An alien from a distant planet had a real problem. He had five groups of scores with their means and simply wanted to know which pairs of means differed significantly from one another. Since there were no statisticians on his planet he was told by a friend to visit planet earth where many scholars practiced this profession. He anxiously boarded his private spacecraft and made the long trek to earth.
The first statistician he visited was at a major university and warmly assured him that his problem had a simple solution. He told the alien to first perform an analysis of variance and if the F-test was significant to follow it up with the Tukey HSD test. The statistician told the alien that if any two means were "honestly" different this method would uncover them. The alien was ecstatic and rushed to a PC to have his data analyzed. The results were mixed. The good news was that his F was significant at the .05 level. But the bad news was that HSD indicated that none of the pairwise differences in means was significant at the .05 level. The poor alien was somewhat demoralized and could not understand the conflicting results. A lab worker boosted his spirits by telling him that Tukey was quite conservative and maybe he still had something if he would just consult another statistician.
With his spirit renewed he visited a second statistician at a major corporation. This statistician smiled smugly and remarked that professors at universities were entirely too conservative. He told the alien to assume a more liberal stance and use the Fisher LSD as a follow-up. He told him that many of his mean differences would now pop up significant and he could return to his planet a happy person. The alien's mental outlook took a big swing toward the upside and he quickly rushed down to the corporation's computing facility for further analysis. But joy soon turned to gloom! Fisher's LSD still reported no significant pairwise differences in means!
By this time the alien was beside himself with frustration and depression. He was ready to board his spacecraft and head home when a little gremlin whispered something in his ear, "Sir alien, there is a wise destitute old statistician of last resort who lives in a dilapidated old house on a hill. His methods are unorthodox but he is well known for wringing the last drop of meaning out of a set of data. You owe it to yourself to pay him a visit." The downtrodden alien felt he had nothing to lose and decided to give it a try.
The poor statistician welcomed the alien into his ramshackle home. The alien related his story how the F-test was significant but the follow-up procedures found NO significant differences between any two means. The statistician listened to his sad tale of woe and then winked at him with a broad smile. "Mr. alien I think I can guarantee some significant results. All you must do is forget your inhibitions, party it up by looking at other comparisons, and use the Scheffe S-test. Some good things will then happen to you."
The alien was quite skeptical but finally agreed to employ this strange test. The kind old statistician then invited him to the cellar of his home where he had stashed away a rusty old rotary calculator. The two sat down and the statistician feverishly pushed the keys. The gears whined, the numbers rolled on the many dials, and the carriage banged back and forth for what seemed like an eternity. Finally, after several hours, the statistician let out a howl! "Mr. alien I have it! I have found a significant difference."
The alien was trembling with sheer excitement and exclaimed "Please kind statistician, don't keep me waiting. Tell me which pairs of means are different."
The statistician blurted out, "ONE-THIRD THE SUM OF MEANS ONE, TWO, AND FOUR IS SIGNIFICANTLY DIFFERENT FROM ONE-HALF THE SUM OF MEANS THREE AND FIVE!!"
There were several moments of deadly silence. Then the alien's mouth dropped and his face grew pale. Like a scared rabbit, he dashed toward his spacecraft and lifted off for home. As he put his craft in warp speed, he shook his head in disbelief. He vowed to visit a psychiatrist as soon as he got home and to NEVER, NEVER use numbers again.
*OK all you students enrolled in a statistics course at the university level, is it possible for the circumstances in this little story to occur in real life? Please drop me an email about my own crazy concocted story!
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