Question

Two-way ANOVA (8 pts)

Research Scenario: A developmental psychologist is looking into the effects of play group size on empathy and whether this differs by age. She has two age groups – four year olds and eight year olds. Each of those age groups is split into three separate groups for an entire semester during structured free time: play alone (n = 8 per age group), dyads (n = 8 per age group), or groups of 4 (n = 8 per age group). At the end of the semester, empathy is measured using the Young Children’s Empathy Measure during the parent-teacher conference (Poresky, 1990), which uses an accuracy scale of 0 – 4, with higher scores indicating more cognitive and affective empathy.

The scores for each group are shown in the table below. Remember to name and define your variables (your two factors and your one dependent variable) under the “Variable View,” then return to the “Data View” to enter and analyze the data. Remember, each factor (i.e. independent variable) is represented within a single column in SPSS using numbers to identify the categories (e.g., 0 = four year olds / 1 = eight year olds). The dependent variable will have its own column, so you will end with three columns of data. (Note the data set is small to ease your burden – use a two-way ANOVA regardless!) Conduct a two-way ANOVA to determine whether age and/or play group size affects empathy.

4 y/o 8 y/o

4 y/o				8 y/o
ALONE	DYAD	FOUR		ALONE	DYAD	FOUR
2.7	2.3	2.4		2.8	3.1	3.8
2.3	2.5	2.6		3.1	3.5	3.6
3.1	3.3	2.6		3	3.1	2.6
2.5	2.4	3.1		3.5	3.4	3
2.6	3	3.2		2.6	3	3.4
2	2.7	3		2.4	2.7	3.3
2.9	2.1	2.7		2.8	2.6	3.1
2.4	2.4	2.6		3.4	3.1	3

9. Paste the relevant SPSS output, including post hocs if necessary.  (2 pts)

10. Create the most appropriate graph(s) for this data given the results (make sure to have axes titles and error bars). (2 pts)

11. Write an APA-style Results section based on your analysis. All homework “Results sections” should follow the examples provided in the presentations and textbooks. They should include the statistical statement within a complete sentence that mentions the type of test conducted, whether the test was significant, and if relevant, effect size and/or post hoc analyses. Don’t forget to include a decision about the null hypothesis. (4 pts)

Answer 1

Solution)

H01= There is no siginificant effect of age group on Empathy.

H11= There is significant effect of age group on empathy.

H02=There is no significant effect of play group on empathy.

H12=There is significant effect of play group on empathy.

we have 3 variables

1. Age group (independent variable)

2.Play group. (independent variable)

3.Empathy. (dependent variable)

To perform 2 way anova

Steps : analyse -- general linear model-- univarate--dependent(empathy)--facor(play group,age group) .

Our entered data in SPSS is

		Age_Group	Play_Group	Empathy
1		four years old	Play Alone	2.7
2		four years old	Play Alone	2.3
3		four years old	Play Alone	3.1
4		four years old	Play Alone	2.5
5		four years old	Play Alone	2.6
6		four years old	Play Alone	2.0
7		four years old	Play Alone	2.9
8		four years old	Play Alone	2.4
9		four years old	Play dyad	2.3
10		four years old	Play dyad	2.5
11		four years old	Play dyad	3.3
12		four years old	Play dyad	2.4
13		four years old	Play dyad	3.0
14		four years old	Play dyad	2.7
15		four years old	Play dyad	2.1
16		four years old	Play dyad	2.4
17		four years old	Play four	2.4
18		four years old	Play four	2.6
19		four years old	Play four	2.6
20		four years old	Play four	3.1
21		four years old	Play four	3.2
22		four years old	Play four	3.0
23		four years old	Play four	2.7
24		four years old	Play four	2.6
25		eight years old	Play Alone	2.8
26		eight years old	Play Alone	3.1
27		eight years old	Play Alone	3.0
28		eight years old	Play Alone	3.5
29		eight years old	Play Alone	2.6
30		eight years old	Play Alone	2.4
31		eight years old	Play Alone	2.8
32		eight years old	Play Alone	3.4
33		eight years old	Play dyad	3.1
34		eight years old	Play dyad	3.5
35		eight years old	Play dyad	3.1
36		eight years old	Play dyad	3.4
37		eight years old	Play dyad	3.0
38		eight years old	Play dyad	2.7
39		eight years old	Play dyad	2.6
40		eight years old	Play dyad	3.1
41		eight years old	Play four	3.8
42		eight years old	Play four	3.6
43		eight years old	Play four	2.6
44		eight years old	Play four	3.0
45		eight years old	Play four	3.4
46		eight years old	Play four	3.3
47		eight years old	Play four	3.1
48		eight years old	Play four	3.0
Total	N	48	48	48

Between-Subjects Factors
		Value Label	N
Age_Group	0.00	four years old	24
	1.00	eight years old	24
Play_Group	1.00	Play Alone	16
	2.00	Play dyad	16
	3.00	Play four	16

Descriptive Statistics
Dependent Variable:   Empathy
Age_Group	Play_Group	Mean	Std. Deviation	N
four years old	Play Alone	2.562	.3462	8
	Play dyad	2.588	.3944	8
	Play four	2.775	.2866	8
	Total	2.642	.3438	24
eight years old	Play Alone	2.950	.3780	8
	Play dyad	3.063	.3068	8
	Play four	3.225	.3808	8
	Total	3.079	.3599	24
Total	Play Alone	2.756	.4033	16
	Play dyad	2.825	.4203	16
	Play four	3.000	.4000	16
	Total	2.860	.4124	48

Levene's Test of Equality of Error Variancesa,b
		Levene Statistic	df1	df2	Sig.
Empathy	Based on Mean	.276	5	42	.924

Tests of Between-Subjects Effects
Dependent Variable:   Empathy
Source	Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared
Corrected Model	2.819a	5	.564	4.574	.002	.353
Intercept	392.735	1	392.735	3186.646	.000	.987
Age_Group	2.297	1	2.297	18.637	.000	.307
Play_Group	.505	2	.253	2.050	.141	.089
Age_Group * Play_Group	.016	2	.008	.066	.936	.003
Error	5.176	42	.123
Total	400.730	48
Corrected Total	7.995	47
a. R Squared = .353 (Adjusted R Squared = .275)

since p-value for Age group =0.000<0.05 , so, we reject our null hypothesis (H01)

and concluded that there is significant effect of age group on empathy.

since, p-value for Play grop =0.141>0.05 so, we do not reject null hypothesis(H02).

and concluded that there is not significant effect of Play group on empathy.

since,p-value for interaction (age*play) group =0.936>0.05 we do not reject null hypothesis .

and concluded that there is not significant effect of (age*play) group on empathy.

From the above table we have seen that only Age group Significantly affects empathy .

but we can not apply post hoc age group because there is only 2 groups in ages i.e four year old and eight year old..