On the Application of Clinical Psychology to Statistics: A Psychodiagnostic Case Study of the “the Standard Deviation”

Charles G. Middlestead, M.A.
University of Maryland

 

Once upon a time there was a family of statisticians called the Numburrs. They lived in an upper middle-class community, a safe town, where there was a low crime rate and small deviations. Eigen, the father, was known for being robust, and Alpha, the mother, was known for her significance in the community. Eigen and Alpha had two children: the daughter was named Anova and her brother was Chi. Eigen valued the trust and responsibility that he had worked hard to develop in his two children. But there were problems, the children were discovering sex. Anova was traditional, whereas her brother was developing homogeneity of regression tendencies. This had Eigen and Alpha attenuated.

Both parents had preplanned the birth of Anova, who was the older child. Chi was another story. Chi’s birth was most unexpected. Alpha had taken the Bonferroni test along with birth control pills to reduce Familywise Type 1 Error, but somehow this all failed and Chi was born. Now that he was a teen, he was proving to be quite a test for independence.

Recently, Alpha had walked into Chi’s room, and discovered him manipulating his variables with a covariate buddy of his, Rho. Instantly, thoughts of autocorrelation and F ratios popped into her mind and she new that Chi was going to be trouble now that he was able to test his own significance.

When Eigen came home that evening, Alpha intercepted him and they both sloped to the living room to discuss their problematic son. To their horror, Anova was with her new boyfriend, Gamma, lying on the sofa, and engaged in goodness-of-fit, pair-wise contrasts, and multiple regressions. Alpha shrieked, “Anova has a sex dummy in my living room!” Eigen grabbed Gamma by his decimals and threw him out of the house. With Gamma factored out of the equation, the two badly shaken parents collected their over-sexed children and brought them into the kitchen for a family meeting.

Eigen said, “Children, I always thought that we as a family were part of a normal distribution. You children have high degrees of freedom . . . not to mention hormones. You both are ground from all forms of sex until you are 21.68 years old . . . make that 22, I forgot to round up.”

Anova contorted leptokurtically and whined, “But Pops, why should I get grounded just because Chi is square? If his cell size wasn’t so small, he wouldn’t be interested in other guys’ contingency tables! Besides, Gamma and I are computed from the same sample . . . we’re in looooove.”

Chi jumped in, “Hey, wait just a point-interval Sis! I ain’t square, I’m just as robust and orthogonal as Dad, I just have a different standard deviation, that’s all.”

Anova grinned devilishly, “Yes . . . significantly, you’ll always be a sum of squares.”

Just as Chi was getting ready to adjust his sister’s Y-axis, Alpha cried, “Look at yourselves, see how you interact – you’re both mean squares! Where’s your pride, where’s your sibling love, where’s are your critical values?”

The children paused, reflecting on their mother’s iterations. They went over and hugged their parents parsimoniously. They proclaimed, “Mom and Dad, we’re done with sex, we want to minimize our error terms and maximize our power!” Eigen looked at his wife and said, “Honey, I believe their claims to be valid and reliable.” Alpha beamed, “Yes, our little ones have seen the light . . . . Chi will start having straight relationships, and Anova will stop having linear ones!”

With that, they all held hands, formed a Cramer’s V, and lived happily ever after . . . well at least for the product-moment.

© Copyright 1994 Wry-Bred Press, Inc./Glenn Ellenbogen. All rights reserved.

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