Correlation mystery

[nonstoptaxi]

Hi everyone,

another statistical question:

 

If 0= no correlation, 1=perfect correlation, then how can a 'r' statistic be significant (p < .05) when it's stands at .14 for instance? (that's what my spss is reporting). Since this amounts to only 1% of the variance of one variable being accounted for by the variance of the other variable, this really does perplex me.

 

Can someone give some guidance on this? Many thanks,

 

Jon

[Glider]

The strength of a relationship and its level of significance are different things.

 

Significance only tells you the probability of being wrong if you reject the null hypothesis. In this case you have < 5% chance of being wrong by accepting the alternative (experimental) hypothesis that there is a relationship between the two variables. This does not mean the relationship has to be a strong one. It only means that you can be >95% sure that the relationship (however weak) does actually exist.

 

One factor to consider is experimental power, and particularly sample size. This is critical in correlation. With a very large sample, comparitively weak correlations can be reported as significant. With a small sample, comparitively strong correlations can be reported as non-significant. This is why we report n as well as r and p in the results.

 

Another thing to remember is that SPSS, as powerful and useful as it is, is only software; it has no common sense. If you ask it to, it will test for a correlation between number of fillings and heart rate (a completely meaningless test as neither can be considered a valid predictor of the other). SPSS will simply answer your question: is there a statistically significant relationship between variable x and variable y?

 

It is always the responsibility of the researcher to ensure that the question is sensible and to decide whether the answer is meaningful. So, whilst SPSS may report that a correlation r = 0.14 is statistically significant (p < 0.05), it is for you to decide whether this relationship is meaningful. I.e. does such a weak relationship have any real-life meaning? This depends to a large degree on what you are investigating.