Covariance Analysis/Propensity Score

In Chap.  6 , we explored the research theme “Is the ‘New Learning Method’ more effective than the ‘Old Learning Method’?” using an experiment to study the differences between two independent groups. To confirm the effect of a factor through an experiment, it is necessary to conduct a control experiment. A control experiment is an experiment where, apart from the factor whose effect we want to investigate, the state of other conditions is made homogeneous between the experimental group and the control group. Here, the factor whose effect we want to investigate is called the treatmenttreatment. But what if, at the stage of preparing the experimental and control groups, the two groups were not homogeneous from the start? For example, if the experimental group had inherently higher average academic abilities than the control group, the difference in final exam scores might just be a result of the difference in academic abilities of the groups.