Final answer:
The pretreatment equivalency/between-group equivalency assumption states that differences in outcomes observed in different treatment groups are solely due to the treatments and not potential lurking variables. Random assignment of subjects ensures equal distribution of lurking variables. The null hypothesis assumes equal normal distribution for all treatment groups.
Step-by-step explanation:
The pretreatment equivalency/between-group equivalency assumption is a key concept in experimental design. It states that when subjects are randomly assigned to different treatment groups, any differences observed in the outcomes (response variable) are solely due to the different treatments administered and not due to any potential lurking variables.
By randomly assigning subjects to treatment groups, it ensures that all potential lurking variables are spread equally among the groups. This allows us to establish a cause-and-effect connection between the explanatory variable (treatment) and the response variable.
The null hypothesis in this context assumes that all treatment groups are samples from populations with the same normal distribution. The alternative hypothesis states that at least two groups come from populations with different normal distributions.