As part of a larger study of family functioning, a total of 104 families (adoles
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As part of a larger study of family functioning, a total of 104 families (adolescents, mothers, and fathers) participated in this study. All participating families in the current study included an adolescent, the mother, and the father. Adolescents were required to have at least monthly face-to-face contact with their biological mother and their biological father for inclusion....
Participants completed the age-appropriate version of the Harter Self-Perception Profiles, which conceptualize self-esteem as perceived competence in multiple domains. The social acceptance domain assesses participants’ perceptions of feeling accepted by peers, feeling popular, and feeling comfortable around others. The physical appearance domain assesses participants’ self-perceptions of their attractiveness and their satisfaction with their appearance. The athletic competence domain assesses participants’ feelings of their competence in sports and other physical activities. The global self-worth subscale assesses participants' feelings about themselves overall (i.e., not tied to any specific domain...).
In order to test for the racial/ethnic group differences..., a series of ANOVAs was completed for each informant (adolescents, mothers, and fathers). Significant ANOVAs were followed up by post hoc Duncan's tests.
According to the ANOVA, should the set of three means for adolescents on “Physical appearance” be declared to be statistically significant? (yes/no) Explain your answer.
Table 1 Means and Standard Deviations for SelfEsteem Race/ethnicity Caucasian African American His Latino/Latina F-Value Social acceptance 1.17 3.15 (76) 3.13 (.74) 3.38 (51) Adolescents 3.25 (.60) 1.21 3.23 (67) 3.44 (.55) Mothers 3.20 (66) 2.98 (.71) 3.36 (.62) 2.81 Fathers Physical appearance 2.82 (.85) 3.06 (.77 2.92 (75) Adolescents 2.70 (.70) 2.49 (.84) 2.82 (84) Mothers 3.13 (65) 2.79 (51) 3.14 (82) Fathers Athletic competence 2.79 (.87) 2.96 (.80) 3.18 (66) 1.96 Adolescents 2.04 79' 2.49 (78) 2.07 (64)" 3.95 Mothers 2.88 (.750 2.79 (.58) Fathers Global self-worth 3.25 (.65) 3.34 (.60) 3.35 (.66) 0.23 Adolescents 3.24 (71) 0.39 3.17 (76) 3.32 (67) Mothers 2.96 (.62) 3.33 (72) 3.38 (.53) 4.59 Fathers Note. Standard deviations are in parentheses. Different superscripts signify significant mean differences. pExplanation / Answer
For adolescents on “Physical appearance” cannot be declared to be statistically significant because p-value of it is much greater than 0.05.
In ANOVA, the null hypothesis states that the population means are all equal. Usually, we can consider a significance level of 0.05 i.e, it indicates a 5% risk of concluding that a difference exists when there is no actual difference. If the p-value is less than or equal to significance level we reject the null hypothesis and not all population means are equal.
But here the p-value for adolescents on “Physical appearance” is greater than 0.05(significance level which we considered). So we do not have significant evidence to reject the null hypothesis that the population means are not equal.
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