How can you use the ANOVA to reject a null hypothesis? How is it related to the F-critical value?
If the null hypothesis criteria are not met by the relevant calculations (compared to the F-value) then it must be rejected.
It is important to note that ALL statistical ‘tests’ relate to some continuous function of probabilities. It remains to the individual to decide what level of ‘uncertainty’ (and risk) they can live with. There is no “magic number” that is deterministic. Whether the probability of rain is 10% or 90%, it MIGHT rain! Only the individual can evaluate the cost/benefit ratio of going out for picnic or not. Some will go where others will not.
Related to that is the supreme importance of a properly stated hypothesis!! In most cases, it must ask/answer ONLY ONE question – yes/no, based on your risk/uncertainty value. One can lead to another, but anytime more than one question/condition is asked in a hypothesis statement, the answers will be ambiguous at best, and worthless at worst.
The various tests, critical values and names are related to the specific types of calculations and distribution curves expected. They all result statistically in the same outcome – am I willing to accept my hypothesis as more likely than random occurence, or not.