In the following translated text from a section entitled Simple Pseudoreplication there's mention that the fact that students from a school were selected randomly isn't sufficient since they're not independent, which I emboldened. If we'd do the experiment, why would we need to randomly select student? Why not just pick the ones closest to the school in case we want to go meet their parent or have look where they do their homework? The quote is finished in the 1st comment.
Thank you kindly
Simple pseudoreplication is the case where we have several observations, but only one real experimental unit per treatment (absence of real repetitions). We can have several measurements in two plots, but the observations are not independent. For example, if we are interested in the effect of interventions by a remedial teacher for the success of students with learning difficulties, we could hire a remedial teacher to help students with learning difficulties. in a school and compare with students in a school without a remedial teacher. We could randomly select students in difficulty in each school and compare their academic success. Even with 50 students randomly chosen from each school, we only have two real experimental units: the two schools. Indeed, students in the same school are not independent. If a difference is detected between the two schools, it may be due to a difference in the characteristics of these two schools (rich or disadvantaged neighborhood, other learning support, better teachers) or to the help provided by the orthopedagogue: the two effects are confused. In this example, it is necessary to increase the number of experimental units rather than the observations on the same unit. To do this, it is necessary to randomly select students with learning difficulties in different schools and randomly assign the treatment (interventions of a remedial teacher or not) to each to obtain a completely random system (1 student in 1 school = 1 experimental unit ).