In: Math
A developmental psychologist would like to know whether there is a difference in the sociability scores of children according to the number of siblings they have. He chose three random samples of n = 5 children each according to three groups and measured their level of sociability using a standardized test. The scores are shown in the table below. Do the scores indicate significant differences among the three groups?
| 
 No Sibling**  | 
 x^2  | 
 SS1  | 
 One Sibling**  | 
 x^2  | 
 SS2  | 
 Two Siblings**  | 
 x^2  | 
 SS3  | 
| 
 4  | 
 16  | 
 0.36  | 
 7  | 
 49  | 
 0.16  | 
 8  | 
 64  | 
 0.04  | 
| 
 5  | 
 25  | 
 0.16  | 
 7  | 
 49  | 
 0.16  | 
 9  | 
 81  | 
 0.64  | 
| 
 7  | 
 49  | 
 5.76  | 
 6  | 
 36  | 
 0.36  | 
 7  | 
 49  | 
 1.44  | 
| 
 3  | 
 9  | 
 2.56  | 
 6  | 
 36  | 
 0.36  | 
 8  | 
 64  | 
 0.04  | 
| 
 4  | 
 16  | 
 0.36  | 
 7  | 
 49  | 
 0.16  | 
 9  | 
 81  | 
 0.64  | 
| 
 23  | 
 115  | 
 9.2  | 
 33  | 
 219  | 
 1.2  | 
 41  | 
 339  | 
 2.8  | 
a. Using the 5 steps of hypothesis testing, test at α .05. (15 pts)
b. Conduct two post hoc tests, Tukey’s HSD Test and the Scheffe Test, both at α .05, and compare your answers. (9 pts)
Need help with the ten step by hand ANOVA ... specifically the sum of squres/between/within calculations in the hypothesis testing
and the steps associated with the post hoc tests
Thank you!!