Assignment:
Q. A researcher is interested in the phenomenon of gender segregation. She wants to examine whether children gradually spend more or less time with their opposite-sex playmates. Therefore, she followed a group of primary school students and observed their time spent playing with opposite-sex classmates in school. The observations were made when the students were at grade 1, grade 3, and grade 6 respectively. Below are the data, in which a higher number denotes more time spent playing with opposite-sex classmates:
Grade 1 Grade 3 Grade 6
Student 1 5 7 5
Student 2 3 5 6
Student 3 4 7 5
Student 4 5 6 4
a. What are the independent variable and dependent variable of this study?
b. Write down the omnibus null hypothesis and the alternative hypothesis for the overall effect of the independent variable.
c. Conduct a proper statistical test by hand calculation to test the omnibus hypothesis with 5% as the level of significance (α). (For this exercise, the data assumptions like normality of population distribution can be taken as reasonably met.) Show your calculation formulae and steps. In case you decide to conduct an ANOVA, include a summary ANOVA table as part of your output but you are not required to conduct any post-hoc comparisons. Decide whether to reject the null hypothesis or not and state the basis of your decision.
d. Calculate the effect size in terms of eta-squared and omega-squared.