Once upon a time, a psychologist conducted a survey and gathered considerable amounts of data. However, as is the case many times, the data sat on the shelf gathering dust. But, one year, the psychologist decided to resurrect the data. Not being exactly sure of what to do though, the data was given to a few students to play with and summarize.Well, as you might expect, one student did it one way, another student did it another way, and a third student even did it entirely different from the other two. Because of this, the psychologist suddenly became interested in a different question and .. proclaimed to the world:
"How goes this VARIANCE OF ANALYSIS?"
*Many thanks to Dennis Roberts of Penn State for his original offering.
Why did the naive researcher stop at the lumber yard before analyzing his data?A stuttering statistician told him, " A A... 2 x 4 A A...ANOVA wood...would be needed for his...his analysis."
*Thank goodness the poor researcher did not have to lug a bunch of 4 x 4 treated posts in his car! This is another home grown joke.
What did the new statistics professor do when his lecture on analysis of variance flopped in front of a large class?He had to go OVA ANOVA ANOVA it again!!!
*I have to feel sorry for the poor chap when he gets to repeated measures designs. I hope my little joke was not a big FLOP!!
A One-Way ANOVA and a Two-Way ANOVA were talking shop one day. The One-Way said, "I sure do envy the interaction you have with your variables."The Two-Way frowned and replied, "Yah, but the minute it diminishes to any significant extent they really become independent and go their own separate ways."
*Bet you didn't know that ANOVAS could talk! I had to get their permission to print this.
Why did the statistician do such a horrid job of laying tile on his bathroom floor?He incorrectly PARTITIONED SOME OF THE SQUARES!!
*This explains why you never see a statistician's bathroom featured in BETTER HOMES AND GARDENS!
A consulting statistician and his client sat down together for the first time.Client: "I desparately need your help interpreting the significant three-way interaction in this factorial ANOVA. What are your fees?"
Statistician: "One hundred dollars for three questions."
Client: "Isn't that a little steep?"
Statistician: "Not really! Now what is your third question?"
*The client's third question was probably "Where is the door"? This is a sad situation where lack of two-way interation prevented the discussion of three-way interaction! Yes, I admit this one is all mine!
A naive researcher approached a statistician one day about analyzing some data.Researcher: "How do I test the difference between four treatment group means?"
Statistician: "Perform an Analysis of Variance."
Researcher: "But I don't want to test the difference in the group variances!"
Statistician: "You aren't! You are comparing the ratio of the variation between the group means to the combined variation within the groups to see if it is beyond chance."
Researcher: "You simply don't understand. You persist in talking about variation which does not interest me in the least!"
Statistician(Exasperated and Angry): "O.K. I have an alternative for you which is called the Interocular Test. Just examine any difference in the means and if it STRIKES YOU RIGHT BETWEEN THE EYES, declare it significant!!!"
*Isn't it rather ironic that the significance of the differences between a set of means can be tested by the ratio of two variances? Sir Ronald Fisher was very cagey when he perfected this seemingly contradictory procedure. This little story is my own so you know where to shoot the barbs.
A ONE-WAY ANOVA shouted at a TWO-WAY ANOVA: "STOP! Turn around - You are going the wrong way!"The TWO-WAY ANOVA yelled back: "Sorry! I will turn when I see an interaction!"
*Well, maybe ANOVA's should be required to pass a drivers test. Who would have dreamed ANOVA's would be driving fancy cars in the 21st Century. The attribution on this one points a one-way arrow at yours truly!
Student A: What is the name of the theorem in statistics that states the sum of squares total is equal to the sum of squares between groups plus the sum of squares within groups ( i.e., h2=a2+b2 )?Student B: Oh that is easy. That is called the Pythagorean Theorem.
Student A: I am sorry but that is wrong. You must have the right triangle for the Pythagorean theorem to hold and we did not assume that here.
Student B: OK so I had the wrong triangle. if you assume the right triangle then this statement becomes the Pythagorean Theorem.
Student A: You are now correct and it demonstrates how closely interwined the relationship is between geometry and statistics!
*Holy Cow! What kind of statistics course are these students taking? Poor Pythagorus. He knew all about triangles and squares but statistics and variances never entered his life. The above statement is called the Basic Theorem of Analysis of Variance but the Pythagorean Theorem has no connection with it. In words, it simply states that if you take any set of scores, divide them up into a number of groups(not necessarily equal n's) and compute the three sums of squares, then ssT = ssB + ssW. This assumes nothing about triangles or where the scores came from. Elegant huh?
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