Question

Q.1 A social psychologist is interested in whether the amount of couple photos (photos featuring the couple together) people post on social media would vary across relationship stages. He administered a questionnaire to a group of couples (one questionnaire for each couple) at the anniversaries of their first year, second year, third year, and fourth year of dating. The questionnaire asked about the total amount of couple photos they posted in social media during the past year. Below are the data, with a higher number denoting more couple photos posted:

	first year	second year	third year	fourth year
student 1	200	190	150	100
student 2	250	200	145	120
student 3	190	220	160	105
student 4	170	180	165	140

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 of your chosen statistical test can be taken as reasonably met.) Show your calculation formulae and steps. In case you decide to conduct an ANOVA, 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.

Answer 1

a. What are the independent variable and the dependent variables of this study?

Ans: The independent variable and the dependent variables of this study are total amounts of a couple of photos and the years of anniversaries respectively.

b. Write down the omnibus null hypothesis and the alternative hypothesis for the overall effect of the independent variable.

Null Hypothesis: The mean amounts of a couple of photos for these four years are the same.

Alternative Hypothesis: At least a year has significant mean amounts of a couple of photos.

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 of your chosen statistical test can be taken as reasonably met.) Show your calculation formulae and steps. In case you decide to conduct an ANOVA, 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.

ANOVA table

Source	DF	SS	MS	F	P
Between	3	19630	6543	14.1	0.000
Within	12	5569	464
Total	15	25198

S = 21.54 R-Sq = 77.90% R-Sq(adj) = 72.38%

Comment: The p-value is less than 0.05 level of significance. Hence, reject the null hypothesis and conclude that at least a year has significant mean amounts of a couple of photos at the 0.05 level of significance.

d. Calculate the effect size in terms of eta-squared and omega-squared.

Ams: eta-squared=19630/25198=0.7790