I am analysing a stack of data to see if changes in PPR are correlated with changes in EPSCs after LTP induction. On graphpad 6 I use the function to correlate and I have a strong r but a non significant p. I don't know how to explain that. Anyone can please help me?
I thought it can be because of the few amount of data I am correlating (n= 7; r= 0.0557; p= 0.1994).
Thanks
The correlation is independent of sample size, whereas the p value is affected by sample size. What is more important to you, the correlation or the p value?
For me is more important to know the correlation between these datas. If there is no significant p value, means there is no difference between the data but this does not imply that there is no correlation also, right? What I also don't get is if the correlation and the p value are independent here
Actually, I just saw that your correlation is 0.0557 (at first glance I thought that it was 0.557). It would be hard to believe that such a low correlation (close to zero) would be meaningful in any context.
However, getting to my point about sample size and p values, I will demonstrate the effect here, using Stata and the correlation = 0.557.
* define correlation matrix
matrix C = (1, 0.557 \ 0.557, 1)
* generate X and Y variables with a correlation of 0.557 and sample size of 7
corr2data X Y, n(7) corr(C)
* run a pairwise correlation and get p-value
pwcorr X Y, sig
* result r=0.5570, p=0.1940
* Rerun this whole thing exactly the same way but use sample size of 100
* result r=0.5570, p
You can focus on the effect size rather than p-value. This implies that you have a high effect size once your r value is high. Yet the low number of samples is always a problem. Good luck
Find attached some papers about the subject.
Following up on Ariel's example, the 95% CI with n = 7 (computed via corrci command) is very wide.
corrci X Y
(obs=7)
correlation and 95% limits
X Y 0.557 -0.338 0.923
HTH.
Greetings,
The correlation you listed (r=0.0557) tells you that you are looking at two variables that appear to have little to no collinearity. I fully agree with Ariel that for such low correlation (and numerically speaking even lower coefficient of determination) statistical significance is bound to be low.
However, statistical significance will be more dependent on the sample size than on the degree of correlation/determination. Consequently, for very large sample sizes with almost no collinearity, you may see highly statistically significant results, and vice versa (e.g., you may see very high correlation/determination without statistical significance in a small sample).
The key questions here are: (a) is correlation or significance more important? ; (b) what is the expected vs observed degree of correlation? ; (c) what is the significance of such relationship(s) in practical application of research?
That last question is perhaps the most relevant... two further examples:
1) If you happen to look at variables that may have high degree of correlation but the resultant change in process or practice makes little to no practical significance, then you should be asking the "who cares?" question
2) If you happen to look at variables with small degree of correlation, but even the slightest change in the associated process or practice will result in dramatic practical consequences, then the approach should be "can't ignore it"...
The main point here -- correlate your research results with their impact on real life processes and practices. If your research leads to any change that results in more than minimal process or practice alteration, then you should never ignore it. And please remember... change can be both positive or negative, so going from one level of correlation to another may result in either desirable or undesirable change, regardless of significance. You will not know the associated consequences until you either accurately model or actually implement said change.
Hope this helps,
Stan.
I think the original first answer given are the best. His R = 0.0557 is obviously a typo (considering the corresponding p-value). He is considering a R = 0.557.
In summary, your sample size if the main issue here.
I have a similar question. I am running a correlation between age (two groups old vs young) and a variable. The correlation is -.103 with a p value of .070. I am interpreting this as there is difference in the relationship between age and the variable for both groups, is that correct?
As others mentioned the significance is sensitive the sample size. There may be a very weak correlation on a very large file, which will end up shown to be statistically significant. This correlation is not to be ignored if the underlying implications of such a weak correlation make sense to be reported to the research community. Any r > 0.1 on a large file is always something to look into.
Hello everyone,
I apologize for jumping in, but I have a similar problem.
I calculated Spearman's correlation for several different combination of variables. In some cases, the correlation is low, for example 0.15 (which would mean that variables are not correlated), but the sig. is lower than 0,05 (which would mean that correlation is significant, n=225). If H0 is "there is no correlation", while H1 is "there is correlation between variables", how should I interpret results? If I look Sig. I would need to reject H0 and conclude that there is correlation between variables, but if I look at the Spearman's coefficient the conclusion should be that there is no correlation. At the same time, I have a case (different sample, n=10 , not the same as in my first example) where correlation is 0,50, but sig. is higher than 0,05. Is that mean that I should accept H0 (there is no correlation), even if the correlation is 0,40?
I see that the reason is probably the size of the sample, but I'm not sure how to interpret the results and whether the results can remain as they are or I have to do some new, additional testing?
Thank you a lot in advance!
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