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correlation

Hi 

Is this true that in some analyses, especially Microbial diversity, linear correlations are weak, but still biologically significant by weak I mean 0.27 or -0.14, 0.07,-0.08? I dont agree that this true

if a correlation is weak but significant would it mean it is correlated having above values.

Any comments?

Thanks

Re: correlationThanksRe: correlation

I encourage you to think of correlation as a descriptive statistic...not an inferential statistic. Once you start talking about 'significance' you are in inferential statistics land...not descriptive statistics land.

Re: correlation

Jim provided an excellent response. This is just a little added advice: make sure you are checking your data/model for non-linearity, outliers, unaccounted variables of time, temperature or mixtures.

 

Open this link from University of Florida Health and scroll down to the plot of  Fuel Used vs. Speed, it is a picture of a strong relationship, but a small correlation negative linear correlation.

http://bolt.mph.ufl.edu/6050-6052/unit-1/case-q-q/linear-relationships/

 

Of course a classic example can be found in the Anscombe data. Run the script below. Y1 is what is expected for a 0.66 RSquare ( approx 0.816 linear correlation). Y2 and Y3 have a much stronger relationships: Y3 is weakened by an outlier and Y2 has a quadratic relationship with X (wrong model). Then look at Y4, the data results look more like an outlier, the result is inconclusive.  Diagnostic plots and residual anayses are recommended procedures for and "modeling" of relationships.     

dt = open("$sample_data/Anscombe.jmp");

dt << run script("The Quartet");

qwin = Window("The Quartet");

xx= (qwin<<CHILD></CHILD>

 

Re: correlationThank you JimRe: correlation

There is not  a fixed rule on this.   The topic of study has to be taken into account.

Re: correlationThanks Jim
This is what I thought. knowing that the number is very small would you count this as a weak correlation or would you neglect it ?Re: correlation

Statistical significance of a correlation does not mean that the correlation is relivant or important.  Statistical significance basically implies that the value of the correlation is probably a true relationship.  And even correlations of .27 or -.14 can be significant, but the amount of the relationship between the measurements isn't very strong.