

#### mmercker

##### Member
Hi, it's a free open source software, you can just download and install it. In case you do this, I can provide you a template code for the multilevel analysis

#### Jurij

##### New Member
Hi, I have downloaded R. I recommend myself for the template you offered. My e-mail is: jurijhl@gmail.com
Is the following procedure ok? I should firstly run a Mixed linear effect ANOVA analysis. If it gives p-value(s) below 0,05, I need to run additional t-tests between individual shoe conditions. Is there maybe a function (test), which compares all the post-hoc tests at once? Thank you. Regards,

JH