As part of a larger study of family functioning, a total of 104 families (adoles

Question

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 fathers on “Physical appearance” be declared to be statistically significant? (yes/no) Explain your answer. (2 points)

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. p

Explanation / Answer

There are a total of 104 families meaning 104 fathers for each of the domain; physical appearance specifically.

We don't know the eaxct number from each ethnicity but that's not pertinent. There are 3 groups (Caucasian, Afro-American and Hispanic)

dfnumerator = k-1 where k is no of groups

                = 3-1 = 2

dfdenominator = n-k, where n is no of samples

                    = 104 - 3 = 101

F2,101 = 3.086 at a 95% level.

Fstat= 3.16 (from the output) which is greater than 3.086 (critical value)

This in turn implies that we REJECT NULL and conclude that there is a statistically significant difference in means among the 3 races.

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