When to switch off the continuity correction in chisq.test function? From this Research paper Table1 Association of RAD51-AS1 expression with clinicopathological features of EOC patients I see that p-value is calculated based on Chi-square test.
 Age   Low-RAD51-AS1  High-RAD51-AS1 P-value
 <50    25 (38.5)      17 (26.6)       0.149
 ≥50    40 (61.5)      47 (73.4)

For the Variable Age the p-value is 0.149
But when I calculated with correct=T it gave a different value. 
data <- data.frame(x= c(25, 40), y=c(17, 47))
chisq.test(data, correct = T)

    Pearson's Chi-squared test with Yates' continuity
    correction

data:  data
X-squared = 1.5728, df = 1, p-value = 0.2098

And When I gave correct=F I got the p-value which is seen in the Research paper.
chisq.test(data, correct = F)

    Pearson's Chi-squared test

data:  data
X-squared = 2.0794, df = 1, p-value = 0.1493

I would like to know when to use correct=F and correct=T
 A: The test statistic is approximately $\chi^2$ distributed. According to Agresti in Categorical Data Analysis, Yates said Fisher recommended the hypergeometric distribution for an exact test. And Yates proposed this correction so the continuity corrected $\chi^2$ test approximates the result of the exact test. But nowadays, any computer can perform Fisher's exact test. In R:
fisher.test(data)$p.value
[1] 0.1889455

So instead of using the correction, you might as well use the exact test. So there is no good reason to use the continuity correction nowadays. All of this usually only matters at small sample sizes. At large sample sizes, all the methods should be quite similar.
However, at small sample sizes, one is usually better off performing a mid-P test. This is because Fisher's exact test is based on the hypergeometric distribution. This distribution is discrete, so at small sample sizes, it can only return a limited number of p-values. And Fisher's exact test usually ends up being conservative.
For the same data, a mid-P test would return:
library(epitools)
oddsratio(as.matrix(data))$p.value

         NA
two-sided midp.exact fisher.exact chi.square
     [1,]         NA           NA         NA
     [2,]  0.1560137    0.1889455  0.1492988

.156 which is between the uncorrected $\chi^2$ of .149 and the Fisher test of .189. All of them are lower than the continuity corrected $\chi^2$ p-value of .201. Agresti recommends the mid-P test at small sample sizes. For what it's worth, you know the sample size is small when the test you use matters.
Agresti's Categorical Data Analysis text is a very good resource for these topics.
