what is the importance of representiveness in statistics?

Answer 1

ANOVA theory strives to analyze variance and to ascribe it to some effect. If the sample space is not representative, effects may be identified that are not real effects, and the ability to detect inter-actions, effects occurring in concert may lead to fictional conclusions. For example, if you are studying the potential for a chemical to be a fertilizer, the plants to be analyzed in a soil plot need to be planted in all parts of the plot. If plants are planted in what turns out to be a good soil, the effect of the soil may be attributed to the fertilizer. Similar errors can occur in polling. If you were to do a poll of Republican candidates in Utah, and Matt Romney did very well, you might be concluding something that might not be true in area where a small percent of the population is LDS in religion.