Hmisc::rcorr gives a 0 pvalue but not cor.test

Question

I need to get correlation AND pvalues for a matrix so I tried rcorr from Hmisc package. The issue is that I have a 0 pvalue for a pair which give me 1.036733e-59 with cor.test function.

I used pearson for each function.

Here is a reproductible example.

library(Hmisc)
A <- c(6.32451531850417,6.396670829087,6.86361544161307,6.69938199174752,13.165463943882,6.90981191583279,13.1464308794264,6.52552248884005,6.08631376117103,6.61690829991384,6.77722148405774,6.49620534991742,6.5518962525994,6.2497899855603,6.8646997315825,6.69081335429442,6.70869072803975,6.87789921476436,6.56641042358147,6.84013201548233,6.69568254965127,6.70640778501988,6.62246110671344,6.67829056829049,6.65799888115762,6.24141301052501,6.69746610666983,6.68902124059975,6.64539017705934,6.81328563238539,7.06715007760963,6.75490752235589,6.49012918187287,12.7208750140264,6.73382593460874,6.35761704581448,7.28515563569873,6.67369856749724,6.66992764180906,6.40471908440153,6.30772659143547,6.45098473518897,6.60578485189021,6.50990123242974,6.40449000722152,6.50128036958986,6.66306523170188,6.45702244416934,6.28566653849103,6.42625738798208,6.88706148070107,6.35110357440403,6.68612827575002,6.58213967827742,6.37737813156623,6.38199814182166,6.7091244513399,6.46266526892103,6.46052608198987,6.57481275927555,6.60832078443043,6.75222494716443,6.55842628702281,6.67547286814189,6.51448496000258,6.67177207392162,6.69153307744344,6.69836071289889,6.6615217504183,6.63805883879528,6.36018525770115,6.50727400620095,6.38370628835495,6.81563624248625,6.62298705858254,6.41641698679136,6.29103959938316,6.64396635235954,6.76381424552375,6.51339014760998,6.63043442032935,6.93781852637583,6.59535594885934,7.0997394675434,6.19171479075248,6.28123555799257,6.43057159585162,6.5869614799051)
B <- c(3.9995637786823,3.48601398807956,4.03812725251975,3.81851391342822,11.7502675850666,3.98407110753864,11.8300601767337,3.59623022007111,3.47594268425866,3.39485541409169,3.96156903705731,3.84385038139104,4.40329546631133,3.69704624452915,3.87264919566187,3.90460396437268,3.45875737518772,3.95915349682997,4.37078882304428,3.79514714207642,3.85315638891753,3.82101134020264,3.76652556154815,3.78168978057991,4.38817115664092,3.67188258569308,3.93083752538972,4.09512848434603,3.76017250778245,3.93149619446255,3.73967734750671,3.79329645229012,3.72530038941995,11.6296199270195,3.76362438867387,3.52361952114506,5.05916028061208,3.78174363576111,3.77862237861648,3.96446993299436,3.95420785742674,3.65350904888874,3.74208843021492,3.7864852643104,3.34969922277165,3.76699340323312,3.90279649287842,3.48792692835044,3.54100392028721,3.73429478892297,4.07755160257201,3.71095088992823,3.96086251069495,3.62303629160269,3.50473542630912,3.45494734742944,3.62764756649661,3.50045819158303,4.75363129670227,3.66796624908498,4.41415957987699,3.61676764219056,4.35208487010989,3.63812742107392,3.61369595503799,3.6738293973286,3.79492785542216,4.89013596433762,3.70204962677728,3.52121048655018,3.59305187045436,3.58411383210404,3.50590908471792,3.73025791048932,4.0143103011064,3.6584374210132,3.72337929455363,3.7766291637304,3.55626499087112,4.11134785621808,4.03941383606145,3.81034661576582,4.15448306192498,4.73600249458588,3.57585585559837,3.76987550019725,3.72667260885011,3.55088410428519)
C <- c(5.0828344582765,5.44171716119668,5.50349616275127,6.20354287213394,6.99263387581131,5.53286444824163,6.66169084634442,5.16933585666197,4.99851910038837,5.18468358275925,5.94408569177543,5.38879105718559,5.1963019014005,4.90579273695638,5.40610158292019,5.97408534843616,5.6634072236913,5.71035471476711,5.30554917408064,5.60513350695794,5.59638539269362,5.54571609819415,5.26763404068582,5.88068748660826,5.20462261826007,5.28737753968805,5.41548211806564,5.23988511286448,5.45891799263611,5.33513304020226,5.38926947164349,5.78004326608306,5.53385821088178,6.70309488254236,5.72120763082083,5.43668800424696,5.31591419975872,5.55446882414854,5.39756885193532,5.34660398519912,4.98008442404427,5.07080405039416,5.03893220932515,5.11538656986937,5.19477846798434,5.27241946711687,5.15677380833086,5.20070799769709,5.611572982919,4.83939324104591,5.36607457080691,5.21935359026813,5.70039096365024,5.29675323855941,5.02690902121225,5.04349564595055,5.17171742744466,5.21386568112692,5.25785400845595,4.77688955147304,5.89435056128631,5.44712026551928,5.31047450193841,5.11339046941959,5.23862350238358,5.39464522888807,5.24658651925926,5.13548147374252,5.04054442277134,5.0942112627996,4.8247921182326,5.21145125468889,5.25857361278046,5.01095797437389,5.6214184959344,5.07188964223442,5.17615526987811,5.3227559035551,5.43031530449701,5.27626866543545,5.45060599999116,5.2667271685913,5.12852923511888,5.2622926326258,5.35048009048626,4.92554974015645,5.14856255783588,5.75558021935756)
mtx <- cbind(A,B,C)
rcorrelation <- rcorr(mtx, type="pearson")
rcorrelation$P["A","B"] # 0
rcorrelation$P["A","C"] # 2.220446e-16
cor.test(A,B, method="pearson")$p.value # 1.036733e-59
cor.test(A,C, method="pearson")$p.value # 2.181905e-16

How to have 1.036733e-59 as pvalue with rcorr ?

I have a biggest matrix and a lot of 0 for some pvalues and I need to print (I used "rank" in the original post before editing it) them, even if they are all close to 0...

Thanx

PS: there is a small (minor ?) difference for the pair A/C with the 2 functions but it's not my problem at this moment...

Answer 1

The differences (which are infinitesimal, by the way) are probably due to the correlation test being implemented differently. AFAICT rcorr uses Fortran, while cor.test is most using some things implemented in C. The implementation of the test in rcorr returns exactly 0 on some cases, while cor.test returns a value with over 60 decimal digits.

If you want to mimic the behaviour of rcorr, in which you get p-values for all the pairs of columns in a matrix, you can use combn and apply do something like this:

get_corr_p <- function(x) {
  # the x argument is a vector of length two with the variable names
  cor.test(get(x[1]), get(x[2]))$p.value
}
apply(combn(c("A", "B", "C"), 2), 2, get_corr_p)

But as has been noted by @Roland, ranking p-values does not make sense. Conceptually, you use p-values to check if the risk of erroneously rejecting a hypothesis (a correlation coefficient equal to 0, in this case). Usually, a threshold for this risk is set at 5%, so if p<0.05 then the risk of saying "there is a correlation" and that not being true is low enough, and we can make that statement. There is no such thing as "more significant", either the difference is significant or it isn't (given the threshold you selected). It is a yes/no thing, so it makes no sense to rank p-values.