I am calculating the correlation values between two data sets of size 257. I want to know what is the critical value of correlation for a sample size of 257. I tried searching on the web, but critical values corresponding to 100, 200 and 500 are seen but not 257 specifically.
So, what is the formula to calculate the correlation critical value? There are a few online tools to calculate that, but I would like to know the formula so that I can integrate it into the code I am using so as to get correlation values along with the critical values.
First of all, Ben Babcock's answer was awesome. I have adapted his R code to the t-distribution (so that you WILL get the same critical r values as you see in the tables). I also managed to simplify it a bit, but ultimately this is just a modification of Ben's code.
critical.r
Have a look at Fisher transformations: http://en.wikipedia.org/wiki/Fisher_transformation
Here is a code snippet for (I guess) R: https://personality-project.org/r/html/fisherz.html
Note that you typically test whether you correlation is significantly higher than 0. With large enough sets any non-zero correlation can be significant. If you want to compare two correlation coefficients (e.g. two alternative models for the same data) you can use this: http://www.lesn.appstate.edu/olson/stat_directory/Statistical%20procedures/Correlations/a_test_of_the_equivalence_of_two.htm
Dear Ravi, this is the formula. It's a little complex:
n: number of your pairs
r: correlation coefficient you've calculated
e: 2.71828
Pi:3.1416
If the result is less than 0.05 the correlation is significant. it tells the exact p-value you seeking for.
Cheers
This may be beside the scope of the question, but in case your data are time series, make sure to check that there is no autocorrelation within the series. While the correlation coefficient is not particularly sensitive to this, the significance is. I believe this is commonly overlooked.
Best of luck,
Tom
Dear Tom, I don't see any mentions of time series here. But if there exist, you're right the series trend should be considered.
Dear Ravi, I should note that in such big data as yours the critical value of coefficients change very small with change in the number of data and can be negligible.
Statistical software (minitab or statistic) exists along with the calculation of R2 Pearson, the P value associated. If p
Hello Ravi,
This is probably too late of an answer, but I had the same question myself when attempting to correct for familywise error in a correlation problem (typically gives you off-the-wall critical alphas, as you know). After dusting off some old stats books and talking with some smart folks, I tried my best to implement what Robbie was suggesting above using R. The following ideas are certainly not original to me, though I did make my homemade R code. Enjoy!
# Critical Pearson's R value from N, critical alpha, and null correlation
# value (typically zero, but it doesn't have to be).
# Two-tailed, significant difference from any specified correlation value
# using the basic z test formula typically used with Fisher's r to z.
critical.r.function
First of all, Ben Babcock's answer was awesome. I have adapted his R code to the t-distribution (so that you WILL get the same critical r values as you see in the tables). I also managed to simplify it a bit, but ultimately this is just a modification of Ben's code.
critical.r
Is there any online source to calculate the Critical value for r for given df
Adding two to the df gives you n, which will work with either Elizabeth's or my own code (critical r functions). Use that to get your answer.
Thanks Mr.Ben Babcock. If u dont' mind pls illustrate for the calculation of r table value for N= 414 at 0.05 level of significance
Thanks Mr.Ben Babcock. I don't know programming.
Kindly give the formula so that i can try manually
please i want critical values for a sample size of 218 significance of 0.05.
The critical value of the "Pearson Correlation Coefficient" can be found by this formula:
Critical Value of r = Sqrt((t^2) / (t^2 + df))
(where the t values are from the Critical t Table)
df = n - 2
You can see all the formulas and the links to the tables here:
https://onedrive.live.com/view.aspx?resid=45E1BEFAF548E9C0!12883&ithint=file%2cdocx&app=Word&authkey=!AMhh0MwjaBWVTxI
@ Savarimuthu vincent de paul
You can use this calculator to solve many questions on Hypothesis Testing including finding the critical values.
http://www.hypothesis-testing.appspot.com/
Thank u. I checked with N=100. The value coincides with r table value.
Congrats
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