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# Spearman's Rank and PMCC Watch

1. I have a few basic stats questions which I'd appreciate if someone could help me answer. These are conceptual really.

a) Often I'm asked to come up with a graph which has a Spearman's Rank coefficient of 1 but a PMCC which is not 1. For such a case, would it be acceptable to use an exponential-type curve (just sketching, talking about the shape) - as it wouldn't fit a straight line (so PMCC is not 1) but if you move to a higher x-value you will still always get a higher y-value? If Spearman's rank has to be -1 but the PMCC not quite -1, can I use a downward sloping graph of increasing negative gradient?

b) My spec says "understand that the value of a correlation coefficient is unaffected by linear transformations (coding) of the variables". Does this mean that if you translate the scatter points, it will not affect either the PMCC or Spearman's rank? What else does it mean? ("Coding" is confusing me.)

Thanks a lot.
2. Any help?
I have a few basic stats questions which I'd appreciate if someone could help me answer. These are conceptual really.

a) Often I'm asked to come up with a graph which has a Spearman's Rank coefficient of 1 but a PMCC which is not 1. For such a case, would it be acceptable to use an exponential-type curve (just sketching, talking about the shape) - as it wouldn't fit a straight line (so PMCC is not 1) but if you move to a higher x-value you will still always get a higher y-value? If Spearman's rank has to be -1 but the PMCC not quite -1, can I use a downward sloping graph of increasing negative gradient?

b) My spec says "understand that the value of a correlation coefficient is unaffected by linear transformations (coding) of the variables". Does this mean that if you translate the scatter points, it will not affect either the PMCC or Spearman's rank? What else does it mean? ("Coding" is confusing me.)

Thanks a lot.
a) Yes and Yes.
b) Translation does not affect Spearman's Rank, provided everything is translated the same amount.
See mathematical properties for the PPMCC http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient
4. (Original post by joostan)
a) Yes and Yes.
b) Translation does not affect Spearman's Rank, provided everything is translated the same amount.
See mathematical properties for the PPMCC http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient
Thanks

What sort of graph would have a Spearman's rank which is not equal to 1 but a PPMCC which is roughly equal to 1? (Question in my textbook to which I don't know the answer)
Thanks

What sort of graph would have a Spearman's rank which is not equal to 1 but a PPMCC which is roughly equal to 1? (Question in my textbook to which I don't know the answer)
All y increasing as x increases, (i.e. correlated) except one which is different perhaps?
6. (Original post by joostan)
All y increasing as x increases, (i.e. correlated) except one which is different perhaps?
That's what I was thinking, I guess it comes down to whether that will impact the PMCC much or not.

I just tried a case where 1 variable out of 7 was changed and the PMCC dropped from 1 to 0.83 so the impact is pretty significant. Obviously once the order is changed from exact Spearman's Rank is no longer exactly 1. Do you think this fits the roughly equal to 1 criterion though?
That's what I was thinking, I guess it comes down to whether that will impact the PMCC much or not.

I just tried a case where 1 variable out of 7 was changed and the PMCC dropped from 1 to 0.83 so the impact is pretty significant. Obviously once the order is changed from exact Spearman's Rank is no longer exactly 1. Do you think this fits the roughly equal to 1 criterion though?
You can't get it any nearer than only one variable changed.
Obviously if there were more variables, the effect would be less marked.

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