I have two dataframes one with two (or more) individuals (denoted by sampleID) denoted by TEST and the other consisting of just 3 columns called REF.

I want to add REF onto TEST based upon the overlaps between the "chr","start","end" columns of REFand the corresponding (in order) columns of TEST: "Chromosome","Start","End".

I want the definition of overlap to be that in order for a REF interval to overlap a TESTinterval, it must cover >50% of TEST interval. 

I've been playing around with GenomicRanges. However, the findOverlap function only allows me to specify the minOverlap as the number of overlapping positions rather than a fraction of the interval covered. So, using GenomicRanges, how can I do this?

Some example input:

REF = structure(list(chr = c("1", "1", "1", "1", "1", "1", "1", "1", 
"1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1"), 
    start = c(766101L, 1627918L, 4421060L, 7324468L, 8053732L, 
    8182462L, 8182584L, 8182584L, 8206130L, 8804237L, 10369546L, 
    10370541L, 10543836L, 10656324L, 12354307L, 12841928L, 12845863L, 
    12909237L, 12909965L, 13444908L), end = c(809773L, 1672603L, 
    4424115L, 7325408L, 8067990L, 8189854L, 8189285L, 8189285L, 
    8209321L, 8812660L, 10377983L, 10377983L, 10545046L, 10657912L, 
    12357076L, 12971833L, 12883096L, 12927107L, 12918079L, 13468022L
    ), Deft = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
    1, 1, 1, 1, 1)), .Names = c("chr", "start", "end", "Deft"
), row.names = c(217L, 568L, 1340L, 1691L, 1804L, 1811L, 1812L, 
1813L, 1819L, 1880L, 2017L, 2020L, 2041L, 2049L, 2224L, 2282L, 
2284L, 2332L, 2335L, 2424L), class = "data.frame")

TEST = structure(list(sampleID = c("SID1331", "SID1331", "SID1331", 
"SID1331", "SID1331", "SID1331", "SID1331", "SID1331", "SID1331", 
"SID1331", "SID1337", "SID1337", "SID1337", "SID1337", "SID1337", 
"SID1337", "SID1337", "SID1337", "SID1337", "SID1337", "SID1337"
), Chromosome = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 10L, 
10L, 11L, 11L, 11L, 11L, 11L, 12L, 12L, 12L, 12L), Start = c(61735L, 
7541291L, 32664866L, 45935056L, 55449273L, 117769301L, 117892183L, 
167580307L, 172458743L, 172852403L, 129495492L, 129526092L, 198572L, 
112837740L, 112847206L, 132105712L, 132126171L, 150442L, 23261653L, 
23270278L, 28135989L), End = c(7539746L, 32664843L, 45934562L, 
55445562L, 117767918L, 117886211L, 167580003L, 172457651L, 172851634L, 
214938359L, 129525791L, 135506704L, 112837593L, 112846803L, 132104437L, 
132122974L, 134944770L, 23261612L, 23268885L, 28131521L, 52920414L
)), .Names = c("sampleID", "Chromosome", "Start", "End"), row.names = c(1L, 
2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1000L, 1001L, 1002L, 1003L, 
1004L, 1005L, 1006L, 1007L, 1008L, 1009L, 1010L), class = "data.frame")

Make your GRanges:

refGR <- makeGRangesFromDataFrame(REF)
testGR <- makeGRangesFromDataFrame(TEST)

Find overlaps:

hits <- findOverlaps(refGR, testGR)

Compute percent overlap and filter the hits:

overlaps <- pintersect(refGR[queryHits(hits)], testGR[subjectHits(hits)])
percentOverlap <- width(overlaps) / width(testGR[subjectHits(hits)])
hits <- hits[percentOverlap > 0.5]

Note that none of the sample data passes the filter. It is not clear what you mean by adding REF onto TEST. One example is merging the "Deft" column from REF into TEST:

TEST$Deft <- NA
TEST$Deft[subjectHits(hits)] <- REF$Deft[queryHits(hits)]