The most effective way to combat β-thalassemias is to prevent the birth of children with thalassemia major. Therefore, a cost-effective screening method is essential to identify β-thalassemia traits (BTT) and differentiate normal individuals from carriers. We considered five hematological parameters to formulate two separate scoring mechanisms, one for BTT detection, and another for joint determination of hemoglobin E (HbE) trait and BTT by employing decision trees, Naïve Bayes classifier, and Artificial neural network frameworks on data collected from the Postgraduate Institute of Medical Education and Research, Chandigarh, India. We validated both the scores on two different data sets and found 100% sensitivity of both the scores with their respective threshold values. The results revealed the specificity of the screening scores to be 79.25% and 91.74% for BTT and 58.62% and 78.03% for the joint score of HbE and BTT, respectively. A lower Youden's index was measured for the two scores compared to some existing indices. Therefore, the proposed scores can obviate a large portion of the population from expensive high-performance liquid chromatography (HPLC) analysis during the screening of BTT, and joint determination of BTT and HbE, respectively, thereby saving significant resources and cost currently being utilized for screening purpose.