Table 3. LRT analysis and Tukey’s pairwise test (p≤0.05) for genomic selection prediction considering the 2^nd, 3^rd, and 4^th cross-validation strategies to estimate the effect of population structure for fresh root yield, dry root yield and dry matter content.

Deviance	DF	Fresh root yield		Dry root yield		Dry matter content
		${\mathit{r}}_{\widehat{\mathit{y}}\mathit{y}}$	b	${\mathit{r}}_{\widehat{\mathit{y}}\mathit{y}}$	b	${\mathit{r}}_{\widehat{\mathit{y}}\mathit{y}}$	b
Methods	4	79.75*	855.48*	70.99*	479.64*	10.81*	375.23*
Cross validation	1	581.54*	85.18*	512.58*	149.22*	490.46*	277.74*
Population structure	1	1956.77*	342.7*	1716.17*	611.94*	1466.70*	778.03*
Tukey multiple comparison test
BayesB		0.0821B (0.1770)	1.5013B (0.0902)	0.1327B (0.1539)	1.4778C (0.0805)	0.2675B (0.1480)	1.3458C (0.0818)
BLASSO		0.0773B (0.1738)	1.4105C (0.1059)	0.1434B (0.1604)	1.6179B (0.1330)	0.2779AB (0.1382)	1.4896A (0.1461)
G-BLUP		0.0848B (0.1756)	1.6941A (0.1856)	0.1415B (0.1808)	1.6519A (0.0795)	0.2735AB (0.1427)	1.4179B (0.1397)
RKHS		0.1176A (0.1680)	1.6866A (0.1995)	0.1722A (0.1808)	1.6631A (0.0795)	0.2840A (0.1366)	1.4181B (0.1443)
RR-BLUP		0.0858B (0.1736)	1.6903A (0.1870)	0.1415B (0.1808)	1.6493A (0.0795)	0.2752AB (0.1459)	1.4214B (0.1414)

$r_{\widehat{y}y}$: predictive ability; b: bias, DF: degrees of freedom.

*significance deviance for 5% probability in χ² test.

Major letters indicate significance difference between genomic prediction methods (p<0.05) by Tukey’s pairwise test. Standard error for the genomic prediction method is in parentheses.