This means that the test subjects wont necessarily be representative of the population. Random assignment means assigning test subjects to different treatments in the study. Randomization is the best way of making sure that the necessary control in the study is present. They are related to both internal and external validities as they increase both. Internal validity is the validity of the effect discovered in the study, and external validity is the validity in which the cause-effect relationship holds up when measurements are changed. The randomization increases both validities.
a. Threats to the validity of the research about the two school groups include the fact that the number of students in each group isnt specified, and if it isnt above 30- the research isnt valid since at least 30 test subjects are needed to conduct a test on statistical hypotheses (even more according to different, more rigid approaches).
A way to increase the external validity in this subject is to increase the number of test subjects in each group as much as possible, so that the results are as accurate and representative as possible, and also in order for them to be at least over 30, which is the agreed upon number of test subjects needed in a group in order to be able to test the validity of hypotheses.
b. The threat to the validity of the study is mainly that the teacher had a pretest and a posttest for classes A and B while only having the posttest for classes C and D. it is impossible to deduce from this that the former classes are superior to the latter ones because of the introduction of the new materials and methods. She should have done both tests on all classes. Furthermore, there is a need to control possible intervening variables to make sure that there is a statistical link between these new materials and methods to the score achieved in the post test (the link can be a correlation and then it wouldnt be legitimate