significantly different or significantly similar?

#1
Hi everyone,

I'm writing up my masters dissertation in biomechanics. I have carried out a study where 6 racehorses jumped over a hurdle on a synthetic (riding school) surface and a week later over the hurdle on a grass surface. I measured all the appropriate joint angles (marked on the horses for the computer to measure- I won't bore you with it too much!). With the resulting data I carried out non-parametric tests- one Wilcoxon signed rank to test differences and one spearman's coefficient to test correlation. The problem i'm having is this: where P=<0.05 and the initial hypothesis is retained (I hypothesised the horses do jump differently on turf compared to synthetic surface) on the spearman's the two sets of data correlate (r=> 0.6). So how can they be significantly different but also correlate? Its probably really obvious and I've massively overthought it but any help would be much appreciated!!
Many thanks,
Sara
 
#2
I think it has to do with data coming from the same horse, so correlation is quite likely in repeated measures designs, as is the case with your study. I could be wrong though.

Also this may sound like nitpicking but I assure you it's not: your alternative hypothesis is that the horses jump differently in the different conditions and your null hypothesis is that they do not. But the null is always implied! You don't retain the alternative hypothesis, you simply reject (or retain) the null - this is because you are doing "null hypothesis significance testing", which gets its name from the fact that you are calculating the probability value of obtaining an effect of at least that magnitude given that the null hypothesis is in fact true.
 

Karabiner

TS Contributor
#3
Suppose that you observe subjects a b c d e, and in the first variable they have values 1 2 3 4 5, in the 2nd variable they have 101 102 103 104 105. Obviously, the variables are extremely different with regard to their central tendency, but they are marching perfectly in step (high correlation).

With kind regards

Karabiner