52 Unconscious self-esteem study. Psychologists define implicit self-esteem as unconscious evaluations of one’s worth or value. In contrast, explicit self-esteem refers to the extent to which a person consciously considers oneself as valuable and worthy. An article published in Journal of Articles in Support of the Null Hypothesis (March 2006) investigated whether implicit self-esteem is really unconscious.

A sample of 257 college undergraduate students completed a questionnaire designed to measure implicit self-esteem and explicit self-esteem. Thus, an implicit self-esteem score

(x1) and explicit self-esteem score (x2) were obtained for each. ( Note : Higher scores indicate higher levels of selfesteem.)

Also, a second questionnaire was administered in order to obtain each subject’s estimate of his or her level of implicit self-esteem. The score obtained from this questionnaire was called an estimated implicit selfesteem score (x3). Finally, the researchers computed two measures of accuracy in estimating implicit self-esteem:
y1 = (x3 - x1) and y2 = |x3 - x1|.

a. The researchers fit the interaction model E(y1) = b0 + b1 x1 + b2 x2 + b3 x1 x2 . The t -test of the interaction term, b3, was “nonsignificant,” with a p@value 7 .10. However, both t -tests of b1 and b2 were statistically significant (p@value 6 .001). Interpret these results practically.

b. The researchers also fit the interaction model E(y2) = b0 + b1 x1 + b2 x2 + b3 x1 x2. The t -test on the interaction term, b3, was “significant,” with a p@value 6 .001. Interpret this result practically.