Question

Part lI. Reading Journal Articles: Simple ANOVA(9 points) 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 References Mailings Review View Aav A :-.-.-. |-- 순↓ Aabc.cete! AaBKeddte AaBbCcDe AaabCcDdi. AaBb( A.- No Spacing Headeg1 H Headng 2 Table 1 Mears and Standand Deviations for Racelethnicity Caucasian African American Hispanio Latino/Latina FValue 3.15 (76) 3.13 (74) 323 (67) 3.44 (55) 298 (-71) 3.36 (62) 3.38 (51) 3.25 (60) 320 (66) Adolescents Fathers Adolescents Fathers 1.21 281 2.82 (85) 249 (.84) 2.79(.51)" 3.06 (77) 2.82 (84) 3.14(Ar 2.92 (.75) 3.13 (6st 0.81 3.16 Adolescents Mothers Futhers 2.79 (87) 2.96 (.80) 2.04 (.79)2.49 (78 2.79 (58) 2.90 (68) .18 (66) 2.07 (64) 233 (75) 1.96 3.95 0.27 Global self-worth 3.34060)335 (.86 3.17 (76) 3.25 (.65) 3.24 (71 3.38 (.53 023 039 332 (67) Mothers Fathers 4.59* Note. Sandad deviations are in peenthewes. Different mperscripes signility significant nean differences Ps.0S 1. What is the mean score of adollescents on "Athletic competence" for Caucasians? (1 point) 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. (2 points) 2. 3. According to the ANOVA, should the mull bypothesis for the set of three means for fathers on "Global self-worth" be rejected? (yes/no) Explain your answer. (2 points) 4. Table 1 reports on 12 ANOVAs. How many of them are statitically significant? Explain your answer. (2 points) 5. According to the post hoc tests, which of the following pairs of means for mothers on "Athletic competence" are significantly different? (Orcle one or more. n points A. The difference between Caucasian and Allrican American. 8. The difference between Caucasian and Hispanic/Latino/Latina. C The difference between Arican American and Hispanic/Latino/Latina 6. According to the post hoc tests, which of the following pairs of means for fathers appearance" are significantly different? (Circle one or more.) (1 point) A. The difference between Caucasian and African American. B. The difference between Caucasian and Hispanic/Latino/Latina. C. The difference between African American and Focus ited States FS 20 FS

Answer 1

1) The mean score for Adolescents for Caucasians is 2.82 (from the table)

2) The F value for the three scores on Adolescents is 0.81

The critical value for F is 3.086. This is calculated from the F table with degrees of freedom (2, 101). and 5% level of significance.

How are these dfs got ?

Total degrees of freedom = No of observations -1 = 104-1=103

df of th treatmensts = 3-1 =2 (three levels are Caucasian, Afro and Latino)

df of error = 103-2 =101

As Calculated F is less than 3.086 we do not reject the null hypothesis.

Hence the three means do not differ significantly.

3) If we look at the Fathers for self worth the F value is 4.59

This is more than the critical value of 3.06

Hence the null hypothesis is rejected.

The means differ significantly.

4) Out of the 12 ANOVAs 3 are statistically significant.

These are :

Fathers on physical appearance - F score of 3.16 > 3.06

Mothers on Athletic Competence - F score pf 3.95 > 3.06

Fathers on Global Self Worth - F score of 4.59 > 3.06

The post hoc Duncan Scores are not mentioned here. However the approach is the same. Look at the calculated t scores and compare to critical value . If it is more you reject if it is less you accept.