Question:
Is a correlation coefficiant of 0.68 strong?
anonymous
1970-01-01 00:00:00 UTC
Is a correlation coefficiant of 0.68 strong?
Eleven answers:
Shan
2008-01-15 15:07:13 UTC
A correlation coefficient of 0.68 is not a "strong link", but it is definitely a link. You can safely say that your two variables are related, but you can't say that they are dependent on each other.



If you had a coefficient of at least 0.90 - 0.95, you could hypothesize that motivation increases directly with decision-making power. Instead, you should be saying that there is a clear link between motivation and decision-making power.



Also, you should try correlating it with a different best-fit line. You might get a stronger correlation if you try using a polynomial function, logarithmic function, or an exponential function.
yodellingbear
2008-01-15 15:11:15 UTC
Yes - see the table in http://en.wikipedia.org/wiki/Correlation



If you really want to know the answer, you might want to use so slightly more powerful statistical machinery than you're currently using. I would suggest finding the sum of squares of the residuals for both the y=mx+c fit that I assume you're using and a simple y=c model (i.e. y=the mean of the data). These two possibilities can then be compared using either ANOVA or Aikake's information criterion.



The pdf "Fitting models to biological data using linear and nonlinear regression. A practical guide. " at http://www.graphpad.com/index.cfm?cmd=library.page&pageID=12&categoryID=6 should tell you all you need to know to do these tests.
stephieSD
2008-01-15 15:07:11 UTC
A correlation coefficient alone can NEVER prove a cause and effect relationship. 0.68 is fairly strong. The highest is 1.0, and the lowest is 0.0, so 0.68 is definitely on the "stronger" side. However, 0.8 is definitely stronger than .68. I'd say that .68 is "moderately strong."
anonymous
2008-01-15 15:06:27 UTC
It's quite a strong correlation, but still leaves a bit of room for differences in the two variables.



Correlation coefficients are (in magnitude ) in the range 0 - 1, 1 being perfect correlation.



I'd say that your value is just on the border of saying yes there's a significant correlation.



Think of it as saying that the one variable goes 68% of the way towards explaining the other.
?
2016-05-25 11:46:02 UTC
I don't think so much between the creativeness and the IQ.....my dad was a high school dropout and not always the sharpest knife in the drawer, but man, he could draw! He had true artistic ability. However - maybe more of a correlation between IQ and the NEED to create. The need to create as a means of the mind to stretch and play and refresh and just generally have a little fun before it settles down to "problem-solving" and the other usual tasks it needs to attend to. And if that's true....explains why my brain has been feeling like it's been curling up and dying lately...Am I smart? I dunno...does it mean you're smart when you're doing college-level work in junior high? When the guidance counselor is trying to get you take a Mensa test at age 15? (I took my anarchy seriously in those days.) I know I feel like a caged tiger if I can't DO something. And when I'm content...I write. And it would be nice to find one brain that can really truly try to keep up with me. Oh. Uh-oh.....LOL ((((((( < I > )))))))
Speeddemon
2008-01-15 15:12:16 UTC
anything above 0.6 is considered a strong correlation. this correlation shows they are associated but not necessarily directly causal of each other.



is X the cause of Y?

is y the cause of X?

or, is Z the cause of a rise in both X and Y?
Goldie Locks
2008-01-15 15:05:17 UTC
1 is a strong link and - 1 is a strong negative link.

.68 is between these two so it would be a moderate link.

Think of the correlation like a line or continueum.





-1_strong neg link--------0--no-correlation------------- +1stong positive link
Kara
2008-01-15 15:04:33 UTC
moderately. a correlation coefficient of -1 and 1 are the strongest and 0 means no correlation. Therefore .86 is strong and .13 is weak
invsque
2008-01-15 15:03:59 UTC
1 means perfect correlation while 0 means no correlation.



That is not a strong correlation.
hfshaw
2008-01-15 15:40:35 UTC
A value of r=0.68 is actually fairly large. It means that r^2 = 46.2% of the variance in your dependent variable can be explained by a linear relationship between the independent and dependent variables. In your case, almost half (46%) of the "motivation" of your employees can be "explained" by their degree of involvement with decision-making.



The actual *significance* of r depends on how many data points are in your sample, and can be quantified using what is called the "t-test". If certain assumptions about the data are true (e.g., the errors are normally distributed), then one can determine what the probability of getting a particular value of r is, simply by chance. That is, we ask what the probability of getting r = 0.68 is, if, in reality, the data are completely uncorrelated (r is actually equal to zero).



First, we calculate the t-statistic for the data:



t = r * sqrt((N-2)/(1-r^2))



where N is the number of observations (data points) in your sample, and N-2 is the number of "degrees of freedom" in your sample. (It's two less than N because one has to assume that the mean and variance of the real population are equal to the mean and variance of your sample.)



Then one compares the value of t calculated above with probability of obtaining that value for a t-distribution with the same number of degrees of freedom. That's the probability of getting the observed r value by chance. You then have to assess whether that probability is significant.



There are actually two cases to be considered here. If one's hypothesis about the relationship between the independent and dependent variables has a particular sign or direction (e.g., higher involvement will result in higher motivation) then one does a "1-tailed" comparison,whereas if the hypothesis makes no assumption as to the sign of the correlation (e.g., involvement will affect motivation, either positively or negatively), then one does a "2-tailed" comparison. In your case, I think the 1-tailed comparison is appropriate.



The little web applet at the second source below will do these calculations for you. In your case, for the sake of illustration, if you had data on 10 employees (N = 10), then the 1-tailed probability of getting a value of r=0.68 by chance, if there is actually no correlation, is 1.5%. (The 2-tailed probability is 3.0%). Most people would consider this highly significant, and one can "reject" the hypothesis that there is no correlation between the variables.



Before you do any of this, however, you should plot your data and look at it! Do the data seem to cluster around a straight line, or is there curvature in the cloud of data? Are there "odd" (outlier) data points? Are all the data, with few exceptions, clustered in one "cloud"? Remember that the usual correlation coefficient *only* ascertains the degree of linear (straight-line) correlation between your variables. If the data have an obvious non-linear relationship, then a linear correlation coefficient is not the appropriate measure to use to determine if there is a statistically significant relationship between your variables.



Finally, you need to remember that correlation is *not* a proof of causality. That is, just because A and B are correlated does not mean that A causes B, or that B causes A. For instance, if C causes A and C causes B, but A has no effect of B, A and B will still be acausally correlated because of their mutual dependence on C.



For example, I can imagine that only highly paid managers are involved in decision-making, and that highly paid employees are highly motivated. One would then find that decision-makers are highly motivated, yet the real "cause" of their motivation is the fact that they are highly paid, not that they are involved in decisions.
rlk_117
2008-01-15 15:03:18 UTC
No, that's pretty weak.

A strong one would be at least .90


This content was originally posted on Y! Answers, a Q&A website that shut down in 2021.
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