I'm not sure what you mean by testing correlation with a t-test, since correlation is usually tested with Pearson's r, Spearman's ρ, or Kendall's τ. But anyway, there is no need to look up critical values from a table anymore, pretty much any statistical software or programming software includes these distributions. For example, in R, you can look up the critical value at any alpha level from a t distribution with any number of degrees of freedom. (Anyway, with a large number of degrees of freedom, the t distribution approximates the normal distribution, i.e. the critical value for two-tailed alpha=.05 approaches ±1.96.)

Dear Suman Maity,

There are the tables for the values of quantile of student's t-distribution with V degrees of freedom and Alpha significance level when the degrees of freedom is infinite. For example:

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as Stephen above, i'm not too sure what you're asking exactly

anyway, when it comes to spatial data, testing often (i have not said "always" ... but ... "very often" might be appropriate) becomes a tricky problem requiring more than a simple t-test (or whatever other simple test) because of the autocorrelation problem (residuals in locations close to each other tend to behave in the same way, therefore breaking the iid assumption ...)

so the problem might not be that you have too many degrees of freedom (the normal approximation is just fine) but rather that you might have many many spurious degrees of freedom !

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you can have a look here :

http://www.whoi.edu/cms/files/DormannEcography30_57164.pdf

"Spatial auto-correlation is a subtle, less obvious form of subsampling (Fortin and Dale 2005): samples from within the range of spatial autocorrelation around a data point will add little independent information (depending on the strength of autocorrelation), but unduly inflate sample size, and thus degrees of freedom of model residuals, thereby influencing statistical inference."

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Dear All

I am not at all talking about auto-correlation. My problem is very simple. I have precipitation data from model and observation for whole indian domain(with grid size 330 X 220). I have found the correlation from them and want to check the statistical significance of the correlation (how much confident). Now as the dimension of the variable is large (72600) therefore the degrees of freedom for the data will be 72600-2=72598. When I will apply the students t test for that I will not find any table for that large degree of freedom from where I will collect significant cutoff value. My question how to tackle the problem?

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it seems to me that this might precisely be a case where autocorrelation might spoil your analysis (residuals at neighbouring points on your grid might tend to behave similarly and therefore violate the independence assumption behind the test ; in other words, neighbouring points might not bring any "new" information and therefore should not count as degrees of freedom)

anyway, if you want to go for a t-test with a gazillion of degrees of freedom, you can safely use the gaussian approximation of the student law as explained by Stephen above

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the degree of freedom will be the number of time step for both temporal and spatial correlation.

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@ Monalisa Sahoo

i would not be so sure ; subsampling seems a tricky thing ; if i understand you correctly (apologies if it not the case), the finer the sampling step of a continuous process i use, the more degrees of freedom i get ; this sounds strange : assuming some kind of uniform continuity of my process, below a given step size, my successive (or neighbouring, if i sample a spatial process) samples will be essentially equal, which means that the successive samples i collect are so much correlated that i am not adding any degree of freedom (aka independent information) to my analysis

this is the basic understanding i gathered from the reference below, but i'd appreciate any alternative arguments !

http://www.whoi.edu/cms/files/DormannEcography30_57164.pdf

"Spatial auto-correlation is a subtle, less obvious form of subsampling (Fortin and Dale 2005): samples from within the range of spatial autocorrelation around a data point will add little independent information (depending on the strength of autocorrelation), but unduly inflate sample size, and thus degrees of freedom of model residuals, thereby influencing statistical inference."

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