Question

Two-Way ANOVA Extra Credit Worksheet

PSYC2002C-007

A researcher wants to know whether TV time is related to amount of sharing for boys and girls. To test this, the researcher splits 24 boys and 24 girls into even groups to undergo conditions of no TV, 1 hour of TV, 2 hours of TV, and 3 hours of TV, then measures the number of times they shared toys or food with the other children in their group in an hour-long play-time afterwards.

The resulting data is shown below:

	No TV	1 Hour of TV	2 Hours of TV	3 Hours of TV
Boys	8	5	6	7
	6	6	4	9
	5	3	5	8
	7	5	6	10
	8	4	5	8
	7	4	6	9
X̄	6.8	4.5	5.3	8.5
∑X	41	27	32	51
∑X2	287	127	174	439
Girls	6	3	3	3
	5	4	2	3
	5	5	2	2
	6	5	1	1
	7	5	4	2
	5	3	4	3
X̄	5.6	4.1	2.7	2.3
∑X	34	25	16	14
∑X2	196	109	50	36

State the IV’s and the DV: __________________________________________________

What is the factorial notation for the ANOVA? _________________________________

Complete the following table and show your work for Sum of Squares calculations below:

Hint: To find significance, find F-crit for each.

Source	SS	df	MS	F	Significant?	η2
Between Groups
TV
Gender
Interaction
Within Groups
Total

SS_tot =

SS_bn =

SS_TV =

SS_gender =

SS_interaction =

SS_wn =

Was there an interaction effect between the TV time and gender? If so, interpret this effect.

Was there a main effect for TV time? If so, interpret this effect.

Was there a main effect for gender? If so, interpret this effect.

What had the largest effect size? Highlight/bold one of the following:

TV time

Gender

Interaction between TV time and gender

Answer 1

From the given problem:

Independent variables (IV): Two factors Gender and TV time are the independent variables, while

Dependent variable (DV): Number of times they shared toys or food with the other children in their group in an hour-long play-time afterward

In the given problem we have 2 IVs i.e.,

Gender (2 levels: Boys, Girls) and

TV time (4 levels: No TV, 1 Hour of TV, 2 Hours of TV, 3 Hours of TV)

hence, the factorial notation for the ANOVA is 2 * 4

n = Number of trails = 6

c = Number of levels of Time = 4

n = Number of trails = 6

r = Number of levels of Gender = 2

n = Number of trails = 6

From the above table:

Was there an interaction effect between the TV time and gender?

No the interaction effect between the TV time and gender is not statistically significant as the calculated F (= 1.32) < the tabulated F{0.05,3,40} (= 2.84) at 5% level of significance and (3, 40) degrees of freedom

Was there a main effect for TV time?

No the main effect TV time is not statistically significant as the calculated F (= 0.85) < the tabulated F{0.05,3,40} (= 2.84) at 5% level of significance and (3, 40) degrees of freedom

Was there a main effect for gender?

Yes, the main effect gender statistically significant as the calculated F (= 5.33) > the tabulated F{0.05,3,40} (= 4.08) at 5% level of significance and (1, 40) degrees of freedom

Interpretation:

Gender has significance in sharing toys or food with the other children in their group in an hour-long play-time afterward.

Gender has the largest effect size