Spearman's Rank - why a postive correlation on something that should be negative?

Question

okay, im really confused on this spearman's rank thing!
basically, i did an environmental quality survey and a population count, and found a correlation between the two: as the number of people increases, the environmental quality in that area decreses (gets poorer basically).
(does this mean that its a negative correlation right? im not sure, so tell me :P)
i tried to do a spearman's rank thing to prove this correlation, but instead of getting a number like -0.875 or whatever, i got a postive number: +0.9963.......

but doesnt this mean its a postive correlation then? or does it mean that im right? sooo confused, i hope someone can help mee! obvz, 10 points to whoever has the best nswer, but all suggestions are welcome x

thanks so much x :)

Answer 1

Are you sure you didn't invert the environmental quality rankings by mistake? In other words, did you give the rank "1" to the area with the best enironmental quality? Here's an example of how it should work:

Area A Population 100 Envionmental quality Index 95

Area B Population 200 Envionmental quality Index 90

Area C Population 10000 Envionmental quality Index 80

Area D Population 1000 Envionmental quality Index 87

Area E Population 2000 Envionmental quality Index 88



Area A Pop Ranking 1 EQI Ranking 5 Di=4 Di2=16

Area B Pop Ranking 2 EQI Ranking 4 Di=2 Di2=4

Area C Pop Ranking 5 EQI Ranking 1 Di=4 Di2=16

Area D Pop Ranking 3 EQI Ranking 2 Di=1 Di2=1

Area E Pop Ranking 4 EQI Ranking 3 Di=1 Di2=1



Spearman coefficient = -0.9



However if you inverted the EQI rankings you'd get

Area A Pop Ranking 1 EQI Ranking 1 Di=0 Di2=0

Area B Pop Ranking 2 EQI Ranking 2 Di=0 Di2=0

Area C Pop Ranking 5 EQI Ranking 5 Di=0 Di2=0

Area D Pop Ranking 3 EQI Ranking 4 Di=1 Di2=1

Area E Pop Ranking 4 EQI Ranking 3 Di=1 Di2=1



Spearman coefficient = 0.9833

Answer 2

How did you measure environmental quality? Did you assign an index for environment quality?

Regardless, both the Perason correlation and the Rank correlation should show the same results.

(1) Compute the r (Pearson correlation) and verify it is negative.

(2) Draw an x-y scatter plot with environment data on the y-axis and number of people on the x-axis. See if the graph slopes upward or downward (approximately).

(3) If they still show different results, check your formula and calculation.



If everything proves the correlation is still negative, then that is what the result shows for your area.

Answer 3

cidyah is largely right.



However, it is possible for pearson and spearman correlations to be quite different - even being of different signs, because they measure different things. One measures linear association, the other monotonic association.



however, I think the most likely explanation is that larger numbers on the environmental quality might mean worse, not better environment - which is why cidyah is asking about how it's defined.

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