Test difference between means and variances of entire collection (EC) and core set (CS) for quantitative traits by Sign test (\(+\) versus \(-\)) (Basigalup et al. 1995; Tai and Miller 2001) .

`signtest.evaluate.core(data, names, quantitative, selected)`

- data
The data as a data frame object. The data frame should possess one row per individual and columns with the individual names and multiple trait/character data.

- names
Name of column with the individual names as a character string

- quantitative
Name of columns with the quantitative traits as a character vector.

- selected
Character vector with the names of individuals selected in core collection and present in the

`names`

column.

A data frame with the following components.

- Comparison
The comparison measure.

- ChiSq
The test statistic (\(\chi^{2}\)).

- p.value
The p value for the test statistic.

- significance
The significance of the test statistic (*: p \(\leq\) 0.01; **: p \(\leq\) 0.05; ns: p \( > \) 0.05).

The test statistic for Sign test (\(\chi^{2}\)) is computed as follows.

\[\chi^{2} = \frac{(N_{1}-N_{2})^{2}}{N_{1}+N_{2}}\]

Where, where \(N_{1}\) is the number of variables for which the mean or variance of the CS is greater than the mean or variance of the EC (number of \(+\) signs); \(N_{2}\) is the number of variables for which the mean or variance of the CS is less than the mean or variance of the EC (number of \(-\) signs). The value of \(\chi^{2}\) is compared with a Chi-square distribution with 1 degree of freedom.

Basigalup DH, Barnes DK, Stucker RE (1995).
“Development of a core collection for perennial *Medicago* plant introductions.”
*Crop Science*, **35**(4), 1163--1168.

Tai PYP, Miller JD (2001).
“A Core Collection for *Saccharum spontaneum* L. from the World Collection of Sugarcane.”
*Crop Science*, **41**(3), 879--885.

```
data("cassava_CC")
data("cassava_EC")
ec <- cbind(genotypes = rownames(cassava_EC), cassava_EC)
ec$genotypes <- as.character(ec$genotypes)
rownames(ec) <- NULL
core <- rownames(cassava_CC)
quant <- c("NMSR", "TTRN", "TFWSR", "TTRW", "TFWSS", "TTSW", "TTPW", "AVPW",
"ARSR", "SRDM")
qual <- c("CUAL", "LNGS", "PTLC", "DSTA", "LFRT", "LBTEF", "CBTR", "NMLB",
"ANGB", "CUAL9M", "LVC9M", "TNPR9M", "PL9M", "STRP", "STRC",
"PSTR")
ec[, qual] <- lapply(ec[, qual],
function(x) factor(as.factor(x)))
signtest.evaluate.core(data = ec, names = "genotypes",
quantitative = quant, selected = core)
#> Comparison ChiSq p.value significance
#> 1 Mean 1.6 0.20590321 ns
#> 2 Variance 3.6 0.05777957 ns
```