# Question

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. 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 self-esteem 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) = β0 + β1x1 + β2x2 + β3x1x2 . The t -test of the interaction term, β3, was “nonsignificant,” with a p-value 7 .10. However, both t -tests of β1 and β2 were statistically significant (p-value 6 .001). Interpret these results practically.

b. The researchers also fit the interaction model E(y2) = β0 + β1x1 + β2x2 + β3x1x2. The t -test on the interaction term,β3, was “significant,” with a p-value 6 .001. Interpret this result practically.

y1 = (x3 - x1) and y2 = |x3 - x1|.

a. The researchers fit the interaction model E(y1) = β0 + β1x1 + β2x2 + β3x1x2 . The t -test of the interaction term, β3, was “nonsignificant,” with a p-value 7 .10. However, both t -tests of β1 and β2 were statistically significant (p-value 6 .001). Interpret these results practically.

b. The researchers also fit the interaction model E(y2) = β0 + β1x1 + β2x2 + β3x1x2. The t -test on the interaction term,β3, was “significant,” with a p-value 6 .001. Interpret this result practically.

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