Does zero-mean-unit-variance standardization have an influence on knn?

I just recently started to deal with data mining. Even after reading some articles it's still not always clear to me, when scaling makes sense, when to use which scaling and when (in general) it has no effect.

As it is my understanding, standardizing data so it has a mean of 0 and a variance of 1 should have a significant influence on knn - since attributes with different distribution will be standardized and so the distances may change dramatically.

However, I conducted some experiments in weka, for instance with the diabetes example data set. I tried the IBk classifier with k=3 for the original data and then for the standardized data - Yet the results are 1:1 the same. So my questions are:

• Is my assumption wrong that zero-mean-unit-variance has a significant effect on knn?
• If not, why is there no difference in the classification result in weka?

Edit: I did this little calculation:

x    y    z    length
------------------------------
0    0    0    0
0    100  3    103
1    50   5    56

Mean an variance for x, y and z:

       x    y        z          
mean    0.33    50.00    2.67   
var     0.33    2500.00  6.33

After scaling:

x    y     z     length
------------------------------
-1  -0.02 -0.42  1.44
-1   0.02  0.05  0.93
 2   0     0.37  2.37

So the second result now is closer to (0, 0, 0) after scaling than before, which seems to support my assumption. Then it is still unclear why it seemed to have no effect on the classification in weka.