Validity and Reliability of Mathematical Visual Literacy Skills Based on Avgerinou’s Vilual Literacy Index

There is much literature on visual literacy across different fields of knowledge. Even so, generally there is a gap of literature that deals with measuring mathematical visual literacy skills. The objective of this paper is to produce empirical data on reliability and validity of mathematical visual literacy skills instrument. The development of items was based on the skills outlined Avgerinou’s VL Index (2007. The early stage in validating the instrument required researchers to seek face validity and content validity from panels of experts. Face validity was based on subjective judgements of the items. Meanwhile, content validity was determined by Content Validity Index (CVI) which is computed using Item-CVI (I-CVI) and Scale-CVI (S-CVI). Each mathematical visual literacy skills had accepted S-CVI values ranging from 0.86 to 1.00 but items with low I-CVI values were deleted. Next, construct validity and reliability was determined by using Exploratory Factor Analysis (EFA) and Cronbach’s alpha respectively. The instrument, consisting of 43 items was assessed on 428 pre-university students. Students’ responses were scored using analytical rubric developed by researchers. Using Principal Component Axis (PCA) and varimax rotation, EFA was carried out where 40 retaining items were extracted to 7 factors, representing each visual literacy skills. Kaiser-Meyer-Olkin (KMO) of 0.721, significant Bartlett’s Test of Sphericity (BTS), communalities anti images ranging between 0.308-0.721 and 0.503-0.835 respectively, 7 extracted factors explaining 53.685% of the total variance, factor loadings of ±0.520 and more, and overall Cronbach’s alphas of instrument recorded at 0.82, explained the complete validity and reliability of the instrument.

Delineating G × E interactions by AMMI method for root attributes in ashwagandha [Withania somnifera (L.) Dunal]

In the present study, additive main effects and multiplicative interactions (AMMI) biplot analyses was used to dissect genotype x environment interaction (GEI) and to identify location specific and widely adapted genotypes for root branches, diameter and length in ashwagandha [Withania somnifera (L.) Dunal]. Trials were conducted in randomized complete block design (RCBD) with two replications over three consecutive years at three different locations. ANOVA analysis revealed environment, G×E interaction and genotype effects to contribute significantly (p less than 0.001) towards total sum of squares for root branches (61.00%, 22.18% and 14.00%); root diameter (51.06%, 24.26% and 15.34%) and root length (65.67%, 20.82% and 11.39%). Further, the GEI for these traits was mostly explained by the first, second and third principal component axis (IPCA1, IPCA2 and IPCA3). AMMI1 and AMMI2 biplot analyses showed differential stability of genotypes for root branches, diameter and length with few exceptions. Environmental contribution towards the genotypic performance from AMMI1 and AMMI2 analysis for root traits except environment Bhi16 contribution for root diameter and root length. AMMI1 biplots and simultaneous selection index (SSI) statistics identified SKA-11 as the most desirable genotype for root branches and length while SKA-26 and SKA-27 for root diameter. The ashwagandha genotypes identified for root attributes could be advocated either for varietal recommendation or in varietal development program.

Using AMMI approach to delineate genotype by environment interaction and stability of barley (Hordeum vulgare L.) genotypes under northern Indian shivalik hill conditions

Genotype by environment interaction (GEI) of 18 barley varieties was assessed during two successive rabi crop seasons so as to identify high yielding and stable barley varieties. AMMI analysis showed that genotypes (G), environment (E) and GEI accounted for 1672.35, 78.25 and 20.51 of total variance, respectively. Partitioning of sum of squares due to GEI revealed significance of interaction principal component axis IPCA1 only On the basis of AMMI biplot analysis DWRB 137 (41.03qha–1), RD 2715 (32.54qha–1), BH 902 (37.53qha–1) and RD 2907 (33.29qha–1) exhibited grain yield superiority of 64.45, 30.42, 50.42 and 33.42 per cent, respectively over farmers’ recycled variety (24.43qha–1).

Interpreting genotype×environment interaction in sesame (Sesamum indicum L.)

An understanding of genotype by environment (G×E) interaction would be useful for establishing breeding objectives, identifying the best test conditions, and finding areas of optimal cultivar adaptation. Data from field assays including eight environments and eight elite lines were analysed to identify environmental and genotypic variables related with G×E interaction for yield in sesame multi-environment trials in Venezuela. Both predictable and unpredictable environmental variables were recorded. Yield components were recorded as genotypic variables. Yield and yield components were used to perform additive main effect and multiplicative interaction (AMMI) analysis. Significant differences (P<0·01) for G×E interaction were observed for all variables examined, except for the number of branches per plant. For yield, 0·28 of the total sum of squares corresponded to G×E interaction. Using environmental and genotypic data, correlation analysis was carried out between genotypic and environmental scores of the first interaction principal component axis (IPCA 1) for all variables examined. Significant correlations (P<0·05) were observed between IPCA 1 for yield and content of sand and silt in soil. No significant correlation was found between IPCA 1 score for yield and genotypic variables. These results indicate that edaphic properties at the trial locations play an important role in yield G×E interaction in Venezuelan sesame. These results should help select test sites for sesame in Venezuela to minimize G×E interaction and make selection of superior genotypes easier. Two strategies can be recommended: multi-environment trials at sites with average, not extreme, sand and silt content, or stratification of sites according to sand and silt content.

Genotype × Environment (G × E) Interaction in Southernpea [Vigna unguiculata (L.) Walp] Genotypes in the Southeastern USA

Genotype by environment (G × E) effects in Regional Cooperative Southernpea trials for the southeastern United States were investigated to characterize the extent, pattern, and potential impact of G × E on seed yield of southernpea [Vigna unguiculata (L.) Walp] genotypes. The structure of G × E effects was investigated using the Additive Main Effect and Multiplicative Interaction (AMMI) method. AMMI analyses revealed a highly significant genotype × environment interaction, most of which was partitioned into a genotype × location component of variance. AMMI first principal component axis scores stratified environments into two groups that minimized variation within groups. Biological interpretation of groupings and visual assessment of the AMMI biplot, revealed high-yielding genotypes interacting positively with one group of environments and conversely, low-yielding genotypes interacting positively with the other group. There were some significant rank changes of genotypes as yield potential varied across environments. Some environments showed similar main effects and interaction patterns indicating that most of the G × E effects could be captured with fewer testing sites, and consequently redundancy of some testing environments over years.