# ANOVA with Repeated Measurements based on randomly assigned repetitions

first of all the basic idea of my experiment: changes/differences of reaction time (RT) after 3 different types of sport (a: no jogging=SP1; b: 10min of jogging=SP2 and c: 30min of jogging=SP3); 36 subjects (SUB) are randomly assigned to one of the 6 possible combinations of “sport” (abc, acb, bac, bca, cab and cba, see variable FCT). So the first subject has "a" on day 1, "b" on day 2 and "c" on day 3; the second one might have "a" on day 1, "c" on day 2 and "b" on day 3 [etc...]

Therefore I have the following table containing my raw data:

SUB    SP1    SP2    SP3    RT1    RT2    RT3    FCT
s01     a      b      c     0.1    0.4    0.8    abc
s02     a      c      b     0.6    0.3    0.8    acb
s03     b      a      c     1.0    1.0    0.7    bac
s04     b      c      a     0.3    0.7    0.1    bca
s05     c      a      b     0.3    0.5    0.4    cab
s06     c      b      a     0.0    1.0    0.3    cba
[.]    [.]    [.]    [.]    [.]    [.]    [.]    [.]
s36     c      b      a     0.1    0.9    0.0    cba


In general I think I have to use an ANOVA based on a repeated measurement design - but I have no clue on how to deal with the factor “sport” since it also changes with the repeated measures per subject;

Is it OK to use the variable FCT defined by 6 possible combinations of “sport” as one factor with 6 categories with the repeated measurements-ANOVA?

It depends on the software you are using for this analysis, but you might need to lay your data out differently.

You have the same information laid out twice in the Sport columns (SP1, SP2, SP3) and in the FTC column. You don't need both, but depending on the software you are using, you will need this information either laid out as you have done for FTC, or as you have done for SP1, SP2, SP3.

So the simple answer to this questions is that you need to remove either the SP columns or the FCT column, depending on the format of this information that your software requires. However, Rather than removing these columns you should simply ignore them for the purpose of your analysis - or filter them out, as these columns might be useful for further analysis you do. Can you tell us what software you are using, so we can advise which format you need to use?

It would also help if you make clear your aim. Are you simply tying to see whether RT varies with type of sport. This would require a simple repeated measures one-way ANOVA.

Do you also want to know if a particular combination of sports results in consistently better RTs?

Further i'm not clear on where your 'results' are......are these shown in the RT columns. E.g. S01 obtained an RT of 0,1 for sport A (as shown in the RT1 column). Should the comma be a decimal point?

• Thank you. I am aware that columns SP1, SP2 and SP3 is sort of "redundant" information - I just wanted to be sure that the basic setting of the study is more clear; Regarding the results I am interested in: I want to know if the reaction (=RT) changes over time and I also want to know if the type of sport has an impact on the reaction measuerement. Therefore my idea was to simply define the additional variable FCT wich would be used as an additional factor in the ANOVA... Regardig the software I want to use: SPSS and R - both of them are available here in our departmenet. Mar 17 '14 at 10:23
• Ok, Firstly: If you use SPSS you would need the SP1, SP2, SP3 columns but not the FCT column, in order to run a repeated measures One-way anova. You would then look for a main effect of 'sport' - this will tell you, for example, whether RT get better with SP3 (30mins jogging) compared with SP2 (10mins of jogging) and SP(0mins of jogging). Mar 18 '14 at 11:42
• Secondly: Your 2nd question of interest appears to be "Does the RT (averaged across all sports) increase with any particular combination of sports". Most simply you could do another one-way anova looking at the effect of FCT on RT Score. The DV would be RT (containing an RT score for each participant averaged across sports) and FCT as the IV. This would then tell you if a particular combination of sports resulted in better reaction times across all sports. Mar 18 '14 at 11:51
• Thirdly: Whether FCT can be added as a factor in your first ANOVA (the oneway anova examining the effect of SP on RT) is a more complex issue. You could in theory add it as a factor to this anova. However i'm not sure this is justified. Can you tell me what your is justification for thinking that the order of sports might have an effect on RT is? This might make it more clear if it is worth examining this at all, and whether it is worth adding it to the first ANOVA model Mar 18 '14 at 11:52