# p-Value and results of Cramer's V

I need a bit help for interpreting this results...

I did a correlation analysis with R with the assocstats function. The result is:

$summary Call: xtabs(formula = ~MH[, i] + MH[, j], data = MH) Number of cases in table: 2306 Number of factors: 2 Test for independence of all factors: Chisq = 2806.6, df = 3318, p-value = 1 Chi-squared approximation may be incorrect$object
X^2   df P(> X^2)
Likelihood Ratio 1036.1 3318        1
Pearson          2806.6 3318        1

Phi-Coefficient   : 1.103
Contingency Coeff.: 0.741
Cramer's V        : 0.637

$summary Call: xtabs(formula = ~MH[, i] + MH[, j], data = MH) Number of cases in table: 2343 Number of factors: 2 Test for independence of all factors: Chisq = 118.46, df = 73, p-value = 0.000611 Chi-squared approximation may be incorrect$object
X^2 df   P(> X^2)
Likelihood Ratio 130.83 73 3.8115e-05
Pearson          118.46 73 6.1100e-04

Phi-Coefficient   : 0.225
Contingency Coeff.: 0.219
Cramer's V        : 0.225


But what does the p-value of 1 in this case mean if Cramer's V is 0.637 and therefor show a strong corelation or with 0.000611 with a Cramer's V of 0.225?

And does anyone of you know a good rule of thumb for interpreting Cramer's V?